## Related questions with answers

a. use the technology of your choice to determine the range and sample standard deviation of each of the two data sets. b. compare the two data sets by using your results from part (a). 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 CD. [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]

Solution

Verified(a) $\textbf{ITALIANS}$

$n=70$

The range is the difference between the highest and the lowest value:

$RANGE=Max-Min=148-116=32$

The mean is the sum of all values divided by the number of values:

$\overline{x}=\dfrac{138+133+130+...+138+135+138}{70}=\dfrac{9271}{70}\approx 132.4429$

The variance is the sum of squared deviations from the mean divided by $n-1$. The standard deviation is the square root of the variance:

$s=\sqrt{\dfrac{(138-132.4429)^2+(133-132.4429)^2+....+(135-132.4429)^2+(138-132.4429)^2}{70-1}}\approx 5.7$

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