Reference no: EM131971497

(Outliers.) 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 in the Gulf of Mexico. These data result: (Based on a report in McGraw-Hill Yearbook of Science and Technology, 1983, p. 410.)

(a) Find the sample mean, sample median, and sample standard deviation for these data.

(b) Note that the starred observation in the data set is very different from the others. It is called an outlier. (An outlier is an observation at either extreme of a sample which is so far removed from the main body of the data that the appropriateness of including it in the sample is questionable.) Some apparent outliers are actually misrecorded data points; these can be found and corrected. Other outliers are legitimate observations that just happen to be far removed from the body of the data; these should not be ignored. 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?