Question

The mean and median of the following are same. Find the value of x if the numbers are arranged in ascending order.

1, 3, 4, x, 10, 15, 21

Answer 1

Numbers arranged in ascending order,

1, 3, 4, x, 10, 15, 21

There are 7 numbers, which is odd, so the median is the middle value, i.e., the 4th number.

Median = x

Sum of observations = 1 + 3 + 4 + x + 10 + 15 + 21 = 54 + x

Total number of observations = 7

Mean = `(54 + x)/7`

The mean and median are same.

`(54 + x)/7` = x

54 + x = x × 7

54 + x = 7x

54 = 7x − x

54 = 6x

x = `54/6`

x = 9