The mean of 20 observations is 50. It was later found that two observations 13 and 24 were incorrectly recorded as 31 and 42. The correct mean is:  

Correct option is D

Given:

The mean of 20 observations is 50.

Two observations, 13 and 24, were incorrectly recorded as 31 and 42.

Solution:

We know that the mean of 20 observations is 50, so the total sum of the observations is:

Total sum = Mean × Number of observations = 50 × 20 = 1000

The incorrect values recorded were 31 and 42, but the correct values should have been 13 and 24.

Corrected sum = 1000 − 31 − 42 + 13 + 24 = 964

​$$\text{Corrected mean} = \frac{\text{Corrected sum}}{\text{Number of observations}}$$ 

$$\text{Corrected mean} = \frac{964}{20} = 48.2$$ 

Thus the Correct mean is 48.2.