Find the mean deviation from the mean for the following data: Size: 1 3 5 7 9 11 13 15 Frequency: 3 3 4 14 7 4 3 4

Solution: First we have to construct a table for the given data. Please refer to video for creating complete table.
From the table,
$\sum f_i=42$
$\sum f_i{x}_i==336$
Now, Mean $=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{36}{42}=8$
Now, we will find the deviation from the mean for each $x_i.$
$\therefore \left|d_i\right|=7,5,3,1,1,3,5,7$
$\therefore f_i{d}_i=21,15,12,14,7,12,15,28$
$\therefore$ Mean deviation $=\frac{\sum f_i{d}_i}{\sum f_i}=\frac{124}{42}=\frac{62}{21}=2.95$
So, mean deviation from the mean for the given data is $2.95.$