The mean age of a group of 100 students was found to be 32.02 Years. Later it was discovered that age of 57 was mis read a5 27 . Find the correct mean.

To determine the correct mean age after discovering the misread age, follow these steps: 1. **Calculate the Initial Total Sum:** The initial mean age was calculated as 32.02 years for 100 students. \[ \text{Initial Total Sum} = \text{Mean} \times \text{Number of Students} = 32.02 \times 100 = 3,202 \text{ years} \] 2. **Identify the Misread Error:** - **Incorrect Reading:** One student's age was recorded as **27** years. - **Correct Age:** The actual age should have been **57** years. The misreading caused the total sum to be understated by: \[ 57 - 27 = 30 \text{ years} \] 3. **Adjust the Total Sum:** Add the difference to the initial total sum to get the correct total sum. \[ \text{Correct Total Sum} = 3,202 + 30 = 3,232 \text{ years} \] 4. **Calculate the Correct Mean:** \[ \text{Correct Mean} = \frac{\text{Correct Total Sum}}{\text{Number of Students}} = \frac{3,232}{100} = 32.32 \text{ years} \] **Final Answer:** The correct mean age is **32.32 years**.