The mean of 100 items was found to be 30. If at the time of calculation two items were wrongly taken as 32 and 12 instead of 23 and 12. then the Correct Mean is.

Correct option is D

Given:

1. Number of items ( n ) = 100
2. Incorrect mean = 30
3. Incorrect data points = 32 and 12
4. Correct data points = 23 and 12

Formula Used:

1. Total sum of items (Sum} :
Sum = n $$\times$$​ Mean
2. Adjusted sum:
​$$\text{Adjusted Sum} = \text{Sum} - \text{Error}$$​
3. Correct Mean:
​$$\text{Mean} = \frac{\text{Adjusted Sum}}{n}$$​

Solution:

1. Calculate the incorrect total sum:

​$$\text{Sum} = n \times \text{Mean} = 100 \times 30 = 3000$$​

2. Adjust the total sum:

Replace 32 with 23 (12 remains unchanged):
Change in Sum = 23 - 32 = -9
Adjusted sum:
Adjusted Sum = 3000 - 9 = 2991

3. Calculate the correct mean:

Correct Mean = $$\frac{\text{Adjusted Sum}}{n} = \frac{2991}{100} = 29.91$$​

4. Round the mean:

The rounded mean is 29.9 .

Final Answer:

D. 29.9