Month: July 2020

Probable Error is basically the correlation coefficient that is fully responsible for the value of the coefficients and its accuracy.

As mentioned, probable error is the coefficient of correlation that supports in finding out about the accurate values of the coefficients. It also helps in determining the reliability of the coefficient.

The calculation of the correlation coefficient usually takes place from the samples. These samples are in pairs. The pairs generally come from a very large population. It is quite an easy job to find out about the limits and bounds of the correlation coefficient.

The correlation coefficient for a population is usually based on the knowledge and the sample relating to the correlation coefficient. Therefore, probable error is the easy way to find out or obtain the correlation coefficient of any population. Hence, the definition is:

Probable Error = 0.674 × 1−r2√N

Here, r = correlation coefficient of ‘n’ pairs of observations for any random sample and N = Total number of observations.

About the Values

• There is hardly any correlation between the different variables if the value of ‘r’ turns out to be less than the value of the probable error
• The value of correlation coefficient is generally certain if and only if the value of ‘r’ is around 6 times more than the value of the error.
•  The value of the probable error is in the bounds -1 and +1(-1≤r≤1). So, we can express it in the following manner.

Probable Limit

To get the upper limit and the lower limit, all we need to do is respectively add and subtract the value of probable error from the value of ‘r.’ This is exactly where the value of correlation of coefficient lies.

ρ (rho) = r ± P.E.

Here, the value of rho is nothing but the correlation coefficient of a population. This is also the limit of the correlation of coefficient. Alongside,

Probable Error = 2/3 SE

Here, S.E is Standard Error of Correlation Coefficient

Standard Error = (1-r²)/√N

Standard Error is basically the standard deviation of any mean. It is the sampling distribution of the standard deviation. The standard error is generally used to refer to any sort of estimate belonging to the standard deviation. Therefore, we use probable error to calculate and check the reliability associated with the coefficient.

Advantages of Standard Error

• It helps in finding and reducing the sample errors as well as the measurement errors.
• The standard error of any mean tells about the accuracy of the estimate clearly enough.

Formulas for Calculating Probable Error

Generally, there are three formulas using which we can calculate the probable error. The very first formula is the most common formula to calculate P.E. We use the Pearson product-moment method for calculating the same. It is:

P.E r  _{product-moment} = 0.6745(1-r²)/√N

The second formula is applicable when we need the probable error for rho. We use the Spearman method to calculate the value. The formula for the same is:

P.E. ρ = 0.6745(1-ρ²)/√N {1 + 1.086ρ² + 0.13ρ⁴ + .002ρ⁶}

The third formula is applicable to the Pearson coefficient ‘r.’  We calculate it through ρ by using the transmutation formula. The value is r = 2 sin (πρ/6). The formula is given by:

1. E  r_{found from ρ} = 0.7063 (1 – r²)√N {1 + 1.042r² + 0.008r⁴ + .002r⁶}

Note: The formula that we are using to calculate probable error is valid and applicable if the given population is normal.

Conditions to find Probable Error

We can find the probable error if and only if the given below conditions are taken care of.

• The data that we have must be a bell-shaped curve. This means that the data has to give us a normal frequency curve
• It is important to take the probable error for measuring the statistics from the sample only
• It is compulsory that the sample items are taken off in an unbiased manner and must remain independent of each other’s value

We use this method of construction for computation of index price. As a result, the total cost of any commodity in any given year to the total cost of any commodity in the base year is in percentage form.

Simple Aggregative Price Index – (∑ P_n/ ∑ P₀) * 100

Where

∑P_n = Sum of the price of all the respective commodity in the current time period.
∑P_o = Sum of the price of all the respective commodity in the base period.

The simple aggregative index is very simple to understand. However, there is a serious defect in this method. The first commodity, here, has more influence than the rest two. This is so because the first commodity has a high price than the rest.

Furthermore, if we anyhow change the units, the index number will also go through a change. This is one of the biggest flaws of this methods. Use of absolute quantities turn the tables around. Therefore, considering independent values for the three years would be a better option.

To construct a simple price index, compute the price relatives and average them. Add the price relatives and divide them by the number of items. Table illustrates the construction of a simple index of wholesale prices.

