A company advertises an average of 42,000 miles for one of its new tires. In the
manufacturing process there is some variation around that average. Would the company
want a process that provides a large or a small variance? Justify your answer.
Roughly speaking, the standard deviation indicates how far, on average, the observations
are from the mean. Do you think that for the data set below the standard deviation will
give a good indication of the typical deviation from the mean?
2, 3, 4, 4, 5, 5, 6, 6, 100
What drawback of the standard deviation is illustrated by this example?
Without calculating the standard deviation, compare the standard deviation for the
following data sets. (Note: All data sets have a mean of 30.) Which do you expect to have
the largest standard deviation and which do you expect to have the smallest standard
deviation? Explain your answers in terms of the formula
s =(x –x)2
n – 1 .
Data set 1: 30, 30, 30, 30, 30, 30, 30, 30, 30, 30
Data set 2: 20, 25, 25, 30, 30, 30, 30, 35, 35, 40
Date set 3: 20, 20, 20, 25, 25, 35, 35, 40, 40, 40