Question

Question 11 Find the mean deviation about median for the following data:




Marks Number of girls

0-10 6

10-20 8

20-30 14

30-40 16

40-50 4

50-60 2

Class X1 - Maths -Statistics Page 361

Answer 1

we have to find the mean deviation about the median , so first of all we calculate Median of given data .it's a continuous data .
so, median can be calculated with help of
$MEDIAN=l+\frac{\frac{N}{2}-C}{f}\times\:h$
formula.

see attachment,
here, we get,
$\sum{f_i}=50\\\\\frac{N}{2}=\frac{50}{2}=25\\\therefore,C=14,f=14,l=20,and,h=10\\\\now,Median=l+\frac{\frac{N}{2}-C}{f}\times\:h\\\\=20+\frac{\frac{50}{2}-14}{14}\times\:10\\\\=20+\frac{11\times\:10}{14}\\\\=20+7.86=27.86$
now,
$Mean \:deviation\: about\: the \:median=\frac{\sum{f_i|x_i-M|}}{\sum{f_i}}\\\\=\frac{517.16}{50}\\\\=10.34$