The mean of 36 numbers was found to be 42. Later, it was discovered that one of the numbers, 47, was mistakenly read as 41. Find the correct mean of the given numbers (rounded to two decimal places).

Correct option is B

Given:

Mean of 36 numbers = 42
Incorrect value = 41
Correct value = 47

Formula Used:

​$$Mean = \frac{\text{Sum of all values}}{\text{Total number of values}}$$

​
$$Corrected Mean = \frac{\text{Incorrect Sum} - \text{Incorrect Value} + \text{Correct Value}}{\text{Total number of values}}$$​

Solution:

1. Calculate the incorrect total sum of the 36 numbers:

​$$- Total sum = Mean \times Total numbers$$​​

​$$- Total sum = 42 \times 36 = 1512$$​​

2. Calculate the corrected sum by adjusting the incorrect value:

- Corrected sum = 1512 - 41 + 47

- Corrected sum = 1518

3. Calculate the corrected mean:

​$$Corrected Mean = \frac{1518}{36} \approx 42.17$$​

Answer: The correct mean of the given numbers is 42.17.