Question

In each of Exercises 3.51-3.52,

(a) use the technology of your choice to determine the mean and median of each of the two data sets.

(b) compare the two data sets by using your results from part (a).

The Etruscans. Anthropologists are still trying to unravel the mystery of the origins of the Etruscan empire, a highly advanced Italic civilization formed around the eighth century B.C. in central Italy. Were they native to the Italian peninsula or, as many aspects of their civilization suggest, did they migrate from the East by land or sea? The maximum head breadth, in millimeters, of 70 modern Italian male skulls and that of 84 preserved Etruscan male skulls were analyzed to help researchers decide whether the Etruscans were native to Italy. The resulting data can be found on the WeissStats site. [SOURCE: N. Barnicot and D. Brothwell, "The Evaluation of Metrical Data in the Comparison of Ancient and Modern Bones." In Medical Biology and Etruscan Origins, G. Wolstenholme and C. O'Connor, eds., Little, Brown & Co., 1959}

Short answer

Part (a) The mean and median for Italians are 132.44 and 132, respectively, whereas the mean and median for Etruscans are 143.7 and 143.50.

Part (b) The Etruscans have a larger mean and median than the Italians, and both distributions are roughly symmetric.

Step-by-step solution

Step 1. Given information.

The given statement is:

The maximum head width, in millimeters, of modern Italian male skulls and preserved Etruscan male skulls are supplied to determine whether Etruscans were native to Italy.

Part (a) Step 2. Using MINITAB to calculate the mean and median.

MINITAB is used to calculate the mean and median values.

The following is the procedure for calculating the mean, median, and mode.

• Select Stat >Basic Statistics> Descriptive Statistics from the drop-down menu.
• In the Variables section, type ITALIANS, and ETRUSCANS.
• Select Mean and Median from the Statistic menu.
• Click OK.

Part (a) Step 3. MINITAB output.

The output of MINITAB is displayed below:

The figure shows that the median is 132 and the mean is 132.44 for Italians.

According to the figure, the Etruscan mean is 143.77 and the median is 143.50.

Part (b) Step 1. Compare the results of part (a).

Etruscans' mean and median values are higher than Italians' mean and median values.

The mean and median values for Italians are about equal. As a result, the distribution is roughly symmetric.

The mean and median values for the Etruscans are about comparable. As a result, the distribution is roughly symmetric.