Category: Management Notes

Management Notes

Difference between Correlation and Regression

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Correlation and Regression

Correlation and regression are two important statistical tools used to study the relationship between variables. Both help managers analyze data and make informed business decisions. While correlation measures the degree and direction of relationship between variables, regression explains the cause-and-effect relationship and helps in prediction. Though closely related, their objectives and applications are different.

Correlation

The term correlation is a combination of two words ‘Co’ (together) and relation (connection) between two quantities. Correlation is when, at the time of study of two variables, it is observed that a unit change in one variable is retaliated by an equivalent change in another variable, i.e. direct or indirect. Or else the variables are said to be uncorrelated when the movement in one variable does not amount to any movement in another variable in a specific direction. It is a statistical technique that represents the strength of the connection between pairs of variables.

Correlation refers to a statistical measure that indicates the extent and direction of relationship between two variables. It shows whether variables move together or in opposite directions. Correlation is expressed numerically through the correlation coefficient (r), whose value lies between –1 and +1. A positive value indicates direct relationship, a negative value indicates inverse relationship, and zero indicates no relationship. Correlation does not indicate causation; it only measures association.

On the contrary, when the two variables move in different directions, in such a way that an increase in one variable will result in a decrease in another variable and vice versa, This situation is known as negative correlation. For instance: Price and demand of a product.

The measures of correlation are given as under:

  • Karl Pearson’s Product-moment correlation coefficient
  • Spearman’s rank correlation coefficient
  • Scatter diagram
  • Coefficient of concurrent deviations

Regression

Regression analysis is a statistical technique that establishes a functional or causal relationship between a dependent variable and one or more independent variables. It helps estimate or predict the value of one variable based on the known value of another. Regression provides a mathematical equation that explains how much change in the dependent variable is caused by changes in independent variables. It is widely used in forecasting and planning.

Differences Between Correlation and Regression

1. Meaning and Concept

Correlation and regression differ fundamentally in their basic meaning and conceptual approach. Correlation is a statistical measure that shows the degree and direction of relationship between two variables. It simply answers the question of whether variables are related and how strongly they move together. It does not explain why the relationship exists.

Regression, on the other hand, is a statistical technique that establishes a functional or causal relationship between variables. It explains how one variable (dependent) is affected by changes in another variable (independent). Regression goes beyond association and attempts to quantify the impact of one variable on another. Thus, while correlation is concerned with measuring association, regression focuses on explanation and prediction, making it more powerful for business decision-making.

2. Objective of Study

The objective of correlation is to determine whether a relationship exists between variables and to measure its strength and direction. It helps analysts understand patterns and tendencies in data. Correlation answers questions like: Are sales and advertising related? or Do income and consumption move together?

The objective of regression is to predict or estimate the value of one variable based on another. It is used when a business wants to forecast outcomes, such as predicting sales based on price or estimating costs based on output. Regression analysis provides a mathematical equation that can be used for planning, control, and forecasting. Hence, correlation is mainly descriptive in nature, while regression is both descriptive and predictive, making regression more suitable for managerial decision-making

3. Nature of Relationship

Correlation measures the degree of linear relationship between variables but does not indicate any cause-and-effect connection. Even if two variables are highly correlated, one may not necessarily cause changes in the other. For example, ice cream sales and electricity consumption may show correlation due to seasonal effects, not causation.

Regression, in contrast, assumes a cause-and-effect relationship between variables. It explains how changes in the independent variable bring about changes in the dependent variable. For instance, regression can estimate how much sales will increase due to a specific increase in advertising expenditure. Thus, correlation reflects association only, whereas regression attempts to establish dependence, which is crucial for business forecasting and strategic planning.

4. Treatment of Variables

In correlation, variables are treated symmetrically. There is no distinction between dependent and independent variables. The correlation between X and Y is the same as the correlation between Y and X. Both variables are given equal importance, and the analysis does not require identifying which variable influences the other.

