Question

Following 10 observations are arranged in ascending order as follows. 

2, 3 , 5 , 9, x + 1, x + 3, 14, 16, 19, 20. 

If the median of the data is 11, find the value of x.

Answer 1

Given data in ascending order :

2, 3, 5, 9, x + 1, x + 3, 14, 16, 19, 20. 

∴ Number if observations (n) = 10 (i.e., even) 

∴ Median is the average of middle two observations 

Here, the 5th and 6th numbers are in the middle position.

∴ 11 = (2x + 4)/2

∴ 22 = 2x + 4 

∴ 22 – 4 = 2x 

∴ 18 = 2x 

∴ x = 9