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Let x be the median of the data below: 13, 14, 15, 11, 9, 9, 8, 7, 16, 15, 5, 6, 16, 25, 16, 23, 28, 17 If 6 is replaced by 19 and 13 by 31 in the above data, then the median of the resulting data is y. What is the value of (3x – y)?

Let x be the median of the data below: 13, 14, 15, 11, 9, 9, 8, 7, 16, 15, 5, 6, 16, 25, 16, 23, 28, 17 If 6 is replaced by 19 and 13 by 31 in the above data, then the median of the resulting data is y. What is the value of (3x – y)? Correct Answer 28

Given:

Data is

13, 14, 15, 11, 9, 9, 8, 7, 16, 15, 5, 6, 16, 25, 16, 23, 28, 17

Formula Used:     

If n is odd, then Median = th 

If n is even, then Median = / 2

Calculation:

Let us arrange the data in ascending order, then

5, 6, 7, 8, 9, 9, 11, 13, 14, 15, 15, 16, 16, 16, 17, 23, 25, 28 

Total number(n) = 18

So, Median = / 2

⇒ Median =  / 2

⇒ Median = (9th term + 10th term) / 2 

⇒ (14 + 15) / 2 

⇒ 29/2 = 14.5

So, x = 14.5

If 6 is replaced by 19 and 13 by 31 in the given data, then

13, 14, 15, 11, 9, 9, 8, 7, 16, 15, 5, 19, 16, 25, 16, 23, 28, 17

Again, we will arrange the data in ascending order, then

5, 7, 8, 9, 9, 11, 14, 15, 15, 16, 16, 16, 17, 19, 23, 25, 28, 31

⇒ Median = (9th term + 10th term) / 2

⇒ (15 + 16) / 2 = 31/2

⇒ 31/2 = 15.5

⇒ y = 15.5

So, the value of (3x – y) =

⇒ 43.5 - 15.5 = 28

∴ The value of (3x – y) is 28.

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