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

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

The given observations are 24, 25, 26, x + 2, x + 3, 30, 31, 34.
Median = 27.5
Here, n = 8
Median =

\frac{(\frac{n}{2}) th term + (\frac{n}{2} + 1) th term}{2}

Median =

\frac{(\frac{8}{2}) th term + (\frac{8}{2} + 1) th term}{2}

Median =

\frac{4 th term + 5 th term}{2}

Here the 4th term is x + 2 and 5th term is x + 3.
That is

Median = x + 2 + x + 3 2

27.5 = 2 x + 5 2 27.5 × 2 = 2 x + 5 55 = 2 x + 5 2 x = 55 − 5 = 50 x = 502 = 25

Therefore, the value of x is 25.
Hence, the correct option is 2.

JEE