Question

The mean value of 15 numbers is 20. If one of these numbers is wrongly taken as 45 instead of 15, the correct mean is ______.

Options

• 30

• 15

• 20

• 18

Answer 1

The mean value of 15 numbers is 20. If one of these numbers is wrongly taken as 45 instead of 15, the correct mean is 18.

Explanation:

By formula,

\[\text{Mean} = \frac{\text{Sum of observations}}{\text{No. of observations}}\]

Given, the mean value of 15 numbers is 20.

\[\therefore 20 = \frac{\text{Sum of observations}}{15}\]

⇒ Sum of observations = 20 × 15 = 300.

Given,

One of these numbers is wrongly taken as 45 instead of 15.

Correct sum of observations = 300 − 45 + 15 = 270.

\[\Rightarrow \text{Correct mean} = \frac{\text{Correct sum of observations}}{\text{No. of observations}}\]

\[\Rightarrow \text{Correct mean} = \frac{270}{15} = 18.\]