Class 11

Math

JEE Main Questions

Statistics

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

Here, $N=∑f_{i}=50$

$∴2N =250 =25$

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.

$∴∣d_{i}∣=20,15,10,5,0,5,10,15$

$∴f_{i}d_{i}=140,45,80,25,0,40,40,135$

$∴∑f_{i}d_{i}=505$

$∴$ Mean deviation $=N∑f_{i}d_{i} =50505 =10101 =10.1.$