Question

Find the mean deviation about the mean for the data

Height in cms	95-105	105-115	115-125	125-135	135-145	145-155
Number of boys	9	13	26	30	12	10

Answer 1

The following table is formed.

Height in cms| Number of boys $f_i$| Mid-point $x_i$| $f_ix_i$| $|x_i-\bar{x}$| $f_i|x_i-\bar{x}$|
---|---|---|---|---|---
95-105| 9| 100| 900| 25.3| 227.7
100-200| 13| 110| 1430| 15.3| 198.9
115-125| 26| 120| 3120| 5.3| 137.8
125-135| 30| 130| 3900| 4.7| 141
135-145| 12| 140| 1680| 14.7| 176.4
145-155| 10| 150| 1500| 24.7| 247

Here, $\sum_{I=1}^{6}f_i=100$, $\sum_{I=1}^{6}f_ix_i=12530$

∴ $\bar{x}\frac{1}{N}\frac{1}{N}\sum_{i=1}^{6}f_ix_i=\frac{1}{100}×12530=125.3$

$M.D.(\bar{x})=\frac{1}{N}\sum_{i=1}^{6}f_i|x_i-\bar{x}|=\frac{1}{100}×1128.8=11.28$