Consider the following four data sets.

Data Set I Data Set II Data Set III Data Set IV 1 5 1 9 5 5 2 4 1 8 1 9 5 5 4 4 2 8 1 9 5 5 4 4 2 9 1 9 5 5 4 10 5 9 1 9 5 5 4 10

a. Compute the mean of each data set.

b. Although the four data sets have the same means, in what respect are they quite different?

c. Which data set appears to have the least variation? the greatest variation?

d. Compute the range of each data set.

e. Use the defining formula to compute the sample standard deviation of each data set.

f. From your answers to parts

(d) and (e), which measure of variation better distinguishes the spread in the four data sets: the range or the standard deviation? Explain your answer.

g. Are your answers from parts

(c) and

(e) consistent?