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Let x be median of the data 13,8,15,14,17,9,14,16,13,17,14,15,16,15,14.13, 8, 15, 14, 17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14. If 88 is replaced by 1818, then the median of data is yy, then the sum of xx and yy is equal to:

Solution

✅ Correct Option: 4

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

Current data in ascending order →8,9,13,13,14,14,14,14,15,15,15,16,16,17,17\rightarrow 8,9,13,13,14,14,14,14,15,15,15,16,16,17,17

Median (n = odd) →(n+12)th\rightarrow (\dfrac{n+1}{2})^{th} term =15+12=8th= \dfrac{15+1}{2} = 8^{th} term

Median is 1414.

Now, if 88 is replaced by 1818, we can clearly see that 1818 will become the last term and the new 8th8^{th} term will be 1515

So, new median is 1515.

Sum of both the medians →14+15=29\rightarrow 14+15=29

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