Price index in 1980 = Prices in 1980 / Prices in 1970 x 100

Or ∑P₁/P₀ x 100 = 870/500 x 100 = 174

Using arithmetic mean, price index in 1980 = ∑R/N = 870/5 = 174

The preceding table shows that 1970 is the base period and 1980 is the year for which the price index has been constructed on the basis of price relatives. The index of wholesale prices in 1980 comes to 174. This means that the price level rose by 74 per cent in 1980 over 1970.

Consumer Price Index is also known as the cost of living index.

It represents the average change in price over a period of time, paid by a consumer for a fixed basket of goods and services.

Uses of CPI:

• It indicates the changes in the consumer prices.
• It evaluates the purchasing power of money.
• It is also used for comparison purposes.

Limitations of CPI;

• CPI focuses on a fixed basket, as consumer behaviour cannot be predicted, we can’t be very sure about CPI value to be relevant.
• Quality is not considered while calculating the CPI.
• Inflation effects are not taken into consideration as the basket is fixed.

CPI can be computed using 2 methods:

• Aggregate Expenditure method

CPI = (Total expenditure in current year/Total expenditure in base year)*100; which means;

CPI = Σp1q0/Σp0q0 * 100

• Family Budget method

CPI =  ΣWP/ ΣW

Where P = p1/p0 * 100

The frequency is the number of times an event occurs within a given scenario. Cumulative frequency is defined as the running total of frequencies. It is the sum of all the previous frequencies up to the current point. It is easily understandable through a Cumulative Frequency Table.

Cumulative Frequency is an important tool in Statistics to tabulate data in an organized manner. Whenever you wish to find out the popularity of a certain type of data, or the likelihood that a given event will fall within certain frequency distribution, a cumulative frequency table can be most useful. Say, for example, the Census department has collected data and wants to find out all residents in the city aged below 45. In this given case, a cumulative frequency table will be helpful.

Cumulative Frequency Curve

A curve that represents the cumulative frequency distribution of grouped data on a graph is called a Cumulative Frequency Curve or an Ogive. Representing cumulative frequency data on a graph is the most efficient way to understand the data and derive results.

There are two types of Cumulative Frequency Curves (or Ogives) :

• More than type Cumulative Frequency Curve
• Less than type Cumulative Frequency Curve

A frequency polygon is a graphical form of representation of data. It is used to depict the shape of the data and to depict trends. It is usually drawn with the help of a histogram but can be drawn without it as well. A histogram is a series of rectangular bars with no space between them and is used to represent frequency distributions.

Steps to Draw a Frequency Polygon

• Mark the class intervals for each class on the horizontal axis. We will plot the frequency on the vertical axis.
• Calculate the classmark for each class interval. The formula for class mark is:

Classmark = (Upper limit + Lower limit) / 2

• Mark all the class marks on the horizontal axis. It is also known as the mid-value of every class.
• Corresponding to each class mark, plot the frequency as given to you. The height always depicts the frequency. Make sure that the frequency is plotted against the class mark and not the upper or lower limit of any class.
• Join all the plotted points using a line segment. The curve obtained will be kinked.
• This resulting curve is called the frequency polygon.

Note that the above method is used to draw a frequency polygon without drawing a histogram. You can also draw a histogram first by drawing rectangular bars against the given class intervals. After this, you must join the midpoints of the bars to obtain the frequency polygon. Remember that the bars will have no spaces between them in a histogram.

Question 1: Construct a frequency polygon using the data given below:

Answer: We first need to calculate the cumulate frequency from the frequency given.

We now start by plotting the class marks such as 54.5, 64.5, 74.5 and so on till 94.5. Note that we will also plot the previous and next class marks to start and end the polygon, i.e. we plot 44.5 and 104.5 as well.

Then, the frequencies corresponding to the class marks are plotted against each class mark. Like you can see below, this makes sense as the frequency for class marks 44.5 and 104.5 are zero and touching the x-axis. These plot points are used only to give a closed shape to the polygon. The polygon looks like this:

Declaration and payment of dividend under Companies Act 2013

Dividend: Sec 2(35) provides the definition of dividend which states that dividend includes any “interim dividend”. Where in simple terms, dividend can be defined as the sum of money paid by a company, to its shareholders, out of the profits made by a company, in the proportion to the amount paid-up on the shares held by them (Sec-51).

Note: Preference shareholders are always paid dividend in preference to the equity shareholders.