In regression, variables are treated asymmetrically. One variable is clearly identified as the dependent variable, and the other(s) as independent variables. The entire analysis is based on explaining or predicting the dependent variable. For example, sales may depend on price and advertising. This clear distinction is essential for regression analysis, making it more suitable for practical business applications where cause-and-effect relationships are required.

5. Numerical Measure and Output

Correlation is expressed using a single numerical value, called the correlation coefficient (r). This value ranges from –1 to +1 and indicates only the strength and direction of relationship. A single figure summarizes the entire relationship, which makes correlation easy to compute and interpret but limited in analytical depth.

Regression produces regression equations, such as Y = a + bX, where coefficients show the magnitude of change in the dependent variable due to a unit change in the independent variable. These equations provide detailed quantitative insights and allow prediction. Therefore, while correlation provides a summary measure, regression offers a complete analytical model useful for forecasting and decision-making.

6. Symmetry and Direction

Correlation is symmetric in nature, meaning that correlation between X and Y is exactly the same as correlation between Y and X. There is no concept of direction of dependence in correlation analysis. This symmetry limits its usefulness in predictive analysis.

Regression is not symmetric. Regression of Y on X is different from regression of X on Y. Each regression equation serves a specific purpose depending on which variable is treated as dependent. This directional nature makes regression a powerful analytical tool. It helps managers decide which variable should be predicted and which variables should be used as predictors, making regression more practical for real-world business problems.

7. Use in Prediction and Forecasting

Correlation is not suitable for prediction. Although it indicates the existence of a relationship, it does not provide a mechanism to estimate future values. A high correlation does not necessarily mean accurate forecasting is possible.

Regression is specifically designed for prediction and forecasting. Using regression equations, businesses can estimate future sales, costs, profits, or demand based on known values of independent variables. This makes regression extremely valuable for planning, budgeting, and policy formulation. Thus, correlation is primarily exploratory, while regression is predictive and decision-oriented.

8. Practical Application in Business

Correlation is mainly used for preliminary analysis. It helps identify whether variables are related and whether further analysis is worthwhile. For example, before performing regression, managers often check correlation to see if a relationship exists.

Regression has direct practical applications in business, including sales forecasting, demand estimation, cost control, pricing decisions, and investment analysis. It provides a scientific basis for managerial decisions. Hence, correlation serves as a starting point in analysis, while regression forms the foundation of advanced quantitative decision-making in business.

Key Differences Between Correlation and Regression

Aspect Correlation Regression
Meaning Correlation measures the degree and direction of relationship between two variables. Regression measures the functional and causal relationship between variables.
Nature It shows association only. It shows cause-and-effect relationship.
Objective To determine whether variables are related and how strongly. To predict or estimate the value of one variable from another.
Type of Relationship Indicates linear association only. Explains dependence of one variable on another.
Variables Does not distinguish between dependent and independent variables. Clearly distinguishes dependent and independent variables.
Direction of Influence No direction of influence is implied. Direction of influence is clearly defined.
Numerical Measure Expressed through a single value called correlation coefficient (r). Expressed through regression equations.
Range of Values Lies between –1 and +1. No fixed range for regression coefficients.
Symmetry Symmetric in nature (X with Y = Y with X). Asymmetric (Regression of Y on X ≠ X on Y).
Use in Prediction Not suitable for prediction. Specifically used for forecasting and prediction.
Number of Equations Only one coefficient is calculated. Two regression equations can be formed.
Dependency Assumption No assumption of dependency. Assumes dependency of one variable on another.
Effect of Change in Units Correlation coefficient is unit-free. Regression coefficients depend on measurement units.
Business Application Used mainly for preliminary analysis. Widely used for decision-making and planning.
Analytical Depth Provides limited analytical insight. Provides detailed quantitative analysis.
Management Notes

Rank correlation; coefficient of determination

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Rank Correlation

Sometimes there doesn’t exist a marked linear relationship between two random variables but a monotonic relation (if one increases, the other also increases or instead, decreases) is clearly noticed. A Pearson’s Correlation Coefficient evaluation, in this case, would give us the strength and direction of the linear association only between the variables of interest. Herein comes the advantage of the Spearman Rank Correlation methods, which will instead, give us the strength and direction of the monotonic relation between the connected variables. This can be a good starting point for further evaluation.

