Question

The following numbers are arranged in ascending order: 2, 3, x, y, 7, 9, 12, 14. If their median is 6 and mean is 7, find x and y.

Answer 1

The median is given as 6.

Since there are 8 numbers, the median is the average of the 4th and 5th numbers.

`(y + 7)/2` = 6

y + 7 = 6 × 2

y + 7 = 12

y = 12 − 7

y = 5

Mean = 7

`"Sum of all numbers​"/8` = 7

Sum of all numbers = 7 × 8

= 56

2 + 3 + 7 + 9 + 12 + 14 = 47

Add x + y

47 + x + y = 56

x + y = 56 − 47

x + y = 9

since, y = 5

x + 5 = 9

x = 9 − 5

x = 4

∴ x = 4 and y = 5