Introduction to statistics

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Question

Calculate the mean deviation about median for the following data:

Moderate

Solution

$The class interval containing \frac{N^{th}}{2} or 25^{th} item is 20 - 30 .$
$Therefore, 20 - 30 is the median class.$
$We know that$
$Median = l + \frac{\frac{N}{2} - C}{f} \times h$
$H e r e, l = 20, C = 13, f = 15, h = 10 and N = 50$
$Therefore, Median = 20 + \frac{25 - 13}{15} \times 10 = 20 + 8 = 28$
Thus, mean deviation about median is given by
$M.D. (M) = \frac{1}{N} \sum_{i = 1}^{6} f_{i} |x_{i} - M| = \frac{1}{50} \times 508 = 10.16$

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