The Spearman Rank Order Correlation Coefficient

The Spearman’s Correlation Coefficient, represented by ρ or by rR, is a nonparametric measure of the strength and direction of the association that exists between two ranked variables. It determines the degree to which a relationship is monotonic, i.e., whether there is a monotonic component of the association between two continuous or ordered variables.

Monotonicity is “less restrictive” than that of a linear relationship. Although monotonicity is not actually a requirement of Spearman’s correlation, it will not be meaningful to pursue Spearman’s correlation to determine the strength and direction of a monotonic relationship if we already know the relationship between the two variables is not monotonic.

On the other hand if, for example, the relationship appears linear (assessed via scatterplot) one would run a Pearson’s correlation because this will measure the strength and direction of any linear relationship.

Spearman Ranking of the Data

We must rank the data under consideration before proceeding with the Spearman’s Rank Correlation evaluation. This is necessary because we need to compare whether on increasing one variable, the other follows a monotonic relation (increases or decreases regularly) with respect to it or not.

Thus, at every level, we need to compare the values of the two variables. The method of ranking assigns such ‘levels’ to each value in the dataset so that we can easily compare it.

  • Assign number 1 to n (the number of data points) corresponding to the variable values in the order highest to lowest.
  • In the case of two or more values being identical, assign to them the arithmetic mean of the ranks that they would have otherwise occupied.

The Formula for Spearman Rank Correlation

where n is the number of data points of the two variables and di is the difference in the ranks of the ith element of each random variable considered. The Spearman correlation coefficient, ρ, can take values from +1 to -1.

  • A ρ of +1 indicates a perfect association of ranks
  • A ρ of zero indicates no association between ranks and
  • ρ of -1 indicates a perfect negative association of ranks.
    The closer ρ is to zero, the weaker the association between the ranks.

Coefficient of Determination

The Coefficient of determination is the square of the coefficient of correlation r2 which is calculated to interpret the value of the correlation. It is useful because it explains the level of variance in the dependent variable caused or explained by its relationship with the independent variable.

The coefficient of determination explains the proportion of the explained variation or the relative reduction in variance corresponding to the regression equation rather than about the mean of the dependent variable. For example, if the value of r = 0.8, then r2 will be 0.64, which means that 64% of the variation in the dependent variable is explained by the independent variable while 36% remains unexplained.

Thus, the coefficient of determination is the ratio of explained variance to the total variance that tells about the strength of linear association between the variables, say X and Y. The value of r2 lies between 0 and 1 and observes the following relationship with ‘r’.

  • With the decrease in the value of ‘r’ from its maximum value of 1, the ‘r2’ also decreases much more rapidly.
  • The value of ‘r’ will always be greater than ‘r2’ unless the r2=0 or 1.

The coefficient of determination also explains that how well the regression line fits the statistical data. The closer the regression line to the points plotted on a scatter diagram, the more likely it explains all the variation and the farther the line from the points the lesser is the ability to explain the variance.

Management Notes

Properties of Correlation co-efficient

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The following are the main properties of correlation.

  1. Coefficient of Correlation lies between -1 and +1:

The coefficient of correlation cannot take value less than -1 or more than one +1. Symbolically,

-1<=r<= + 1 or | r | <1.

  1. Coefficients of Correlation are independent of Change of Origin:

This property reveals that if we subtract any constant from all the values of X and Y, it will not affect the coefficient of correlation.

