Question

Question 12 Calculate the mean deviation about median age for the age distribution of 100 persons given below:




Age Number

16-20 5

21-25 6

26-30 12

31-35 14

36-40 26

41-45 12

46-50 16

51-55 9

Class X1 - Maths -Statistics Page 361

Answer 1

first of all we have to the class interval are of uniform , Because interval is irregular.
and then use the formula,
$MEDIAN=l+\frac{\frac{N}{2}-C}{f}\times\:h$
see attachment, here
$N=\sum{f_i}=100\therefore\:\frac{N}{2}=50\\\\\therefore\:Median\:class\:will\:be,30.5-40.5\\\\\implies\:l=35.5,C=37,f=26,h=5\\\\M=l+\frac{\frac{N}{2}-C}{f}\times\:h\\\\M=35.5+\frac{50-37}{26}\times\:5\\\\=35.5+\frac{13}{26}\times\:5\\\\=35.5+2.5=38\\\\hence,M=38$
now,
Mean deviation about the median
$=\frac{\sum{f_i|x_i-M|}}{\sum{f_i}}\\\\=\frac{735}{100}=7.35$