Tag: University of Mumbai BMS Notes

Creativity is a phenomenon whereby something new and somehow valuable is formed. The created item may be intangible (such as an idea, a scientific theory, a musical composition, or a joke) or a physical object (such as an invention, a printed literary work, or a painting).

Scholarly interest in creativity is found in a number of disciplines, primarily psychology, business studies, and cognitive science, but also education, technology, engineering, philosophy (particularly philosophy of science), theology, sociology, linguistics, and economics, covering the relations between creativity and general intelligence, personality type, mental and neural processes, mental health, or artificial intelligence; the potential for fostering creativity through education and training; the fostering of creativity for national economic benefit, and the application of creative resources to improve the effectiveness of teaching and learning.

Qualities of a Creative Person

When you hear the word “creative” what do you think of? Creativity can come in all shapes and forms, bring all sorts of ideas to the surface, and inspire change in the world. But creativity is also a vague term because of how many outlets there are, and with that comes two things: a challenge and an opportunity. For example, it is very easy to walk beside a creative group of people, and become blind to seeing whose intentions are genuine. It is even easier to become blind to your own. Examining personal characteristics from time to time is a cool opportunity to see what traits of yours are being practiced creatively, because we all know humans have plenty of traits in other departments. This can not only help you to gain perspective, but to see what really constitutes as a creative characteristic, which in return may help you see if your ‘creative’ intentions are being practiced or forgotten. I know, a mouthful right? The truth is, sometimes we lose sight of ourselves, sometimes we lose sight of what our purpose is, and sometimes we lose sight of what true creativity is. Creativity stands out, it doesn’t have a certain definition, and it just exists as it is. So what are the characteristics of creative people? And are you one of them? Here’s ten that might put some things into perspective.

1. Energetic

Creative people have a certain energy surrounding them. They tend to radiate a great deal of energy and put their whole heart into what they expend their energy on. This type of energy is different than lets say, hyper-ness, in that it drives the creator into a positive direction and isn’t aimlessly expended. Energy helps the creator to pour passion into their creation and spread energy to others when they see what they have created. Being energetic is often contagious, and creative people love to rub their energy off on other individuals. Trust me, this energy is unlike anything else and if you’ve felt it before, then you’ll know what I am talking about.

2. Intelligent

Being intelligent is another characteristic of being creative. There is an array of wisdom within the mind of a creative person, much like a gift that is hard to find. Creatives are smart and know how to utilize it in all the right areas. They are quick to come with ideas, and resourceful with their surroundings. Intelligence can come in many forms, but creative people tend to practice the abstract, artistic side of intelligence more often than not. Wisdom is a strong characteristic in the mind of a creative, because more intelligence naturally leads to more creative success.

3. Sensitive

While being intelligent is a dominant characteristic, creative people also have a submissive side to them. They are sensitive to many things, because their hearts are constantly open to the world. Being emotional comes easy to them and many things make them cry. Creatives easily see both the joy and pain in everyday life which makes them sensitive to the whole spectrum of living. Being sensitive and vulnerable allows a creative to rip away any self doubt and spill their complete passion and effort into their work. A sensitive heart may be perceived as submissive, but it truly is a gift for a creative to possess.

4. Ambitious

Creatives are highly ambitious in their pursuits. They are always looking for the next project and have an eager hand. Almost nothing discourages their preference to try something new. Constant creating causes creatives to look for more, and ambition gives them more. They seek and seek and eventually find what they are looking for. Whether that be in the smallest part of their day or the biggest event of their life, there is always something to pull from their experience to inspire their work.

5. Naive

Another submissive characterisitc many creatives have is to be naive. Being naive can be a very dangerous thing in this world, and creative people tend to fall into that naive pool quite often. But being naive isn’t entirely dangerous, it can help creatives learn from their mistakes and grow. It can help them open certain doors accidentally which helps them flourish from new discoveries. There is a certain amount of childlike innocence in a creative person because they look at the world with hopeful eyes and try to see the best in humanity. Being curious, or having a wandering spirit, goes hand in hand with being naive; The world is your backyard, but beware of dog, the world might bite back sometimes.

6. Rebellious

Creatives are alot more rebellious than one may think. They take lots of risks and often. They aren’t afraid to mess up because they tend to see the good in it if they do. They may have lots of bruises and scars to prove their mistakes, but their rebellion keeps their heart alive with fire. With a heart full of fire and daring spirit, nothing can hurt a creative, not even the nastiest response from the world. Being rebellious means stepping out of the box and trying something out even it is results in failure, because creatives choose to look at is at an opporunity to grow either way it turns out.

7. Extroverted and Introverted

Can one person be both extroverted and introverted? Creatives sure can! Creative people have two sides to them, the private side and the public side. They can be social and personal, talkative and silent, shy and confident, all in the same body. Being extroverted has its perks and so does being introverted. Creative people are very willing to embrace things, and see the benefits in balancing just the right amount of extroverted, introverted-ness in order to reap all of its benefits.

8. Playful

Being playful is what creatives are all about. They play with ideas until they get the result desired. They play with paints to achieve the right color, play with lens to capture the perfect photo, play with metal to build the right model, and you know quite well creatives ‘play with fire’. Being playful allows a creative to have fun. It allows them to take what they do less seriously and put the joy into it by simply having a good time. And sometimes the best things come by mistake, or by accident, or by playing with fire.

9. Open minded

If there is any person that is open minded, it’s your creative friend, or anyone that is creative in this world for that matter. This is a big one, considering how open to possibilities creatives have to be to reap success. Being open minded allows creatives to climb mountains and venture into secret lands. It allows people to see through another lens without captivating themselve into a box of boundaries or restrictions. Being open minded helps creatives to be set free, and a creative that is free has the sky as their limit.

10. Dreamer

Creatives never stop dreaming. They dream in the day, in their minds constantly, in the evening, in the night and all over again the next day. Creatives dream because of how goal oriented they are, and they dream of these goals realistically in order to motivate them. Creatives can also get carried away, however, just like any individual. But for the most part, this dreaming we are talking of, its untouchable, Because when a creative person wants something they go for it  full heartedly, even if it did start out as a dream.

Creativity means creating something new. In the context of business, it means creation of new ideas, new method or new product/service.

