Insurance companies don’t know whether a policy they’ve written is profitable until the policy matures (expires). To see how they’ve performed recently, an analyst looked at mature policies and investigated the net profit to the company (in $).
a) Make a suitable display of the profits from the data provided.
b) Summarize the central value for the profits with a median and mean. Why do they differ?
c) Given what you know about the distribution, which of these measures might do a better job of summarizing the company’s profits? Why?
d) Summarize the spread of the profit distribution with a standard deviation and with an IQR.
e) Given what you know about the distribution, which of these measures might do a better job of summarizing the spread in the company’s profits? Why?
f) If we were to remove the outliers from the data, how would you expect the mean, median, standard deviation, and IQR to change?