  1. Coefficients of Correlation possess the property of symmetry:

The degree of relationship between two variables is symmetric as shown below:

  1. Coefficient of Correlation is independent of Change of Scale:

This property reveals that if we divide or multiply all the values of X and Y, it will not affect the coefficient of correlation.

  1. Co-efficient of correlation measures only linear correlation between X and Y.
  2. If two variables X and Y are independent, coefficient of correlation between them will be zero.

Karl Pearson’s Coefficient of Correlation is widely used mathematical method wherein the numerical expression is used to calculate the degree and direction of the relationship between linear related variables.

Pearson’s method, popularly known as a Pearsonian Coefficient of Correlation, is the most extensively used quantitative methods in practice. The coefficient of correlation is denoted by “r”.

If the relationship between two variables X and Y is to be ascertained, then the following formula is used:

Properties of Coefficient of Correlation

  • The value of the coefficient of correlation (r) always lies between±1. Such as:
    r=+1, perfect positive correlation
    r=-1, perfect negative correlation
    r=0, no correlation
  • The coefficient of correlation is independent of the origin and scale.By origin, it means subtracting any non-zero constant from the given value of X and Y the vale of “r” remains unchanged. By scale it means, there is no effect on the value of “r” if the value of X and Y is divided or multiplied by any constant.
  • The coefficient of correlation is a geometric mean of two regression coefficient.Symbolically it is represented as:
  • The coefficient of correlation is “zero”when the variables X and Y are independent. But, however, the converse is not true.

Assumptions of Karl Pearson’s Coefficient of Correlation

  1. The relationship between the variables is “Linear”,which means when the two variables are plotted, a straight line is formed by the points plotted.
  2. There are a large number of independent causes that affect the variables under study so as to form a Normal Distribution. Such as, variables like price, demand, supply, etc. are affected by such factors that the normal distribution is formed.
  3. The variables are independent of each other.

Note: The coefficient of correlation measures not only the magnitude of correlation but also tells the direction. Such as, r = -0.67, which shows correlation is negative because the sign is “-“and the magnitude is 0.67.

Management Notes

Scatter Diagram

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Scatter Diagram Method is the simplest method to study the correlation between two variables wherein the values for each pair of a variable is plotted on a graph in the form of dots thereby obtaining as many points as the number of observations. Then by looking at the scatter of several points, the degree of correlation is ascertained.

The degree to which the variables are related to each other depends on the manner in which the points are scattered over the chart. The more the points plotted are scattered over the chart, the lesser is the degree of correlation between the variables. The more the points plotted are closer to the line, the higher is the degree of correlation. The degree of correlation is denoted by “r”.

The following types of scatter diagrams tell about the degree of correlation between variable X and variable Y.

  1. Perfect Positive Correlation (r = +1):

The correlation is said to be perfectly positive when all the points lie on the straight line rising from the lower left-hand corner to the upper right-hand corner.

2. Perfect Negative Correlation (r = -1):

When all the points lie on a straight line falling from the upper left-hand corner to the lower right-hand corner, the variables are said to be negatively correlated.

3. High Degree of +Ve Correlation (r = + High):

The degree of correlation is high when the points plotted fall under the narrow band and is said to be positive when these show the rising tendency from the lower left-hand corner to the upper right-hand corner.

4. High Degree of –Ve Correlation (r = – High):

The degree of negative correlation is high when the point plotted fall in the narrow band and show the declining tendency from the upper left-hand corner to the lower right-hand corner.

5. Low degree of +Ve Correlation (r = + Low):

The correlation between the variables is said to be low but positive when the points are highly scattered over the graph and show a rising tendency from the lower left-hand corner to the upper right-hand corner.

6. Low Degree of –Ve Correlation (r = + Low):

The degree of correlation is low and negative when the points are scattered over the graph and the show the falling tendency from the upper left-hand corner to the lower right-hand corner.