Creativity is the “cognitive process of developing an idea, concept, commodity, or discovery that is viewed as novel by its creator or a target audience.” :Max H. Bazerman

“Creativity is not a quality of a person; it is a quality of ideas, of behaviours or products.” :Teresa M. Amabile

Creativity improves the quality of decisions. It increases the scope of alternatives to be considered for problem-solving. It is essential to deal with problems which are no-repetitive and novel as such problems cannot be solved by pre-defined solutions. They require imaginative thinking for their solution. As no problem has a single solution, creativity helps in generating new ideas that help in taking the final decision.

The creative approach to problem solving assumes the following:

1. There is always a better way of doing things. Past precedents, habits and conventional ways of doing things cannot always guide the future courses of action.
2. Problems have diverse perspectives. Each perspective should be probed, questions should be raised and answers should be found.
3. Things should not be taken for granted. Problems should be redefined and obvious facts should be challenged.
4. There is always scope for improvement. Managers should move from traditional ways to modern, computer-aided ways of managing organizations.
5. Managers should not be afraid of failures. Initial failures will lead to ultimate success.

Creativity in decision-making results in organizational innovations, new technology or new products.

In the era of globalization, competition is so intense that creativity is essential for organizations to take decisions that help in their survival and growth.

The creativity process requires:

1. Convergent thinking
2. Divergent thinking

In convergent thinking, the problem is solved according to pre-defined method or course of action. It pre-supposes solution to the problem and rationally moves towards that solution. Divergent thinking does not solve the problem in a pre-defined way. It analyses different aspects of the problem, views it in different ways and searches for alternative courses of action to solve that problem.

Components of Creativity

Teresa M. Amabile enumerates three components of creativity.

1. Domain skills

A manager can be creative in decision-making if he is theoretically and conceptually aware of the problem and its relevance to the environmental factors. In other words, he must have knowledge of the problem area and also the talent and ability to solve that problem. This is known as domain skill.

2. Creativity skills

The skills to do creative things; to think of new ways of doing the work, to think of new avenues of marketing are the creative skills that help to carry out the decision-making process.

3. Task motivation

Managers do not perform organizational tasks for earning only financial rewards. Money or financial considerations are not the only motives for taking up a novel task. Ego satisfaction and morale boost up are also the considerations that lead to creativity in decision-making.

Process of Creativity

The process of creativity consists of the following steps:

1. Problem finding or sensing

The entrepreneur faces a problem and selects to work on it. He feels curious to solve that problem. He thoroughly familiarizes himself with the problem, analyses its importance for the business and its relationship with other segments of the business.

This helps in identification of the problem as close as possible to reality so that alternatives can be generated which analyse the problem and provide solutions in the right direction. Curiosity leads to development of ideas.

2. Preparation

Once the problem is identified, the decision-maker concentrates on the problem and starts working on it. He collects information, analyses how others are using it and formulates hypotheses to work on. Information may be collected on the basis of past experience, through experience of others and also through study of new researches and innovations done in that field. If he wants to introduce a new product in the market, he studies the consumer buying behaviour before converting that idea into reality.

3. Gestation or Incubation

If, in the preparation stage, the decision-maker is not able to arrive at creative solution to the problem, he moves away from conscious deliberation to sub-conscious development of ideas. He moves away from the problem and engages in other routine activities while still thinking of the problem in his sub-conscious mind.

He thinks over collected information and makes decisions in his sub-conscious mind. He appears to be idle but actually he is trying to correlate what runs in his sub-conscious mind with the happenings around. As lot of information and ideas are already stored in his mind, sub-consciously they are combined and related to each other and help in generation of new ideas important for solving the problem.

4. Insight or Illumination

He thinks of all possible solutions at all times. He thinks of ideas while eating, walking or going to sleep. These ideas are put in writing so that he does not forget them in his conscious mind. In this process, there is flash of ideas in his mind.

These ideas come and go at the speed of light, some of which are spontaneously rejected while others are accepted for further analysis. Sometimes, it results in ideas which the decision ­maker may not have even thought of in his conscious mind.

Social gatherings and meetings may also result in new ideas. Compaq computer company was found as a result of social encounters. Rough sketch of portable computer was drawn on a paper napkin by three friends over lunch which turned into setting up of Compaq computer company.

5. Verification and application

The entrepreneur proves by logic or experiment that the idea can solve the problem and, therefore, can be implemented. He tests the ideas empirically through mathematical models and experimentation. If it is feasible, he applies it to solve the problem. Verification is an essential step in the creativity process because an idea that cannot be implemented is of no use howsoever good it may be.

Climate for Creativity

Managers create a climate that encourages creativity in the following ways:

1. Recognize the need for change

Though people are generally resistant to change, accepting the need for change is necessary to promote creativity. People must feel that they will be benefitted by change.

2. Encourage new ideas

The manager should welcome new ideas. Listening to new ideas and implementing the profitable ones encourages a creative climate in the organisation.

3. Interaction

Interaction with people within and outside the enterprise encourages exchange of useful information and generation of new ideas.

4. Tolerate failure

New ideas may prove to be failures. People should not get disheartened. They should consider time, money and energy in ideas that have failed as investment for bright future prospects.

5. Clear objectives

Managers must have purpose for creativity. They should know what ideas to be tried, when and for what. Clear objectives will optimize the use of time, energy and money.

Creative Problem Solving (CPS) is a method that attempts to approach a problem or a challenge in an innovative way. The process helps redefine problems and opportunities to come up with new responses and solutions.

There are many variations on the basic Creative Problem Solving process, some of which work nicely in group meetings. The simplest form of the process includes these steps:

• Clarify (the objectives, the problem, the facts, the opportunity)
• Generate Ideas (come up with possible solutions or approaches)
• Solve (develop ideas into solutions or experiments)
• Implement (create a plan and secure commitment to next steps)

Creative problem-solving (CPS) is the mental process of searching for an original and previously unknown solution to a problem. To qualify, the solution must be novel and reached independently. The creative problem-solving process was originally developed by Alex Osborn and Sid Parnes.

The process of creative problem-solving usually begins with defining the problem. This may lead to finding a simple non-creative solution, a textbook solution, or discovering prior solutions developed by other individuals. If the discovered solution is sufficient, the process may then be abandoned.

A creative solution will often have distinct characteristics that include using only existing components, or the problematic factor, as the basis for the solution. However, a change of perspective may in many cases be helpful. A solution may also be considered creative if readily available components can be used to solve the problem within a short time limit (factors typical to the solutions employed by the title character in the television series MacGyver).

If a creative solution has broad application: that is, uses that go beyond the original intent, it may be referred to as an innovative solution, or an innovation (some innovations may also be considered an invention).

