Average gives us an idea on the point of the concentration of the observations about the central part of the distribution.

**Measures of
dispersion**

Average gives us an idea on the
point of the concentration of the observations about the central part of the
distribution. If we know the average alone we cannot form a complete idea about
the distribution as will be clear from the following example.

Consider
the series (i) 7,8,9,10,11 (ii) 3,6,9,12,15 and (iii) 1,5,9,13,17. In all these
cases we see that n, the number of observations is 5 and the mean is 9. If we
are given that the mean of 5 observations is 9, we cannot form an idea as to
whether it is the average of first series or second series or third series or
of any other series of 5 observations whose sum is 45. Thus we see that the
measures of central tendency are inadequate to give us a complete idea of the
distribution. So they must be supported and supplemented by some other
measures. One such measure is Dispersion, which provides the nature of
spreadness of the data.

Literal meaning of dispersion is
“scatteredness” we study dispersion to have an idea about the homogeneity or
heterogeneity of the distribution. In the above case we say that series (i) is
more homogeneous (less dispersed) than the series (ii) or (iii) or we say that
series (iii) is more heterogeneous (more scattered) than the series (i) or
(ii).

Various measures of dispersion
can be classified into two broad categories.

(a) The
measures which express the spread of observations in terms of distance between
the values of selected observations. These are also termed as distance
measures.

Example: Range and interquartile
range (or) quartile deviation.

(b) The
measures which express the spread of observations in terms of the average of
deviations of observation from some central value,

Example:
Mean deviation and Standard deviation.

Tags : Descriptive statistics and probability , 11th Business Mathematics and Statistics(EMS) : Chapter 8 : Descriptive statistics and probability

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11th Business Mathematics and Statistics(EMS) : Chapter 8 : Descriptive statistics and probability : Measures of dispersion | Descriptive statistics and probability

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