Question

The following numbers are arranged in ascending order. Find x and the mean if their median is 10.

4, 7, x + 1, x + 5, 15, 20

Answer 1

Numbers are arranged in ascending order: 4, 7, x + 1, x + 5, 15, 20

There are 6 numbers (an even number), the median is the average of the two middle terms, which are the 3rd and 4th terms.

The median is 10

Median = `("3rd term + 4th term")/2`

10 = `((x + 1) + (x + 5))/2`

10 = `(2x + 6)/2`

10 = x + 3

x = 10 − 3

x = 7

substitute the value of x

The numbers are: 4, 7, (7 + 1), (7 + 5), 15, 20

4, 7, 8, 12, 15, 20

number of observations = 6

Mean = `(4 + 7 + 8 + 12 + 15 + 20)/6`

Mean = `66/6`

=11

The value of x is 7 and the mean is 11.