“All innovations [begin] as creative solutions, but not all creative solutions become innovations.” :Richard Fobes

Techniques and tools

Many techniques and tools employed for creating effective solutions to a problem are described in creativity techniques and problem-solving articles.

Creative problem-solving technique categories

1. Mental state shift and cognitive re-framing

Changing one’s focus away from active problem-solving and towards a creative solution set.

2. Multiple idea facilitation

Increasing the quantity of fresh ideas based on the belief that a greater number of ideas will raise the chances that one of these is valuable. This may include randomly selecting an idea (such as choosing a word from a list) and thinking about its similarities to the situation. In turn, this random act may inspire a related idea that would lead to a solution.

3. Inducing a change of perspective

Efficiently entering a fresh perspective may result in a solution that thereby becomes obvious. This is especially useful for solving particularly challenging problems.[6] Many techniques to this end involve identifying independent dimensions that differentiate closely associated concepts.[6] Differentiating concepts helps overcome a tendency to use oversimplified associative thinking, in which two related concepts are so closely associated that their differences are overlooked.

7 Ways to Improve Your Creative Problem-Solving Skills

1. The first step is self-awareness

Simply being aware of and acknowledging the fact that our creative problem skills are limited by the way we think and process information is the first step to breaking some of those patterns. Doing so will then encourage you to find tools, techniques and tricks to overcome those biases and increase your problem solving skills, some are listed below.

2. Detach yourself from the problem

The way we look at a problem is limited by the way we frame it, which in turn is influenced by our past experience, our beliefs and our mental processes. Framing matters, so it is not a surprise to us that 10 out of the 26 Positioning-Roulette approaches to brand positioning focus on the frame of reference and re-framing the brand (that’s almost 40% of all potential approaches). Re-framing the problem or looking for solutions from various perspective (or adjacent fields) is a great way to overcome some of the mental biases that plague us. In our experience the most effective “creativity techniques” use a two-step approach. The first step usually consists in moving away from the problem to facilitate new ideas, the second step then consists in translating those ideas back into solutions that could solve the original problem.

3. Use a framework, a system, to guide your thinking

Most people still don’t seem to realize that there is a method to creativity. Creativity doesn’t just happen. One significant benefit of a more methodic approach is that it helps drive and guide the idea finding process and thus helps overcome the biases and limitations mentioned above. This is where tools like Positioning-Roulette come into play. They help guide your thinking and by doing so act as a distraction from many of your limiting biases. Obviously, I believe that Positioning Roulette is the best and most rigorous framework for the development of positioning platforms and brand stories but the truth is any framework (for example the Maslow hierarchy of needs is another effective framework) will lead to better results than not using any.

4. Show empathy

Empathy is the ability to put yourself in someone else’s shoes without judging. This “someone else” can be a consumer you are trying to convert or another team member during an ideation session. This is a very difficult thing to do but is also a very powerful way to unleash new solutions to a problem. Empathy doesn’t mean that you necessarily agree with the other person’s point of view, it just means that you can see things from their point of view for long enough to consider new solutions that may emerge from this perspective. A simple way to start is to practice empathy with your significant other. You’ll find this improves not only your ability to be creative but also your relationship.

5. Promote diversity of point of views- avoid groupthink

I believe better solutions are generated when developed by a diverse group of people. If you are an intuitive thinker add a more rationally minded person to your ideation session, even if it feels uncomfortable at first. If you’re a team of business people add a creative minded person or artist to your ideation team. The trick here however is not just to add people that have a different working style than you, but also to listen to them and allow their perspective to influence the thinking and ideation process (see point 4). As someone told me once, the best leaders are “integrators”, they are able to listen to various points of view and incorporate those into the final solution. The tremendous side benefit: everyone involved in the process feels heard and takes ownership in the solution.

6. Focus on the right input and stimuli

Using thought starters and inputs from other fields or categories also helps short-circuit your own thinking patterns and boost your creative problem skills (see point three). However, not all thought-starters are created equal. Some will be more relevant to the type of problem you’re trying to solve than others. Looking at the world of ants and how they are organized and trying to draw conclusions on how to position a brand of yogurt might sound like a fun exercise (and it is) but it’s in my opinion a complete waste of time.

7. Expand your own knowledge and experience

The more diverse marketing problems you have worked on, the more cases in different categories you’ve been exposed to, the more flexible and agile your thought processes will become. You’ll be able to pull from a broader pool of know-how and experiences and make more meaningful connections, ultimately leading to new types of solutions. This is where case studies come in handy as a short cut to “experience” (Positioning-Roulette for example is based on over 1200 case studies of effective marketing problem solving from around the world, across many different categories and spanning a time period of 125 years). Knowing how a beer brand solved a trial generation problem in Australia might trigger an innovative solution on how to generate trial for a brand of mouth wash in the US.

Organizational development is a technique used for bringing change in the entire aspect of the organization, rather than focusing attention on the individuals, so that change is readily absorbed.

According to French and Bell, “Organizational development is a long range effort to improve an organization’s problem- solving and renewal processes, particularly, through a more effective and collaborative management of organization culture with special emphasis on the culture of formal work teams with the assistance of a change agent or catalyst and the use of the theory and technology of applied behaviour science, including action research.”

According to Burke, “Organizational development is a planned process of change in an organization’s culture through the utilization of behavioural science technology, research and theory.”

Need for organizational Development

organizational development is a dynamic technique. It uses the behavioural science knowledge to assist the organizations in adjusting easily to the changes. Every organization has a need to remain viable and to survive in the world of change. OD has grown rapidly in response to this need of the organizations. For this purpose it uses the systems approach.

There are two important factors which cause the use of OD for the purpose of implementing planned change:

(i) Training for Change

Employees need training to adjust with the changes. Training for change does not work properly only through reward structure on the job. There should be a proper change in the environment of the organization in which people work, to make the training work proper. Thus, the basic objective of OD is to bring about change in the organizational structure so that it supports training.

(ii) To Help in Making the organizational Culture More Responsive

In a dynamic environment, changes take place very rapidly. This requires a highly receptive and effective organization so that changes are implemented and absorbed to make organizations survive and grow. OD can help a lot in this direction. OD reaches into all aspects of organization culture in order to make it more responsive.

Benefits of organizational Development

Newton Margulies and Anthony Raia have given the following benefits of organizational development.

