Question

The median of a set of ascending order observation 11, 12, 14, 15, x + 1, x + 3, 20, 23, 25, 27 is 17. Then find the value of x.

A. 16

B. 15

C. 18

D. 17

1. C
2. D
3. A
4. B

Answer 1

Correct Answer - Option 4 : B

Given:

The median of the set is 17.

Formula Used:

When number of observation (n) is even,

\(Median = \frac{{Value\;of\;\left( {\frac{n}{2}} \right)th\;observation + Value\;of\;\left( {\frac{n}{2} + 1} \right)th\;observation}}{2}\)

Calculation:

Here, n = 10,

n/2 = 10/2 = 5

and (n/2) + 1 = (10/2) + 1 = 5 + 1 = 6

Value of (n/2)th observation = Value of 5th observation = (x + 1)

and Value of [(n/2) + 1]th observation = Value of 6th observation = (x + 3)

Then, Median = 17

⇒ [(x + 1) + (x + 3)]/2 = 17

⇒ 2x + 4 = 34

⇒ 2x = 30

⇒ x = 15

∴ 15 is the value of x.