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 :

1. 30

2. 15

3. 20

4. 18

By formula,

Mean = $\dfrac{\text{Sum of observations}}{\text{No. of observations}}$

Given, the mean value of 15 numbers is 20.

$\therefore 20 = \dfrac{\text{Sum of observations}}{15} \\[1em] \Rightarrow \text{Sum of observations} = 20 \times 15 = 300.$

Given,

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

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

$\Rightarrow \text{Correct mean} = \dfrac{\text{Correct sum of observations}}{\text{No. of observations}} \\[1em] \Rightarrow \text{Correct mean} = \dfrac{270}{15} = 18.$

Hence, Option 4 is the correct option.