1. Provides opportunities for people to function as human beings rather than mere resources in the production process.
2. Give each member of the organization opportunity to develop to his full potential.
3. Seeks to make the organization more effective in meeting all its goals.
4. Tries to create an environment in which exciting and challenging work can be found.
5. Gives people in the organization the chance to influence how they relate to work, the organization and the work environment.
6. Treats each human being as a person with a complex set of needs, all of which are important in his work and life.

Assumptions of organizational Development

organizational development is based on certain assumptions which are explained as follows:

1. Most of the individuals are motivated by personal growth and development. However, the work habits of a person are a response to work environment rather than personality traits. The attitude of a person towards his job will depend upon his growth potentials, in most of the cases. Therefore, efforts should be made to change the way a person is treated in the organization rather than attempting to change the person. The work habits of a person will change positively only if we change the work environment to suit his requirements.
2. Highest productivity can be achieved only if there is effective integration of individual goals with the organizational goals.
3. OD tends to assume that co-operation is more effective than conflict. In healthy organizations, efforts are made at all levels to treat conflict as a problem subject to problem solving methods. This is because of the reason that conflict tends to erode trust, prohibit collaboration and eventually limit the effectiveness of the organization.
4. Free expression of feelings is an important ingredient for commitment to work. Suppression of feelings adversely affects problem solving, personal growth and satisfaction with one’s work.
5. The level of interpersonal trust, support and co-operation should be as high as possible: because growth of individuals is facilitated by relationships which are open, supportive and trusting.
6. There should be a sense of commitment among the employees in the organization. Agreeing to do something is totally different from committed to do something. Sense of commitment makes it easy to accept change and the implementation of change is even easier when this commitment is based upon participation in the process.
7. Organizational development cannot be implemented in isolation. It must be reinforced by the organization’s total human resource system.

Values of Organizational Development

Tannenbaum and Davis prescribed the values that organizations should develop to undertake OD efforts.

They specify that organizations should move:

1. Away from a view of human beings as essentially bad toward viewing them as basically good.
2. Away from avoidance or negative evaluation of individuals to confirming them as valuable human beings.
3. Away from a view of individuals as “fixed” (i.e. being) toward seeing them as “being in process” (i.e. becoming).
4. Away from resisting and fearing individual differences toward accepting and utilizing them.
5. Away from utilizing an individual primarily with reference to his/her job description to viewing the individual as a whole person.
6. Away from walling off the expression of feelings toward making possible both appropriate expression and effective use of feelings.
7. Away from marksmanship and game playing toward authentic behaviour.
8. Away from use of status for maintaining power and personal prestige towards use of status for organizationally relevant purposes alone.
9. Away from distrusting people to trusting them.
10. Away from avoiding facing others with relevant data toward making appropriate confrontation.
11. Away from avoiding risk taking toward willingness to take risks.
12. Away from a view of process work as being unproductive effort to seeing it as essential to effective task accomplishment.
13. Away from primary emphasis on competition towards a much greater emphasis on co-operation.

From the above values, we can clearly understand why these are considered absolutely essential for the success of an OD programme.

Limitations of organizational Development

OD is an important technique of introducing change. But as a method of inducing change, it has certain limitations also. These are as follows

1. OD is based on the behavioural sciences concepts. Behavioural sciences themselves have many limitations, which are passed on to and applicable to OD also.
2. OD requires the use of certain diligent and highly motivated persons, who can take initiative to bring about change. But in organizations, people are, generally, complacent who are not willing to make the required efforts and they are not helpful in implementing organizational development.
3. OD cannot be applied without giving due consideration to the circumstances existing within the organization. The local circumstances may pose a problem in adapting to change. Task of the organization and the characteristics of its membership also put limitations on the effectiveness of OD.

1. Survey Feedback

Information is collected through survey method. This is the most popular and widely used method of data collection. The managers use this information collected through survey for making decisions. The wide range of data is collected regarding working conditions, quality of work, working hours, wages and salaries, attitude of employees relating to above.

These data are then analyzed by the team of managers. They find out the problem, evaluate the results and find out solutions. Information is collected from all the members of the organization. Managers conduct meetings with their subordinates and discuss the information, allow subordinates to interpret the data. After this plans are prepared for making necessary changes. This procedure is followed at all levels of management involving all the employees of the organization.

2. Team Building

Team Building is another method of organization development. This method is specifically designed to make improvement in the ability of employees and motivating them to work together. It is the organization development technique which emphasizes on team building or forming work groups in order to improve organizational effectiveness.

These teams consist of employees of the same rank and a supervisor. This technique is an application of sensitivity training to the teams of different departments. The teams or work groups are pretty small consisting of 10 to 15 persons. They undergo group discussion under the supervision of an expert trainer usually a supervisor. The trainer only guides but does not participate in the group discussion.

This method of team building is used because people in general do not open up their mind and not honest to their fellows. As they does not mix up openly and fail to express their views to the peers and superiors. This technique helps them express their views and see how others interpret their views. It increases the sensitivity to others’ behaviour.

They become aware of group functioning. They get exposed to the creative thinking of others and socio-psychological behaviour at the workplace. They learn many aspects of interpersonal behaviour and interactions.

3. Sensitivity Training

It is quite popular OD intervention. It is also known as laboratory training. Under this technique the employees in groups are asked to interact. The aim of sensitivity training is to help people understand each other and gain insight so that they feel free and become fearless.

Abraham Korman has rightly observed that, “the assumptions of sensitivity training procedure are that, if these goals are achieved, one will become defensive about himself, less fearful of the intentions of others, more responsive to others and their needs, and less likely to misinterpret others’ behaviours in a negative fashion.

“Under this technique the different groups of employees are allowed to mix up with each other and communicate freely and build up interpersonal relationship. They learn the reflection of their behaviour and try to improve it. In the words of Chris Argyris, “sensitivity training is a group experience designed to provide maximum possible opportunity for the individuals to expose their behaviour, give and receive feedback, experiment with new behaviour and develop awareness of self and of others.”

The employees through this technique know others feelings and behaviour and the impact of their behaviour on others. It builds up openness, improves listening skills, tolerate individual differences and the art of resolving conflicts. It helps in reducing interpersonal conflicts in the organization.

It is up to the executives at the top level of management in the organization to take decision regarding appropriateness of this technique but they must see that the objectives of organizational development are achieved with the help of this method.

However there is every likelihood that some culprits will exploit the opportunity to fulfill their vested goals at the cost of organization’s interests. There is one more serious drawback of the method that it may give rise to groupism in the organization which will defeat the purpose of OD. To make this technique effective and fulfill the purpose of OD, the selection of trainer must be cautiously made. He must be a man of integrity and responsibility and must command respect from the participating groups.

