Question

Find the mean and median of the following:

11, 14, 15, 14, 17, 19

If another number x is added to the given numbers, the new mean is 14. Find the value of x.

Answer 1

Sum of all observations​ = 11 + 14 + 15 + 14 + 17 + 19 = 90

Number of observations = 6

Mean = `"Sum of all observations"/"Number of observations"`

= `90/6`

= 15

Arranging the numbers in ascending order,

11, 14, 14, 15, 17, 19

n = 6 observations

`(n/2)`

= `6/2`

= 3rd

`(n/2 + 1)`

= `6/2 + 1`

= 4th

Median = `(14 + 15)/2`

= `29/2`

= 14.5

If another number x is added to the given numbers,

Now total numbers = 7

New Mean = 14

`(90 + x)/7` = 14

90 + x = 14 × 7

90 + x = 98

x = 98 − 90

x = 8