Question

A group of researchers measure the weight of five participants prior to a clinical weight loss intervention. They record the following weights (in pounds): 150, 100, 250, 200, and 300 pounds. The mean is 200 pounds.

Using the original example of five weights, the researchers added a sixth participant to the sample.

(a) If the sixth participant weighed 240 pounds, will the mean increase, decrease, or not change?

The mean will increase. The mean will decrease.    The mean will not change.

(b) If the sixth participant weighed 200 pounds, will the mean increase, decrease, or not change?

The mean will increase. The mean will decrease.    The mean will not change.

(c) If the sixth participant weighted 170 pounds, will the mean increase, decrease, or not change?

The mean will increase. The mean will decrease.    The mean will not change.

Answer 1

a) The mean will increase because a value higher than 200 is being added to the group.

b) Mean will remain unchanged because a value equivalent to mean is being added to the sample.

c) Mean will decrease because a lower value than mean is being added to the group.

It can be in general understood as follows:

For a sample of 'n' people if mean is 'x', then total weight is nx. When a new value 'y' is added the change in the total due to that new value is what determines the new mean.