NCERT Book Class 11 Maths Statistics Questions

15.1 Overview
In earlier classes, you have studied measures of central tendency such as mean, mode, median of ungrouped and grouped data. In addition to these measures, we often need to calculate a second type of measure called a measure of dispersion which measures the variation in the observations about the middle value– mean or median etc.

This chapter is concerned with some important measures of dispersion such as mean deviation, variance, standard deviation etc., and finally analysis of frequency distributions.

15.1.1 Measures of dispersion
(a) RangeThe measure of dispersion which is easiest to understand and easiest to calculate is the range. Range is defined as:

 Range = Largest observation – Smallest observation

(b) Mean Deviation

(i) Mean deviation for ungrouped data: For n observation x1, x2, ..., xn, the mean deviation about their mean x is given by

(ii) Mean deviation for discrete frequency distribution Let the given data consist of discrete observations x1, x2, ... , xn occurring with frequencies f1, f2, ... , fn, respectively. In this case

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