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

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