Well, subject to the provisions of Companies Act, 2013, All Companies, except those companies which are registered under sec-8 (i.e. Non-profit organizations) can declare dividend.

Under Companies Act 2013, Chapter VIII containing sections, which deals with the provisions related to declaration and payment of dividend. Section 123 to 127 deals with the provisions related to the declaration and payment of dividend.

Conditions required to be satisfied for declaration of dividend

1) Depreciation: Before the declaration of dividend, a company shall provide depreciation to all its depreciable assets, in accordance with the rates or useful life, as the case may be provided in Schedule – II of Companies Act -2013.

2) Transfer to Reserves: A company may, before the declaration of any dividend in any financial year, transfer such percentage of its profits for that financial year, as it may consider appropriate to the reserves of the company.

3) Set off of previous year losses and depreciation: A company shall not declare dividend unless carried over previous losses and depreciation not provided in previous year or years, are set off against profit of the company for the current year.

4) Free Reserves: A company shall not declare or pay dividend out of its reserves, other than free reserves.

Payment of Dividend

According to the provisions of Companies Act 2013, No dividend shall be payable except by way of cash, where dividend payable in cash can also be paid through cheque, warrant or in any electronic mode, to the shareholder who is entitled to the dividend.

Condition: A company who has committed any default in compliance with the provisions of sec 73 and 74 relating to the acceptance and repayment of deposits would be barred to declare dividend.

Interim Dividend

According to the provisions of section 123(3), Board of directors of a company may declare interim dividend during any financial year, out of the profits made by the company during such financial year or out of previous year undistributed profits (subject to Companies (Declaration and Payment of Dividend) Rules, 2014).

As per Section 2(35) “dividend includes interim dividend” signifies that the provisions of Companies Act 2013, applicable to the final dividend to the extent possible, shall also applicable on interim dividend.

Unpaid Dividend Account (Sec 124)

There are some cases wherein, dividend declared by the company has not been paid or claimed and in case where such dividend remained unpaid or unclaimed within 30 days from the date of declaration; company shall take the following necessary steps:

(a) Open a special account with a scheduled bank to be called “Unpaid dividend account of …………………….(Company Limited/Company( Private) Limited”

(b) Transfer the unpaid or unclaimed amount of dividend within a period of 7 days from the expiry of such 30 days, to the special account.

In case of default: If the company committed any default, in transferring such amount to the special account with in the specified time, company shall be liable to pay interest @ 12% p.a. from the date of such default.

Punishment for failure to distribute dividend (Sec 127)

According to the provisions of sec- 127 of the companies act – 2013, if a company fails to pay the dividend, within a period of 30 days from the date of its declaration, to the shareholders who are entitled to the dividend then-

Exceptions to sec- 127: Following are the situation under which, no offence shall be deemed to have been committed, namely:

(a) Where the dividend could not be paid by reason of the operation of any law;

(b) Where a shareholder has given directions to the company regarding the payment of the dividend and those directions cannot be complied with and the same has been communicated to him:

(c) Where there is a dispute regarding the right to receive the dividend

(d) Where the dividend has been lawfully adjusted by the company against any sum due to it from the shareholder

(e) Where, for any other reason, the failure to pay the dividend or to post the warrant within the period under this section was not due to any default on the part of the company.

The various communication devices are used to educate, inform and generate awareness about the merchandise and the services offered by the retailer. These efforts also aim at building store image. The most common modes used for promotion are advertising, sales promotion, personal selling, public relations and publicity.

Retailers usually employ a combination of various elements of promotion mix to achieve promotional and business objectives. The degree and the nature of usage of each of the promotion methods depend on the objectives of the retail firm, product, market profile and availability of resources. Small retailers generally depend on point-of-purchase material provided by the companies which provide the merchandise.

Promotion mix employed by the retailers should be compatible with the desired store image, provide scope for modification if need arises and fit within the budget allocation. Therefore, various retail promotion methods can be compared on the basis of degree of control, flexibility, credibility and cost associated with them.

