Question

Calculate mean deviation from the median for the following distribution: `x_i :` 10 15 20 25 30 35 40 45 `f_i :` 7 3 8 5 6 8 4 9

Answer 1

First we have to construct a table for the given data. Please refer to video for creating complete table.
Here, `N = sum f_i = 50`
`:. N/2 = 50/2 = 25`
So, median class will be `x_i = 30` as it has freuency just greater than `25.`
`:. Median = 30`
Now, we will find the deviation from the median for each class.
`:. |d_i| =20,15,10,5,0,5,10,15`
`:. f_i d_i = 140,45,80,25,0,40,40,135`
`:. sum f_i d_i = 505`
`:.` Mean deviation `= ( sum f_i d_i )/N = 505/50 = 101/10 = 10.1.`