If the median of the data: 24, 25, 26, x + 2, x + 3, 30, 31, 34 is 27.5, then x =
Question:

If the median of the data: 24, 25, 26, x + 2, x + 3, 30, 31, 34 is 27.5, then x =

(a) 27
(b) 25
(c) 28
(d) 30

Solution:

The given observations are 24, 25, 26, x + 2, x + 3, 30, 31, 34.

Median = 27.5

Here, n = 8

Median $=\frac{\left(\frac{n}{2}\right)^{\text {th }} \text { term }+\left(\frac{n}{2}+1\right)^{\text {th }} \text { term }}{2}$

$27.5=\frac{4 \text { th term }+5 \text { th term }}{2}$

$27.5=\frac{(x+2)+(x+3)}{2}$

$27.5=\frac{2 x+5}{2}$

$2 x+5=55$

 

$2 x=50$

$x=25$

Hence, the correct option is (b).

 

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