He plays a crucial role in making the OD programme successful. He should maintain cordial atmosphere throughout the training programme. He must see that each member of the groups learn the behaviour of others and to be creative and get more exposure to group life.

4. Managerial Grid

This technique is developed by industrial psychologists duo Robert Blake and Jane Mouton. The concept of managerial grid identifies two major dimensions of management behaviour. They are people oriented and production oriented behaviours. Attempts are made to pay increased attention to both the variables.

5. Management by Objectives (MBO)

MBO is a technique of management development which was put forward for the first time by Peter Drucker in 1954. It is a method of achieving organizational objectives and a technique of evaluation and review of performance. Under this method objectives of the organization are fixed and responsibility to achieve them lie on the managers and results are expected from them.

Achievement of organizational objectives is considered as the joint and individual responsibility of all managers. It also provides a perfect appraisal system. Performance of the managers is measured against the specific objectives. It is result oriented technique.

George Odiorne observed that MBO is, “a system wherein superior and subordinate managers of an organization jointly identify its common aims, define each individual’s major areas of responsibility in terms of the results expected of him and use these measures as guides for operating the unit, assessing the contribution benefits of its members.”

According to D D White and D A Bednar, “MBO is a technique designed to:-

• Increase the precision of the planning process at the organizational level.
• Reduce the gap between employee and organizational goals.”

6. Brain Storming

It is a technique where a group of five to eight managers come together and find a solution to a problem. As the name suggests it involves storming of the brain to develop creativity in thinking. It gives rise to new ideas. The principle involves in it is that any idea, thought or plan put forward in a meeting must be critically evaluated. The participants are asked to come forward with novel ideas generated in their mind. It works on a premise that everyone has a creative mind and capability to generate new ideas.

Participants are closely observed at the discussion and no expert is provided to conduct the meeting. The participants sit across the table for close communication. The brainstorming technique can generate an atmosphere where people can express freely. This encourages group interaction and creative thinking. The only limitation this method has is that it is time consuming and hence expensive.

7. Process Consultation

The technique of process consultation is an improvement over the method of sensitivity training or T Group in the sense that both are based on the similar premise of improving organizational effectiveness through dealing with interpersonal problems but process consultation is more tasks oriented than sensitivity training.

In process consultation the consultant or expert provides the trainee feedback and tell him what is going around him as pointed out by E H Schein that the consultant, “gives the client ‘insight’ into what is going on around him, within him, and between him and other people.”

Under this technique the consultant or expert provides necessary guidance or advice as to how the participant can solve his own problem. Here the consultant makes correct diagnosis of the problem and then guides the participants.

The consultant according to E H Schein, “helping the client to perceive, understand and act upon process events which occur in the clients’ environment.” Process consultation technique is developed to find solutions to the important problems faced by the organization such as decision making and problem solving, communication, functional role of group members, leadership qualities. Consultant is an expert outside the organization.

8. Quality Circles

Under this system a group of 5 to 12 come together at their own free will during working hours once in a week and discuss out the problems and suggests solution to the management for implementation. The supervisors remain present during the meeting. Quality Circles have their origin in Japan in nineteen sixties which improved the quality, reduced cost and heightened the morale of the workers. The success was due to workers’ participation. Total quality management or TQM is the recent development. This concept was adopted by the USA in 1980.

9. Transactional Analysis

Transactional analysis helps people to understand each other better. It is a useful tool for organizational development but it has diverse applications in training, counselling, interpersonal communication and making analysis of group dynamics. Nowadays, it is widely used as OD technique. It helps in developing more adult ego states among people of the organization. It is also used in process consultation and team building.

Stress is a general term applied to various psychologic (mental) and physiologic (bodily) pressures experienced or felt by people throughout their lives.

Stress is defined as “a state of psychological and physiological imbalance resulting from the disparity between situational demand and the individual’s ability and motivation to meet those needs.”

Dr. Hans Selye, one of the leading authorities on the concept of stress, described stress as “the rate of all wear and tear caused by life.”

Stress can be positive or negative:

• Stress is good when the situation offers an opportunity to a person to gain something. It acts as a motivator for peak performance.
• Stress is negative when a person faces social, physical, organizational and emotional problems.

Factors that are responsible for causing stress are called stressors.

Types of Stress

Many people feel stress after dealing with the loss of a loved one, while going through a divorce or even after a tough day at work, but most people don’t realize is that there are different kinds of stress. The types of stress relate to how the stress comes on or what symptoms are associated with the stress, but psychologists typically differentiate between the different types based on how long the periods last.

1. Physical Stress

A common type of stress is physical stress, which refers to actual physical activities and events that wreak havoc on the human body. One good example is travel. Traveling frequently can send you to different time zones, which makes sleeping and waking difficult. Physical stress also includes stress brought on by sleeping too much, not getting enough sleep, spending too many hours on your feet or working long hours. If you ever spent a day chasing your kids around an amusement park or stuck in an airport and dealing with flight delays, you have likely experienced physical stress.

2. Emotional Stress

Out of all the different kinds of stress, emotional stress is the most common. This can occur after you go through an intense break up or divorce, lose a loved one, have a fight with your spouse or experience any other problem that causes you to feel depressed or anxious. Emotional stress often manifests in the same way that depression does. You may experience weight changes, changes in how you fall asleep or how long you sleep, feelings of isolation and mood swings. Emotional stress can also occur when you feel overwhelmed at home or at work.

3. Traumatic Stress

When thinking about the types of stress, many people don’t think about traumatic stress. Traumatic stress is a type of stress that occurs because of some type of trauma to the human body and may lead to intense pain, coma or even death. It often relates to some kind of physical change that occurs. If you went through an operation, your body may experience stress until you recover from that surgery. A car accident, second or third degree burns or even a case of pneumonia may all cause traumatic stress.

4. Acute vs. Chronic Stress

In addition to the different types of stress, psychologists differentiate between acute stress and chronic stress. According to the American Psychological Association, chronic stress refers to an extended type of stress that impacts people every day of the year and can last for years or even decades. Acute stress is a type of stress that only occurs for a set period of time or only because of certain factors in the environment. This may include the stress you feel after a fight with your kids, a meeting at work or an encounter with another driver on the road. The APA also identifies something called episodic acute stress, which refers to intense periods of stress.

