Question

The following data have been arranged in ascending order 11,14,17,20,22,x,26,28,32,36. Find x if median is 23. If 32 is changed to 23 find new median.

Answer 1

Given data,

11 , 14, 17 , 20 ,22 , x, 26, 28 , 32, 36.

Number of observations ;- 10 (even)

Median of follwing data = $\frac{5th \ term \ + \ 6th \ term}{2} \\ \\ 23 = \frac{22 \ + \ x}{2} \\ \\ 46 = 22 +x \\ \\ x = 24$

x = 24

So observation are :-

11 , 14, 17 , 20 ,22 , 24 , 26, 28 , 32, 36.

New data:-( By interchanging 32 with 23}

11 , 14, 17 , 20 ,22 , 23, 24 , 26, 28 , 36.

Number of terms = 10 (even)

$\textbf{Median of new data} = \frac{5th \ term \ + \ 6th \ term}{2} \\ \\ = \frac{22 \ + \ 23}{2} \\ \\ = 45/2 \\ \\ = 22.5$