Question

A study of the ages of 100 persons grouped into intervals 20—22, 22—24, 24— 26……, revealed the mean age and standard deviation to be 32.02 and 13.18, respectively. While checking, it was discovered that the observation 57 was misread as 27. Calculate the correct mean age and standard deviation.

Answer 1

To correct the mean age, we add 30 to the initial total sum of ages and then divide by the number of persons (100) to find the new mean, which is 32.32 years.

Step-by-step explanation:

The correction of the mean age requires adjusting the previously calculated total sum of ages by removing the incorrect age and adding the correct age. Previously, the mean was calculated with a sum that included 27 instead of 57. To find the correct mean, we have to add 30 (57 - 27) to the total sum of ages. Since the initial mean was 32.02 for 100 people, the total sum with the incorrect age was 32.02 * 100 = 3202. Adding 30 to this sum gives us 3232, and the new mean age is 3232 divided by 100, which is 32.32 years.