The mean of four numbers a, b, c, d is 100. If c = 70, then the mean of the…

Concept. The arithmetic mean of n numbers is their total divided by n, which rearranges to total = mean × n. Removing a known member from a set lowers the total by exactly that member's value and lowers the count by one, so the new mean is (old total − removed value) ÷ (n − 1). The mean itself is never reduced by the removed value.

Applying this to the four numbers a, b, c, d:

1. Total of all four numbers: a + b + c + d = 4 × 100 = 400.

2. The known member c = 70 leaves the group, so a + b + d = 400 − 70 = 330.

3. Three numbers now remain, so their mean = 330 ÷ 3 = 110.

Cross-check. Working backwards, if a, b and d average 110 their total is 330; restoring c = 70 gives 400, and 400 ÷ 4 = 100, which is the mean stated in the question.

Contrast. A frequent slip is to subtract the removed value from the mean instead of from the total (100 − 70 = 30), or to keep dividing by 4 when only three numbers are left. Removal acts on the total and on the count, never on the mean directly.