JIPMAT 2025 (QA) - Let x be median of the data 13, 8, 15, 14, 17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14. If 8 is replaced by 18, then the median of data is y, then the sum of x and y is equal to: | PYQs + Solutions

JIPMAT 2025

Arithmetic

Averages

Medium

Let x be median of the data $13, 8, 15, 14, 17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14.$ If $8$ is replaced by $18$ , then the median of data is $y$ , then the sum of $x$ and $y$ is equal to:

✅ Correct Option: 4

To find the median, firstly we need to arrange the numbers in ascending order -

Current data in ascending order

\rightarrow 8,9,13,13,14,14,14,14,15,15,15,16,16,17,17

Median (n = odd)

\rightarrow (\dfrac{n+1}{2})^{th}

term

= \dfrac{15+1}{2} = 8^{th}

term

Median is

14

Now, if

8

is replaced by

18

, we can clearly see that

18

will become the last term and the new

8^{th}

term will be

15

So, new median is

15

Sum of both the medians

\rightarrow 14+15=29