Question

The following numbers arranged in ascending order have their mean and median same. 4, 4, x − 2, x + 1, x + 3, 12, 13. Find the value of x and the median.

Answer 1

There are 7 numbers in the set. The median is the middle number, which is the 4th value in the sequence.

The median is x + 1

Sum = 4 + 4 + (x − 2) + (x + 1) + (x + 3) + 12 + 13

= (4 + 4 − 2 + 1 + 3 + 12 + 13) + (x + x + x)

= 35 + 3x

The number of values is 7.

Mean = `(35 + 3x)/7`

Since the mean and median are the same,

x + 1 = `(35 + 3x)/7`

7(x + 1) = 35 + 3x

7x + 7 = 35 + 3x

7x − 3x + 7 = 35

4x + 7 = 35

4x = 35 − 7

4x = 28

x = `28/4`

x = 7

Now,  median = x + 1

= 7 + 1

= 8

The value of x is 7 and the median is 8.