7. No Correlation (r = 0):

The variable is said to be unrelated when the points are haphazardly scattered over the graph and do not show any specific pattern. Here the correlation is absent and hence r = 0.

Thus, the scatter diagram method is the simplest device to study the degree of relationship between the variables by plotting the dots for each pair of variable values given. The chart on which the dots are plotted is also called as a Dotogram.

Management Notes

Methods of Studying Correlation

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The Correlation is a statistical tool used to measure the relationship between two or more variables, i.e. the degree to which the variables are associated with each other, such that the change in one is accompanied by the change in another.

The correlation is said to be linear when the change in the amount of one variable tends to bear a constant ratio to the amount of change in another variable. Whereas, the non-linear or curvilinear correlation is when the ratio of the amount of change in one variable to the amount of change in another variable is not constant.

These figures clearly show the difference between the linear and non-linear correlation. To determine the linearity and non-linearity among the variables and the extent to which these are correlated, following are the important methods used to ascertain these:

  1. Scatter Diagram Method
  2. Karl Pearson’s Coefficient of Correlation
  3. Spearman’s Rank Correlation Coefficient; and
  4. Methods of Least Squares

Among these, the first method, i.e. scatter diagram method is based on the study of graphs while the rest is mathematical methods that use formulae to calculate the degree of correlation between the variables.  The researcher may apply either of these methods on the basis of the nature of variables being considered in ascertaining the association between them.

Management Notes

Positive and Negative Correlation

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Correlation can be defined as a statistical tool that defines the relationship between two variables. For, eg: correlation may be used to define the relationship between the price of a good and its quantity demanded. It explains how two variables are related but do not explain any cause-effect relation. It only gives an understanding as to the direction and intensity of relation between two variables. Correlation can be of two types:

A) Positive Correlation

A correlation in the same direction is called a positive correlation. If one variable increases the other also increases and when one variable decreases the other also decreases. For example, the length of an iron bar will increase as the temperature increases.

Two variables are positively correlated when they move together in the same direction. In economics, quantity supplied increases as the price increases. This is because sellers find it profitable to sell when the prices are high, so they will sell more. Thus, we can call price and quantity supplied to be positively correlated. This is also called the law of supply.

B) Negative Correlation

Correlation in the opposite direction is called a negative correlation. Here if one variable increases the other decreases and vice versa. For example, the volume of gas will decrease as the pressure increases, or the demand for a particular commodity increases as the price of such commodity decreases.

Two variables are negatively correlated if they move in opposite directions. For instance, as the price of increases, the quantity demanded declines as the good becomes more expensive relative to when the price had not increased. Thus, we can say that price and quantity demanded are negatively correlated. Note that this is the famous law of demand.

C) No Correlation or Zero Correlation

If there is no relationship between the two variables such that the value of one variable changes and the other variable remains constant, it is called no or zero correlation.

Simple, Partial and Multiple Correlation: Whether the correlation is simple, partial or multiple depends on the number of variables studied. The correlation is said to be simple when only two variables are studied. The correlation is either multiple or partial when three or more variables are studied. The correlation is said to be Multiple when three variables are studied simultaneously. Such as, if we want to study the relationship between the yield of wheat per acre and the amount of fertilizers and rainfall used, then it is a problem of multiple correlations.

Whereas, in the case of a partial correlation we study more than two variables, but consider only two among them that would be influencing each other such that the effect of the other influencing variable is kept constant. Such as, in the above example, if we study the relationship between the yield and fertilizers used during the periods when certain average temperature existed, then it is a problem of partial correlation.

Management Notes

Meaning of Correlation, Importance

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Correlation, in the finance and investment industries, is a statistic that measures the degree to which two securities move in relation to each other. Correlations are used in advanced portfolio management, computed as the correlation coefficient, which has a value that must fall between -1.0 and +1.0

A perfect positive correlation means that the correlation coefficient is exactly 1. This implies that as one security moves, either up or down, the other security moves in lockstep, in the same direction. A perfect negative correlation means that two assets move in opposite directions, while a zero correlation implies no relationship at all.

