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[ zs N, easures of Dispersion, | IA (, , , , [Lp ters stay |, , e Meaning and Definition of Dispersion, e Range of data., , e Variance and Standard Deviation, , e Coefficient of Variation, , (fix rare, , e Concept of Constant and Variable, e Concept of an Average, , e Computation of Mean for Ungrouped and, Grouped Data, , “An average does not tell the full story., It is hardly fully representative of a mass unless, we know the manner in which the individual items, scatter around it. A further description of the series is necessary if we are to gauge how representative the average is.”, , - George Simpson and Fritz Kafka, , Let’s Observe, , In the earlier classes we have learnt about, the measures of central tendency mean, median, and mode. Such an average tells us only about, the central part of the data. But it does not give, any information about the spread of the data. For, example, consider the runs scored by 3 batsmen, in a series of 5 One Day International matches., , 90, 17, 104, 33, 6, , , , All the above series have the same size, (n=5) and the same mean (50), but they are, different in composition. Thus, to decide who, is more dependable, the measure of mean is not, sufficient. The spread of data or variation is a, factor which needs our attention. To understand, more about this we need some other measure., One such measure is Dispersion., , In the above example, observations from, series X and series Z are more scattered as, compared to those in series Y. So Y is more, consistent. The extent of scatter in observations, which deviate from mean is called dispersion., , Activ:, , , , Given two different series, A:0.5, 1, 1.5, 3, 4,8, , B: 2, 2.2, 2.6, 3.4, 3.8,, Find arithmetic means of the two series., Plot the two series on the number line., , Observe the scatter of the data in each series, and decide which series is more scattered., , (Re) Lets Learn 178, , According to Spiegel:, , “The degree to which numerical data tend, to spread about an average value is called the, variation or dispersion of the data.”, , 8.1 Measures of Dispersion :, , Following measures, commonly used —, , of dispersion are the, , (i) Range, (ii) Variance, (iii) Standard deviation