Question

1. textbooks in professors offices if the average number of textbooks in professors offices is 16, the standard deviation is 5, and the average age of the professors is 43, with a standard deviation of 8, which data set is more variable?

Explanation:

Step1: Calculate the coefficient of variation for textbooks

The coefficient of variation formula is \(CV=\frac{s}{\overline{x}}\times100\%\). For textbooks, \(\overline{x} = 16\) (mean) and \(s = 5\) (standard deviation).
\(CV_{textbooks}=\frac{5}{16}\times100\%=\frac{500}{16}\% = 31.25\%\)

Step2: Calculate the coefficient of variation for professors' age

For professors' age, \(\overline{x}=43\) (mean) and \(s = 8\) (standard deviation).
\(CV_{age}=\frac{8}{43}\times100\%=\frac{800}{43}\%\approx18.60\%\)

Answer:

The data set of textbooks in professors' offices is more variable.