Question

Question 4 Find the mean deviation about the median for the data

36, 72, 46, 42, 60, 45, 53, 46, 51, 49

Class X1 - Maths -Statistics Page 360

Answer 1

The given date is 36,72, 46, 60, 45, 53, 46, 51, 49.
now, we have to arrange it in ascending order,
e.g., 36, 42, 45, 46, 46, 49, 51,53, 60, 72.

here, number of observation ( N) = 10 ( an even number )
$Median(M)=\frac{\frac{Nth}{2} observation+(\frac{N}{2}+1)th\: observation}{2}\\\\=\frac{\frac{10}{2}th\: observation+(\frac{10}{2}+1)th\: observation}{2}\\\\=\frac{5th\: observation+6th\: observation}{2}$
now, see in arrangement of ascending order,
5th position = 46
6th position = 49
now,
M = ( 46 + 49)/2 = 47.5

now, mean deviation about Median
$=\frac{\sum{|x_i-M|}}{n}\\\\=\frac{70}{10}\\\\=7$