Ten observations are written in ascending order

Ten observations 6, 14, 15, 17, x + 1, 2x - 13, 30, 32, 34 and 43 are written in ascending order. The median of the data is 24. What is x?

  1. 15
  2. 18
  3. 20
  4. 24

Solution

When the total number of observations, n is even, then median is 

[(n/2)th obs. + (n/2+1)th obs.] / 2

So, median = mean of the 5th and 6th observations.

So,

(x + 1 + 2x - 13) / 2 = 24 

3x - 12 = 48

x = 60/3 = 20

The correct option is C.