For example, large-cap mutual funds generally have a high positive correlation to the Standard and Poor’s (S&P) 500 Index – very close to 1. Small-cap stocks have a positive correlation to that same index, but it is not as high – generally around 0.8.

However, put option prices and their underlying stock prices will tend to have a negative correlation. As the stock price increases, the put option prices go down. This is a direct and high-magnitude negative correlation.

  • Correlation is a statistic that measures the degree to which two variables move in relation to each other.
  • In finance, the correlation can measure the movement of a stock with that of a benchmark index, such as the Beta.
  • Correlation measures association, but does not tell you if x causes y or vice versa, or if the association is caused by some third (perhaps unseen) factor.

Importance of correlation Analysis

Correlation is very important in the field of Psychology and Education as a measure of relationship between test scores and other measures of performance. With the help of correlation, it is possible to have a correct idea of the working capacity of a person. With the help of it, it is also possible to have a knowledge of the various qualities of an individual.

After finding the correlation between the two qualities or different qualities of an individual, it is also possible to provide his vocational guidance. In order to provide educational guidance to a student in selection of his subjects of study, correlation is also helpful and necessary.

Correlation Statistics and Investing

The correlation between two variables is particularly helpful when investing in the financial markets. For example, a correlation can be helpful in determining how well a mutual fund performs relative to its benchmark index, or another fund or asset class. By adding a low or negatively correlated mutual fund to an existing portfolio, the investor gains diversification benefits.

In other words, investors can use negatively-correlated assets or securities to hedge their portfolio and reduce market risk due to volatility or wild price fluctuations. Many investors hedge the price risk of a portfolio, which effectively reduces any capital gains or losses because they want the dividend income or yield from the stock or security.

Correlation statistics also allows investors to determine when the correlation between two variables changes. For example, bank stocks typically have a highly-positive correlation to interest rates since loan rates are often calculated based on market interest rates. If the stock price of a bank is falling while interest rates are rising, investors can glean that something’s askew. If the stock prices of similar banks in the sector are also rising, investors can conclude that the declining bank stock is not due to interest rates. Instead, the poorly-performing bank is likely dealing with an internal, fundamental issue.

Management Notes

Co-efficient of Variation

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The coefficient of variation (CV) is a statistical measure of the dispersion of data points in a data series around the mean. The coefficient of variation represents the ratio of the standard deviation to the mean, and it is a useful statistic for comparing the degree of variation from one data series to another, even if the means are drastically different from one another.

The Formula for Coefficient of Variation is

Where: σ is the standard deviation and μ is the mean.

The coefficient of variation shows the extent of variability of data in sample in relation to the mean of the population. In finance, the coefficient of variation allows investors to determine how much volatility, or risk, is assumed in comparison to the amount of return expected from investments. The lower the ratio of standard deviation to mean return, the better risk-return trade-off. Note that if the expected return in the denominator is negative or zero, the coefficient of variation could be misleading.

The coefficient of variation is helpful when using the risk/reward ratio to select investments. For example, an investor who is risk-averse may want to consider assets with a historically low degree of volatility and a high degree of return, in relation to the overall market or its industry. Conversely, risk-seeking investors may look to invest in assets with a historically high degree of volatility.

While most often used to analyze dispersion around the mean, quartile, quintile, or decile CVs can also be used to understand variation around the median or 10th percentile, for example.