Stress can wreak havoc on the human body. It causes people to feel sick and tired and may lead some to contemplate suicide. Psychologists can help you learn more about the different kinds of stress, show you how to combat that stress and learning coping mechanisms for use at home and work.

Causes of Stress

1. Career Concern

If an employee feels that he is very much behind in the corporate ladder, then he may experience stress. If he seems that there are no opportunities for self-growth, he may experience stress. Hence, unfulfilled career expectations are the significant source of stress.

2. Role Ambiguity

It occurs when the person doesn’t know what he is supposed to do, on the job. His tasks and responsibilities are not clear. The employee is not sure what he is expected to do. It creates confusion in the minds of the worker and results in stress.

3. Rotating Work Shifts

Stress may occur in those individuals who work on different work shifts. Employees may be expected to work on day shift for some days and then on the night shift. That may create problems in adjusting to the shift timings, and it can affect not only personal life but also family life of the employee.

4. Role Conflict

It takes place when people have different expectations from the person performing a particular role. It can also occur if the job is not as per expectation, or when a job demands a certain type of behavior that is against the person’s moral values.

5. Occupational Demands

Some jobs are more demanding than others. Jobs that involve risk, and danger are more stressful. Research findings indicate, job that cause stress needs constant monitoring of equipments and devices, unpleasant physical conditions, making decisions, etc.

6. Lack of Participation in Decision-making

Many experienced employees feel that management should consult them on matters affecting their jobs. In reality, the superiors hardly ask the concerned employees before taking a decision. That develops a feeling of being neglected, which may lead to stress.

7. Work Overload

Excessive workload leads to stress as it puts a person under tremendous pressure. Work overload may take two different forms:

• Qualitative work overload implies performing a job that is complicated or beyond the employee’s capacity.
• Quantitative work overload is a result of many activities performed in a prescribed time.

8. Work Underload

In this, case, too little work or very easy work is expected on the part of the employee. Doing less work or jobs of routine and simple nature would lead to monotony and boredom, which can lead to stress.

9. Poor Working Conditions

Employees may be subject to poor working conditions. It would include bad lighting and ventilation, unhygienic sanitation facilities, excessive noise, and dust, presence of toxic gasses and fumes, inadequate safety measures, etc. All these unpleasant conditions create physiological and psychological imbalance in humans thereby causing stress.

10. Lack of Group Cohesiveness

Every group is characterized by its cohesiveness, although they differ widely in its degree. Individuals experience stress when there is no unity among work group members. There are mistrust, jealousy, frequent quarrels, etc., in groups and this lead to stress to employees.

11. Interpersonal and Intergroup Conflict

These conflicts take place due to differences in perceptions, attitudes, values and beliefs between two or more individuals and groups. Such conflicts can be a source of stress for group members.

12. Organizational Changes

When changes occur, people have to adapt to those changes, and this may cause stress. Stress is higher when changes are significant or unusual like transfer or adoption of new technology.

13. Lack of Social Support

When individuals believe that they have the friendship and support of others at work, their ability to cope with the effects of stress increases. If this kind of social support is not available, then an employee experiences more stress.

Job Stress also called occupational stress, work-related stress is a negative response (stress) that occurs in workplaces due to various demands or situations people find themselves in and not having enough resources to deal with it. Perceptions of loss and harm result in an individual’s stress response being triggered. Having inadequate coping resources is typically at the root of this reaction. The greater the emphasis on the consequences of failing, the greater will be the stress response.

Causes of Stress

Common causes of work-related stress include:

• Sudden deadlines or demanding job
• Harassment or bullying
• Stereotypes
• Gender discrimination
• Social isolation
• Work-home conflict
• Violence
• High risk jobs
• Unpleasant relationship with boss and/or co-workers
• Constant work contact

Factors such as the following impact one’s response to stress:

• Personality factors
• Level of job expertise
• Social support (family, co-workers & friends)
• Health status and disability
• Gender, ethnicity, and age
• Financial demands
• Life conditions outside the workplace

Signs and Symptoms of Stress

It is vital that you pay attention to signs of stress and take measures to deal with it effectively. Here are some indications of the presence of stress. Keep in mind that some of your symptoms may also be due to certain illnesses:

Problems with emotional health

• Mood changes
• Increased anxiety
• Depressed or pessimistic thought and feeling
• Low self-esteem
• Increased sense of irritation, sensitive or easily hurt
• Loss of motivation

Problems with mental health

• Confusion
• Concentration problems
• Poor memory

Problems with physical health

• High blood pressure
• Sweating
• Stress related rashes
• High cholesterol
• Muscle tension
• Sleep problems

Other behavioral changes

• More than normal absence from work
• Arriving late to work more than usual
• Changes in eating habits
• Increased use of drugs, alcohol, or nicotine
• Behavior effected by mood changes
• Changes in sleep patterns

Prolonged stress can lead to physical and mental illness. Therefore, it is important that you do not ignore stress symptoms for too long. Be sure to see your general physician and talk to your human resources manager or boss.

Consequences of Stress (Frone, Kelloway, & Barling, 2005)

Stress itself is not necessarily harmful, but persistent and prolonged stress can be harmful. As seen in the below graphic, not all stress is bad. However, prolonged stress without adequate resources to help one deal with adversities can lead to harmful outcomes.

Consequences occur at both the individual and the organizational level:

Individual Level Consequences

• Poor psychological and mental health outcomes (e.g., anger, depression, anxiety, posttraumatic stress syndrome, burnout, etc.)
• Impaired physiological processes (e.g., cardiovascular reactivity, elevated levels of various hormones, impaired immune function)
• Physical disease outcomes (e.g., hypertension, stroke, cancer, ulcers and gastrointestinal disorders, musculoskeletal disorders, migraine headaches)
• Detrimental behavioral outcomes (sleep disturbance; alcohol, tobacco, and illicit drug use; poor eating habits; intimate partner violence)

Organization Level Consequences

• Poor psychological and emotional outcomes (e.g., job dissatisfaction, low organizational commitment)
• Indicators of poor physical health (absence due to illness, workers’ compensation claims)
• Work-related behavioral impairment (injuries, poor job performance, on-the-job substance use)

Everyone who has ever held a job has, at some point, felt the pressure of work-related stress. Any job can have stressful elements, even if you love what you do. In the short-term, you may experience pressure to meet a deadline or to fulfill a challenging obligation. But when work stress becomes chronic, it can be overwhelming — and harmful to both physical and emotional health.

