Question

The numbers of students in the 8 schools in a district are given below.
(Note that these are already ordered from least to greatest.)
185, 235, 255, 266, 269, 303, 370, 381
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Suppose that the number 381 from this list changes to 237. Answer the following.
(a) What happens to the median?
(b) What happens to the mean?
O It decreases by 0
O It increases by 0
O It stays the same.
O It decreases by 0
O It increases by 0
O It stays the same.

Answer 1

Part (a)

The middle values were nitially 266 and 269, but now they are 255 and 266. Thus, the median changes from 267.5 to 260.5, meaning it decreases by 7.

Part (b)

The sum before the change is 2264, but after, it is 2120. This means the sum decreased by 144, and thus the mean decreased by 16.