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

Observations are arranged in ascending order as follows:

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

As, the number of observations = 10, which is an even number.

∴ The numbers in the five and six observations will come to the middle.

Median = 11

∴ Median = `((x + 1) + (x + 3))/2`

∴ 11 = `(2x + 4)/2`

∴ 11 × 2 = 2x + 4

∴ 22 = 2x + 4

∴ 22 − 4 = 2x

∴ 2x = 18

∴ x = `18/2`

∴ x = 9

So, the value of x is 9.