Unfortunately, such long-term stress is all too common. In fact, APA’s annual Stress in America survey has consistently found that work is cited as a significant source of stress by a majority of Americans. You can’t always avoid the tensions that occur on the job. Yet you can take steps to manage work-related stress.

Common Sources of Work Stress

Certain factors tend to go hand-in-hand with work-related stress. Some common workplace stressors are:

• Low salaries
• Excessive workloads
• Few opportunities for growth or advancement
• Work that isn’t engaging or challenging
• Lack of social support
• Not having enough control over job-related decisions
• Conflicting demands or unclear performance expectations.

Effects of Uncontrolled Stress

Work-related stress doesn’t just disappear when you head home for the day. When stress persists, it can take a toll on your health and well-being.

A stressful work environment can contribute to problems such as headache, stomachache, sleep disturbances, short temper and difficulty concentrating. Chronic stress can result in anxiety, insomnia, high blood pressure and a weakened immune system. It can also contribute to health conditions such as depression, obesity and heart disease. Compounding the problem, people who experience excessive stress often deal with it in unhealthy ways such as overeating, eating unhealthy foods, smoking cigarettes or abusing drugs and alcohol.

Taking Steps to Manage Stress

1. Track your stressors

Keep a journal for a week or two to identify which situations create the most stress and how you respond to them. Record your thoughts, feelings and information about the environment, including the people and circumstances involved, the physical setting and how you reacted. Did you raise your voice? Get a snack from the vending machine? Go for a walk? Taking notes can help you find patterns among your stressors and your reactions to them.

2. Develop healthy responses

Instead of attempting to fight stress with fast food or alcohol, do your best to make healthy choices when you feel the tension rise. Exercise is a great stress-buster. Yoga can be an excellent choice, but any form of physical activity is beneficial. Also make time for hobbies and favorite activities. Whether it’s reading a novel, going to concerts or playing games with your family, make sure to set aside time for the things that bring you pleasure. Getting enough good-quality sleep is also important for effective stress management. Build healthy sleep habits by limiting your caffeine intake late in the day and minimizing stimulating activities, such as computer and television use, at night.

3. Establish boundaries

In today’s digital world, it’s easy to feel pressure to be available 24 hours a day. Establish some work-life boundaries for yourself. That might mean making a rule not to check email from home in the evening, or not answering the phone during dinner. Although people have different preferences when it comes to how much they blend their work and home life, creating some clear boundaries between these realms can reduce the potential for work-life conflict and the stress that goes with it.

4. Take time to recharge

To avoid the negative effects of chronic stress and burnout, we need time to replenish and return to our pre-stress level of functioning. This recovery process requires “switching off” from work by having periods of time when you are neither engaging in work-related activities, nor thinking about work. That’s why it’s critical that you disconnect from time to time, in a way that fits your needs and preferences. Don’t let your vacation days go to waste. When possible, take time off to relax and unwind, so you come back to work feeling reinvigorated and ready to perform at your best. When you’re not able to take time off, get a quick boost by turning off your smartphone and focusing your attention on non-work activities for a while.

5. Learn how to relax

Techniques such as meditation, deep breathing exercises and mindfulness (a state in which you actively observe present experiences and thoughts without judging them) can help melt away stress. Start by taking a few minutes each day to focus on a simple activity like breathing, walking or enjoying a meal. The skill of being able to focus purposefully on a single activity without distraction will get stronger with practice and you’ll find that you can apply it to many different aspects of your life.

6. Talk to your supervisor

Employee health has been linked to productivity at work, so your boss has an incentive to create a work environment that promotes employee well-being. Start by having an open conversation with your supervisor. The purpose of this isn’t to lay out a list of complaints, but rather to come up with an effective plan for managing the stressors you’ve identified, so you can perform at your best on the job. While some parts of the plan may be designed to help you improve your skills in areas such as time management, other elements might include identifying employer-sponsored wellness resources you can tap into, clarifying what’s expected of you, getting necessary resources or support from colleagues, enriching your job to include more challenging or meaningful tasks, or making changes to your physical workspace to make it more comfortable and reduce strain.

7. Get some support

Accepting help from trusted friends and family members can improve your ability to manage stress. Your employer may also have stress management resources available through an employee assistance program (EAP), including online information, available counseling and referral to mental health professionals, if needed. If you continue to feel overwhelmed by work stress, you may want to talk to a psychologist, who can help you better manage stress and change unhealthy behavior.

In probability theory, the sample space (also called sample description space or possibility space) of an experiment or random trial is the set of all possible outcomes or results of that experiment. A sample space is usually denoted using set notation, and the possible ordered outcomes are listed as elements in the set. It is common to refer to a sample space by the labels S, Ω, or U (for “universal set”). The elements of a sample space may be numbers, words, letters, or symbols. They can also be finite, countably infinite, or uncountably infinite.

For example, if the experiment is tossing a coin, the sample space is typically the set {head, tail}, commonly written {H, T}. For tossing two coins, the corresponding sample space would be {(head,head), (head,tail), (tail,head), (tail,tail)}, commonly written {HH, HT, TH, TT}. If the sample space is unordered, it becomes {{head,head}, {head,tail}, {tail,tail}}.

For tossing a single six-sided die, the typical sample space is {1, 2, 3, 4, 5, 6} (in which the result of interest is the number of pips facing up).

A subset of the sample space is an event, denoted by E. Referring to the experiment of tossing the coin, the possible events include E={H} and E={T}.

A well-defined sample space is one of three basic elements in a probabilistic model (a probability space); the other two are a well-defined set of possible events (a sigma-algebra) and a probability assigned to each event (a probability measure function).

Another way to look as a sample space is visually. The sample space is typically represented by a rectangle, and the outcomes of the sample space denoted by points within the rectangle. The events are represented by ovals, and the points enclosed within the oval make up the event.

Equally likely outcomes

Some treatments of probability assume that the various outcomes of an experiment are always defined so as to be equally likely. For any sample space with N equally likely outcomes, each outcome is assigned the probability 1/N. However, there are experiments that are not easily described by a sample space of equally likely outcomes for example, if one were to toss a thumb tack many times and observe whether it landed with its point upward or downward, there is no symmetry to suggest that the two outcomes should be equally likely.