  • The coefficient of variation (CV) is a statistical measure of the dispersion of data points in a data series around the mean.
  • In finance, the coefficient of variation allows investors to determine how much volatility, or risk, is assumed in comparison to the amount of return expected from investments.
  • The lower the ratio of standard deviation to mean return, the better risk-return trade-off.
Management Notes

Mean Deviation and Standard Deviation

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Mean Deviation

Mean deviation is a measure of dispersion that indicates the average of the absolute differences between each data point and the mean (or median) of the dataset. It provides an overall sense of how much the values deviate from the central value. To calculate mean deviation, the absolute differences between each data point and the central measure are summed and then divided by the number of observations. Unlike variance, mean deviation is expressed in the same units as the data and is less sensitive to extreme outliers.

The basic formula for finding out mean deviation is :

Mean Deviation = Sum of absolute values of deviations from ‘a’ ÷ The number of observations

Standard Deviation

Standard deviation is a widely used measure of dispersion that indicates the average amount by which each data point deviates from the mean. It is calculated by first finding the variance, which is the average of squared deviations, and then taking the square root of the variance. Standard deviation provides a more interpretable measure of spread, as it is in the same units as the original data. A higher standard deviation indicates greater variability, while a lower value indicates data points are closer to the mean, indicating less spread or consistency.

Usually represented by s or σ. It uses the arithmetic mean of the distribution as the reference point and normalizes the deviation of all the data values from this mean.

Therefore, we define the formula for the standard deviation of the distribution of a variable X with n data points as:

Management Notes

Quartile Deviation

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The Quartile Deviation is a simple way to estimate the spread of a distribution about a measure of its central tendency (usually the mean). So, it gives you an idea about the range within which the central 50% of your sample data lies. Consequently, based on the quartile deviation, the Coefficient of Quartile Deviation can be defined, which makes it easy to compare the spread of two or more different distributions. Since both of these topics are based on the concept of quartiles, we’ll first understand how to calculate the quartiles of a dataset before working with the direct formulae.

Quartiles

A median divides a given dataset (which is already sorted) into two equal halves similarly, the quartiles are used to divide a given dataset into four equal halves. Therefore, logically there should be three quartiles for a given distribution, but if you think about it, the second quartile is equal to the median itself! We’ll deal with the other two quartiles in this section.

  • The first quartileor the lower quartile or the 25th percentile, also denoted by Q1, corresponds to the value that lies halfway between the median and the lowest value in the distribution (when it is already sorted in the ascending order). Hence, it marks the region which encloses 25% of the initial data.
  • Similarly, the third quartileor the upper quartile or 75th percentile, also denoted by Q3, corresponds to the value that lies halfway between the median and the highest value in the distribution (when it is already sorted in the ascending order). It, therefore, marks the region which encloses the 75% of the initial data or 25% of the end data.

For a better understanding, look at the representation below for a Gaussian Distribution:

The Quartile Deviation

Formally, the Quartile Deviation is equal to the half of the Inter-Quartile Range and thus we can write it as:

Qd=(Q3–Q1)/2

Therefore, we also call it the Semi Inter-Quartile Range.

  • The Quartile Deviation doesn’t take into account the extreme points of the distribution. Thus, the dispersion or the spread of only the central 50% data is considered.
  • If the scale of the data is changed, the Qd also changes in the same ratio.
  • It is the best measure of dispersion for open-ended systems (which have open-ended extreme ranges).
  • Also, it is less affected by sampling fluctuations in the dataset as compared to the range (another measure of dispersion).
  • Since it is solely dependent on the central values in the distribution, if in any experiment, these values are abnormal or inaccurate, the result would be affected drastically.

The Coefficient of Quartile Deviation

Based on the quartiles, a relative measure of dispersion, known as the Coefficient of Quartile Deviation, can be defined for any distribution. It is formally defined as:

Coefficient of Quartile Deviation = {(Q3–Q1)/(Q3+Q1)}×100

Since it involves a ratio of two quantities of the same dimensions, it is unit-less. Thus, it can act as a suitable parameter for comparing two or more different datasets which may or may not involve quantities with the same dimensions.

So, now let’s go through the solved examples below to get a better idea of how to apply these concepts to various distributions.

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