The mean of 100 observations is 50. If one of the observation which was 50 is replaced by 150, the resulting mean will be

1. 50.5

2. 51

3. 51.5

4. 52

By formula,

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

Given,

Mean of 100 observations is 50.

$\therefore 50 = \dfrac{\text{Sum of observations}}{100} \\[1em] \text{Sum of observations} = 50 \times 100 = 5000.$

Since, observation which was 50 is replaced by 150.

So,

Sum of observation = 5000 - 50 + 150 = 5100.

New mean = $\dfrac{5100}{100}$ = 51.

Hence, Option 2 is the correct option.