Question

The mean of 31 results is 60. If the mean of the first 16 results is 58 and that of the last 16 results is 62, then the 16th result is:

• A. 59
• B. 60
• C. 61
• D. 60.5

Hint:

To find a specific element in overlapping averages, sum up the total contributions and subtract the overcounted value.

Answer 1

The Correct Option is B

Given: - Mean of 31 results = 60 → Total sum: \[ 31 \times 60 = 1860 \] - Mean of first 16 results = 58 → Total sum: \[ 16 \times 58 = 928 \] - Mean of last 16 results = 62 → Total sum: \[ 16 \times 62 = 992 \] Since the 16th result is counted twice in both first and last 16 results, we remove it: \[ \text{16th result} = 1860 - (928 + 992 - x) \] \[ x = 1860 - 1920 \] \[ x = 60 \]
Thus, the 16th result is 60.