GNDU B.Com (Bachelor of Commerce)

Chapter 2: Measures of Central Tendency: Mean, Median and Mode

Summary

A measure of central tendency is a single value that represents an entire set of data by indicating its centre or typical value, making large masses of figures easy to grasp and compare. The most common average is the arithmetic mean, found by dividing the sum of the observations by their number; for ungrouped data \(\bar{x}=\dfrac{\sum x}{n}\), and for grouped data \(\bar{x}=\dfrac{\sum fx}{\sum f}\). When items differ in importance, a weighted mean is used, where each value is multiplied by its weight: \(\bar{x}_w=\dfrac{\sum wx}{\sum w}\). The arithmetic mean is rigidly defined and based on all observations but is unduly affected by extreme values. The median is the middle value when the data are arranged in order; it divides the series into two equal halves and is not affected by extreme values, making it useful for open-ended or skewed data. The mode is the value that occurs most frequently and represents the most typical item; it is useful in business for finding the most popular size or item. An empirical relationship for a moderately skewed distribution links the three: \(Mode = 3\,Median - 2\,Mean\). A good average should be rigidly defined, based on all observations, easy to understand, capable of further algebraic treatment and not unduly affected by extreme values; the choice among mean, median and mode depends on the nature of the data and the purpose of the study.

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