Question

The following numbers are pre-arranged in ascending order. Their median is 12. Find the value of x and their mean.

6, 9, x, x + 2, x + 3, 19

Answer 1

There are 6 numbers (even count), so the median is the average of the 3rd and 4th values.

Median = `(x + (x + 2))/2`

= `(2x +2)/2`

= x + 1

The median is 12, so:

x + 1 = 12

x = 12 − 1

x = 11

Now substitute x = 11 into the numbers

6, 9, 11, 13, 14, 19

Sum of observations = 6 + 9 + 11 + 13 + 14 + 19 = 72

Total number of observations = 6

Mean = `"Sum of observations"/"Total number of observations"`

= `72/6`

=12