Temperature differences between the warm upper surface of the ocean and the colder deeper levels can be utilized to convert thermal energy to mechanical energy. This mechanical energy can in turn be used to produce electrical power using a vapor turbine. Let X denote the difference in temperature between the surface of the water and the water at a depth of 1 kilometer. Measurements are taken at 15 randomly selected sites i the Gulf of Mexico. These data result in the following temperatures:
22.5 23.8 23.2 22.8 10.1
23.5 24.0 23.2 24.2 24.3
23.3 23.4 23.0 23.5 22.8
a) Construct a double stem-and-leaf diagram for these data.
b) Find the sample mean, sample median, and sample standard deviation for these data.
c) Note that the starred observation in the data set is very different from the others. It is a potential outlier. Construct a box plot for these data to verify that the value 10.1 does, in fact, qualify as an outlier.
d) To see the effect of this outlier, drop it from the data set and calculate the sample mean, median, and standard deviation for the remaining 14 observations. Which measure is least affected by the presence of the outlier? Do you see why it is desirable to report both the mean and median of a data set?