Question

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 and y

Answer 1

The sum of x and y is 19

Step-by-step explanation:

The data:

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

Arrange data in acceding order.

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

Number of data = 15

This is odd number.

Median $=\dfrac{n+1}{2}$

Median $=\dfrac{15+1}{2}$

Median = 8th term

Median = 14

x = 14

8 is replaced by 18

New data: 9, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 18

Number of data = 15

This is odd number.

Median $=\dfrac{n+1}{2}$

Median $=\dfrac{15+1}{2}$

Median = 8th term

Median = 15

y = 15

The sum of x and y

x + y = 14 + 15

x + y = 19

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