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,  \(\sum_{I=1}^{6}f_i=100\), \(\sum_{I=1}^{6}f_ix_i=12530\)

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

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