Consider the following two sample data sets. Sample A Sample B 121 171 158 171 152 170 173 184 163 168 169 171 157 85 145 190 183 185 165 172 196 140 173 206 170 159 172 172 174 169 161 187 100 199 151 180 142 166 171 167 170 188

a. Construct a box plot for each data set.

b. Identify any outliers that may exist in the two data sets. Applet Exercise 2.7 Use the applet Standard Deviation to determine whether an item in a data set may be an outlier. Begin by setting appropriate limits and plotting the data below on the number line provided in the applet. 10 80 80 85 85 85 85 90 90 90 90 90 95 95 95 95 100 100 NW NW L02109

a. The green arrow shows the approximate location of the mean. Multiply the standard deviation given by the applet by 3. Is the data item 10 more than 3 standard deviations away from the green arrow (the mean)? Can you conclude that the 10 is an outlier?

b. Using the mean and standard deviation from part

a, move the point at 10 on your plot to a point that appears to be about 3 standard deviations from the mean. Repeat the process in part a for the new plot and the new suspected outlier.

c. When you replaced the extreme value in part a with a number that appeared to be within 3 standard deviations of the mean, the standard deviation got smaller and the mean moved to the right, yielding a new data set where the extreme value was not within 3 standard deviations of the mean. Continue to replace the extreme value with higher numbers until the new value is within 3 standard deviations of the mean in the new data set. Use trial and error to estimate the smallest number that can replace the 10 in the original data set so that the replacement is not considered to be an outlier. Applying the Concepts—Basic