The mean of a set of data is 5. What will be the new mean if 10 is subtracted…

Concept: For a data set of n values, mean = (sum of values) / n. If the same constant k is subtracted from every value in the set, the sum decreases by k × n, so the new mean = (sum − kn)/n = mean − k. In other words, subtracting a constant from every value shifts the mean by exactly that constant.

1. Let there be n data values with mean 5, so the sum of all values = 5 × n = 5n.

2. Subtracting 10 from each of the n values reduces the total sum by 10 × n = 10n.

3. New sum = 5n - 10n = -5n.

4. New mean = new sum ÷ n = -5n ÷ n = -5.

Cross-check: Using the shift property directly - new mean = original mean - constant subtracted = 5 - 10 = -5, which matches the value obtained by working through the sum and count.

So the new mean is -5.