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 11, the correct mean is:
1). 29.4
2). 29.5
3). 29.8
4). 29.9
We know that, sum of n numbers = mean of n numbers × n
Given that, the mean of 100 items was found to be 30.
The sum of 100 numbers = mean of 100 numbers × 100
⇒The sum of 100 numbers = 30 × 100 = 3000
Now, at the time of calculation, two items were wrongly taken as 32 and 12 instead of 23 and 11.
∴ The actual sum = 3000 – 32 + 23 -12 + 11 = 2990
The correct mean = the correct sum ÷ 100
⇒ The correct mean = 2990 ÷ 100 = 29.9