Though most random phenomena do not have equally likely outcomes, it can be helpful to define a sample space in such a way that outcomes are at least approximately equally likely, since this condition significantly simplifies the computation of probabilities for events within the sample space. If each individual outcome occurs with the same probability, then the probability of any event becomes simply:

P ( e v e n t ) = number of outcomes in event/ number of outcomes in sample space

For example, if two dice are thrown to generate two uniformly distributed integers, D1 and D2, each in the range [1…6], the 36 ordered pairs (D1, D2) constitute a sample space of equally likely events. In this case, the above formula applies, such that the probability of a certain sum, say D1 + D2 = 5 is easily shown to be 4/36, since 4 of the 36 outcomes produce 5 as a sum. On the other hand, the sample space of the 11 possible sums, {2, …,12} are not equally likely outcomes, so the formula would give an incorrect result (1/11).

Another example is having four pens in a bag. One pen is red, one is green, one is blue, and one is purple. Each pen has the same chance of being taken out of the bag.

The sample space S= {red, green, blue, purple}, consists of equally likely events. Here, P(red)=P(blue)=P(green)=P(purple)=1/4.

Sample event

A sample event refers to subset pertaining to sample space that comprises of sample space, empty set (A event that is impossible and possesses zero probability) and singleton set (it is also known as an elementary event). Other event stands to be proper subset pertaining to the sample space which generally comprises of different elements.
Event under the probability theory refers to set of outcome ascertained out of the experiment to which the assigning of probability is done. One outcome might be considered as element pertaining to multiple events that are different from one another. A complimentary event is defined by the event which comprises of event that is not happening and together it defines Bernoulli trial.

Sample event basically refers to something that happens or occurs. For instance flipping of count stands to be an event. Passing by the bench in the park while walking is also counted as an event. There are 1 or more outcomes associated with every event. For example, coin flipping stands to be an event, however, attaining a tail stands to be the outcome of such event. Walking in park stands to be an event, however identifying the friend in park stands to be the outcome associated with the event.

Thus it can be said event stands to be subset pertaining to sample space that comprises of sample space, none or all of the outcome. The event will be considered as a simple event in case it has only 1 sample point. If there are 2 or more sample points underlying an event the same will be considered as compound events. The event will be known as null space in case there is no sample point underlying an event.

In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. A single outcome may be an element of many different events, and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. An event defines a complementary event, namely the complementary set (the event not occurring), and together these define a Bernoulli trial: did the event occur or not?

Typically, when the sample space is finite, any subset of the sample space is an event (i.e. all elements of the power set of the sample space are defined as events). However, this approach does not work well in cases where the sample space is uncountably infinite. So, when defining a probability space it is possible, and often necessary, to exclude certain subsets of the sample space from being event.

A simple example

If we assemble a deck of 52 playing cards with no jokers, and draw a single card from the deck, then the sample space is a 52-element set, as each card is a possible outcome. An event, however, is any subset of the sample space, including any singleton set (an elementary event), the empty set (an impossible event, with probability zero) and the sample space itself (a certain event, with probability one). Other events are proper subsets of the sample space that contain multiple elements. So, for example, potential events include:

• “Red and black at the same time without being a joker” (0 elements),
• “The 5 of Hearts” (1 element),
• “A King” (4 elements),
• “A Face card” (12 elements),
• “A Spade” (13 elements),
• “A Face card or a red suit” (32 elements),
• “A card” (52 elements).

Since all events are sets, they are usually written as sets (e.g. {1, 2, 3}), and represented graphically using Venn diagrams. In the situation where each outcome in the sample space Ω is equally likely, the probability P {\displaystyle P} of an event A is the following formula:

The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of the possible values that X can take, each value being weighted according to the probability of that event occurring. The expected value of X is usually written as E(X) or m.

• E(X) = S x P(X = x)

So the expected value is the sum of: [(each of the possible outcomes) × (the probability of the outcome occurring)].

In more concrete terms, the expectation is what you would expect the outcome of an experiment to be on average.

Example

What is the expected value when we roll a fair die?

There are six possible outcomes: 1, 2, 3, 4, 5, 6. Each of these has a probability of 1/6 of occurring. Let X represent the outcome of the experiment.

Therefore P(X = 1) = 1/6 (this means that the probability that the outcome of the experiment is 1 is 1/6)
P(X = 2) = 1/6 (the probability that you throw a 2 is 1/6)
P(X = 3) = 1/6 (the probability that you throw a 3 is 1/6)
P(X = 4) = 1/6 (the probability that you throw a 4 is 1/6)
P(X = 5) = 1/6 (the probability that you throw a 5 is 1/6)
P(X = 6) = 1/6 (the probability that you throw a 6 is 1/6)

E(X) = 1×P(X = 1) + 2×P(X = 2) + 3×P(X = 3) + 4×P(X=4) + 5×P(X=5) + 6×P(X=6)

Therefore E(X) = 1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6 = 7/2

So the expectation is 3.5 . If you think about it, 3.5 is halfway between the possible values the die can take and so this is what you should have expected.

Expected Value of a Function of X

To find E[ f(X) ], where f(X) is a function of X, use the following formula:

• E[ f(X) ] = S f(x)P(X = x)

Example

For the above experiment (with the die), calculate E(X²)

Using our notation above, f(x) = x²

f(1) = 1, f(2) = 4, f(3) = 9, f(4) = 16, f(5) = 25, f(6) = 36
P(X = 1) = 1/6, P(X = 2) = 1/6, etc

So E(X²) = 1/6 + 4/6 + 9/6 + 16/6 + 25/6 + 36/6 = 91/6 = 15.167

The expected value of a constant is just the constant, so for example E(1) = 1. Multiplying a random variable by a constant multiplies the expected value by that constant, so E[2X] = 2E[X].

A useful formula, where a and b are constants, is:

• E[aX + b] = aE[X] + b

[This says that expectation is a linear operator].

Variance

The variance of a random variable tells us something about the spread of the possible values of the variable. For a discrete random variable X, the variance of X is written as Var(X).

• Var(X) = E[ (X – m)² ]            where m is the expected value E(X)

This can also be written as:

• Var(X) = E(X²) – m²

The standard deviation of X is the square root of Var(X). 

Note that the variance does not behave in the same way as expectation when we multiply and add constants to random variables. In fact:

• Var[aX + b] = a²Var(X)

You is because: Var[aX + b] = E[ (aX + b)² ] – (E [aX + b])² .

= E[ a²X² + 2abX + b²] – (aE(X) + b)²
= a²E(X²) + 2abE(X) + b² – a²E²(X) – 2abE(X) – b²
= a²E(X²) – a²E²(X) = a²Var(X)