Let x be the 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 the data is y. What is the sum of the values of x any y?

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This question was previously asked in

CTET July 2019 Paper 2 Maths & Science (L - I/II: Hindi/English/Sanskrit)

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Answer 1

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

First of all, we arrange the data in ascending order, then

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

Total number (n) = 15

As we know,

Median = [(n + 1)/2]^th = [(15 + 1)/2]^th = [16/2]^th = 8^th number

8^th number is 14

So, x = 14

If 8 is replaced by 18 then,

13, 18, 15, 14, 17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14

Again, we arrange the data in ascending order, then

9, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 18

Total number (n) = 15

Median = [(n + 1)/2]^th = [(15 + 1)/2]^th = [16/2]^th = 8^th number

8^th number is 15

So, y = 14

x + y

⇒ 14 + 15

⇒ 29