Henry Cavendish, an English chemist and physicist (1731€“1810), approached many of his experiments using quantitative measurements. He was the first to accurately measure the density of the Earth. Following are 29 measurements (ranked for your convenience) of the density of the Earth done by Cavendish in 1798 using a torsion balance. Density is presented as a multiple of the density of water.

a. Describe the data set by calculating the mean, median, and standard deviation.
b. Construct a histogram and explain how it demonstrates the values of the descriptive statistics in part a.
c. Find the 5-number summary.
d. Construct a box-and-whiskers display and explain how it demonstrates the values of the descriptive statistics in part c.
e. Based on the two graphs, what €œshape€ is this distribution of measurements?
f. Assuming that Earth density measurements have an approximately normal distribution, approximately 95% of the data should fall within 2 standard deviations of the mean. Is this true?

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4.88 5.07 5.10 5.26 5.27 5.29 5.29 5.30 5.34 5.34 5.36 5.39 5.42 5.44 5.46 5.47 5.50 5.53 5.55 5.57 5.58 5.61 5.62 5.63 5.65 5.68 5.75 5.79 5.85 Source: The data and descriptive information are based on material from Do robust estimators work with real data?" by Stephen M. Stigler, Annals of Statistics 5 119771, 1055-1098