First slide

Introduction to statistics

Question

The mean deviation (approximately) from the mode for the data, is 20, 25, 30, 18, 15, 40

Moderate

A

6.71
B

4.52
C

7.61
D

5.33

Solution

We have,
Mean $= \frac{20 + 25 + 30 + 18 + 15 + 40}{6} = \frac{148}{6}$
Median $= \frac{20 + 25}{2} = \frac{45}{2}$
$∴$ Mode = 3 Median -2 Mean $= \frac{135}{2} - \frac{148}{3} = \frac{109}{6}$
Hence, mean deviation about mode is given by
$\begin{array}{l} \frac{|20 - \frac{109}{6}| + |25 - \frac{109}{6}| + |30 - \frac{109}{6}| + |18 - \frac{109}{6}| + |15 - \frac{109}{6}| + |40 - \frac{109}{6}|}{6} \\ M.D. = \frac{11 + 41 + 71 + 1 + 19 + 131}{36} = \frac{274}{36} = 7.61 \end{array}$

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