The four important types of retail marketing mix are discussed below:

1. The ‘Product’ Mix

The basic components of product mix are:

(ii) Packaging

(iii) Brand

(iv) Product Item

(v) Product line

The various product mix strategies are:

(i) Launching new products from time to time

(ii) Alteration of Existing Products

(iii) Eliminate an entire line or reduce assortment within it

(iv) Trading Up

(v) Trading Down

(vi) Product life cycle management

The retail product mix is device so as to develop an appropriate promotion strategy for the store depending on the target market to be reached. Once the target market is identified and positioning strategy defined, the retailers employ various tools of product mix to reach out to consumers. These efforts also aim at building store image.

Retailers usually employ a combination of various elements of product mix to achieve promotional and business objectives. The degree and the nature of usage of each of the promotion methods depend on the objectives of the retail firm, product, market profile, and availability of resources.

2. The ‘Price’ Mix

Price has always been one of the most important variables in retail buying decision. It is the factor which makes or mars a retail organization. It is also the easiest and quickest element to change. Pricing helps an organization to achieve its objective. This is particularly significant for new market entrants who need to first establish a brand and then enjoy increasing profits as the brand gets market acceptability. For a customer, price is the main reason to visit a particular store.

A pricing strategy must be consistent over a period of time and consider retailer’s overall positioning, profits, sales and appropriate rate of return on investment. Lowest price does not necessarily neet be the best price, but the lowest responsible price is the best right price. The difference between price and cost is the profit, which can be very high when the salesperson wants to exploit an urgent situation.

To survive in the retail business, retailers need to seek cash flow, profitability and overall growth in order to consolidate their market position. But pricing cannot be determined in isolation. Costs and operating expenses are equally important while establishing the retail price.

Servicing pricing pursues the ‘doctrine of pricing of goods’, therefore, they are either cost-based or market based. Within this, these pricing can be profit oriented, government controlled, consumer oriented or competition oriented. Pricing needs certain considerations before actually determining it. The market position of the product, consumer perception and stage of the product life cycle, competitor’s strategy and overall marketing strategy needs to be considered.

The components of price mix are:

(i) Organizational objectives

(ii) Competition

(iii) Cost and profit

(iv) Credit terms

(v) Discount etc.

(vi) Fixed and variable costs

(vii) Pricing options

(viii) Pricing policies

(ix) Proposed positioning strategies

(x) Target group and willingness to pay

3. The ‘Place’ Mix

The retailer should keep in mind the fact that his ‘product’ should be available near the place of consumption so that the consumers can easily buy it. If the brand preferred by the consumer is not easily available at a convenient location, he may buy some other brand in the same product category.

Hence, the retailer has to ensure that the product is available to the target consumers whenever required. There are two major components of place: marketing channels and physical distribution (logistics management). Channel decisions affect considerably the elements of marketing mix and involve a long term commitment of resources.

Intermediaries involved in channel network are independent (at times contractual) organizations hence their needs must be taken into account while evaluating channel alternatives. The success of marketing efforts, to a large extent depends on the sound distribution network.

Physical distribution involves transportation, warehousing, material handling, bulk packaging etc. Some of these activities are carried out by intermediaries. A considerable coordination is required among various channels to seek maximum results of marketing operations.

Following are the components of a retail price mix:

(i) Distribution channels

(ii) Intermediary

(iii) Distance Factor

(iv) Inventory Level

(v) Transportation

(vi) Warehousing and Storage

4. The ‘Promotion’ Mix

After deciding upon the budget, retailer should determine the appropriate promotional mix a combination of advertising, public relations, personal selling and sales promotion. Small retailers having limited funds may use store displays, hoardings, direct mail, flyers and publicity methods to attract customer traffic, while on the other hand, retailers having no bar on finance, may use print or television media for their sales promotion activities.

The retail promotion mix varies from retailer to retailer and nation to nation depending upon technological advancement, nature of competition and availability of finance etc. Retailers design a promotional mix in compliance with store’s objectives such as positioning of the organization, attracting customers, increasing sales turnover, clear out seasonal merchandise, announcing special events and educating public about the organization and its offerings.

Retailers generally spend their promotional budget on developing advertisement campaigns and on other sales promotion activities. A retailer has a variety of sales promotion methods to promote its goods and services. Therefore, promotion mix used by the retailer should be compatible with the desired store image, budget allocation and flexible enough to modify whenever need arises.

These various promotional vehicles may by compared on the basis of following issues:

(i) Cost of the method

(ii) Its reach

(iii) Degree of flexibility

(iv) Credibility

(v) Control over media