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 given data on the number line provided in the applet. Here is the data set:

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 three 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 three 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 three standard deviations of the mean, the standard deviation got smaller and the mean moved to the right, yielding a new data set whose extreme value was not within three standard deviations of the mean.
Continue to replace the extreme value with higher numbers until the new value is within three 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.

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