Question

A data set has nine values. The mean of the set is 5. When a tenth value is added, the mean becomes 6. What is the tenth value?

Answer 1

The tenth value is 15

Solution:

Given that, data set has 9 values

The mean of the set is 5

Number of values = 9 and mean = 5

The mean is given by formula:

`mean = \frac{\text{Sum of terms}}{\text{Number of terms}}`

`5 = \frac{\text{Sum of 9 terms}}{9}\\\\sum\ of\ 9\ terms = 5 * 9 = 45`

When a tenth value is added, the mean becomes 6

Let the tenth value be "x"

New mean is given as:

`6 = \frac{\text{sum of 9 terms} + x}{10}\\\\sum\ of\ 9\ terms + x = 60`

The tenth value is given as:

sum of 9 terms + x = 60

45 + x = 60

x = 60 - 45

x = 15

Thus the tenth value is 15