Question

Question 10 Find the mean deviation about the mean for the data




Height in cms Number of boys

95-105 9

105-115 13

115-125 26

125-135 30

135-145 12

145-155 10



Class X1 - Maths -Statistics Page 361

Answer 1

we have to find out Mean deviation about Mean so, firstly we have to find out Mean by using formula

$Mean(\overline{x})=A+\frac{\sum{f_id_i}}{\sum{f_i}}\times \: h$
and then, use formula
$=\frac{\sum{f_i|x_i-\overline{x}|}}{\sum{f_i}}$

see attachment ,
here

$\sum{f_i}=100\\\\\sum{f_id_i}=-47$
so,
$Mean(\overline{x})=A+\frac{\sum{f_id_i}}{\sum{f_i}}\times \: h \: \\ \\ \: \: = 130 + \frac{ - 47}{100} \times 10 \\ \\ = 130 + ( - 47) \times \frac{1}{10} \\ \\ = 130 - 4.7 \\ \\ = 125.3$
now,
Mean deviation about Mean
$=\frac{\sum{f_i|x_i-\overline{x}|}}{\sum{f_i}}\\\\=\frac{1128.8}{100}\\\\=11.288$