ANSWER TO FRAME 27.

a. mean = X = ΣX = 184 = 46.0

n

4

b. This is a sample mean because only four observations from the population were used in

computing it.

In a later text, we will use the sample mean to make a statement about the population mean. For

the time being, note that the sample mean and the population mean DO NOT USUALLY GIVE THE

SAME VALUE.

ANSWER TO FRAME 28.

Sample 1 mean = X = ΣX = 114 = 22.80

n

5

Sample 2 mean = X = ΣX = 10,080 = 2016

n

5

Note the effect of extreme values on the sample mean. Although only one value changed, the

mean was changed significantly. This points out the key characteristic that the mean is affected

by extreme values and it may not be representative of all values in the sample (or population).

ANSWER TO FRAME 29.

Ordering the data gives: 2, 7, 8, 19, 22, 24, 28, 31. Since there are an even number of

observations we must find the mean of the middle two values. This would be (19 + 22) /2 = 20.5.

The median is then 20.5.

Note that, if you forgot to order the data, you would have computed the median to be

(19 + 7) /2 = 13. This is incorrect. The data must be ordered.