Problem 24
Exercise 22 looked at distances PGA golfers can hit the ball. The standard deviation of these average drive distances is \(9.3\) yards, and the quartiles are \(Q_{1}=282\) yards and \(Q_{3}=294\) yards. a) Write a sentence or two describing the spread in distances based on i) the quartiles. ii) the standard deviation. b) Do you have any concerns about using either of these descriptions of spread? Explain.
Problem 25
A clerk entering salary data into a company spreadsheet accidentally put an extra " \(0^{\prime \prime}\) in the boss's salary, listing it as \(\$ 2,000,000\) instead of \(\$ 200,000 .\) Explain how this error will affect these summary statistics for the company payroll: a) measures of center: median and mean. b) measures of spread: range, IQR, and standard deviation.
Problem 26
A meteorologist preparing a talk about global warming compiled a list of weekly low temperatures (in degrees Fahrenheit) he observed at his southern Florida home last year. The coldest temperature for any week was \(36^{\circ} \mathrm{F}\), but he inadvertently recorded the Celsius value of \(2^{\circ}\). Assuming that he correctly listed all the other temperatures, explain how this error will affect these summary statistics: a) measures of center: mean and median. b) measures of spread: range, IQR, and standard deviation.
Problem 28
During contract negotiations, a company seeks to change the number of sick days employees may take, saying that the annual "average" is 7 days of absence per employee. The union negotiators counter that the "average" employee misses only 3 days of work each year. Explain how both sides might be correct, identifying the measure of center you think each side is using and why the difference might exist.
Problem 29
A small warehouse employs a supervisor at $$\$ 1200$$ a week, an inventory manager at $$\$ 700$$ a week, six stock boys at $$\$ 400$$ a week, and four drivers at \(\$ 500\) a week. a) Find the mean and median wage. b) How many employees earn more than the mean wage? c) Which measure of center best describes a typical wage at this company: the mean or the median? d) Which measure of spread would best describe the payroll: the range, the IQR, or the standard deviation? Why?
Problem 30
The frequency table shows the heights (in inches) of 130 members of a choir. \(\begin{array}{c|c|c|c} \text { Height } & \text { Count } & \text { Height } & \text { Count } \\ \hline 60 & 2 & 69 & 5 \\ 61 & 6 & 70 & 11 \\ 62 & 9 & 71 & 8 \\ 63 & 7 & 72 & 9 \\ 64 & 5 & 73 & 4 \\ 65 & 20 & 74 & 2 \\ 66 & 18 & 75 & 4 \\ 67 & 7 & 76 & 1 \\ 68 & 12 & & \end{array}\) a) Find the median and IQR. b) Find the mean and standard deviation. c) Display these data with a histogram. d) Write a few sentences describing the distribution.
Problem 31
In March 2006, 16 gas stations in Grand Junction, CO, posted these prices for a gallon of regular gasoline: \(\begin{array}{llll} 2.22 & 2.21 & 2.45 & 2.24 \\ 2.27 & 2.28 & 2.27 & 2.23 \\ 2.26 & 2.46 & 2.29 & 2.32 \\ 2.36 & 2.38 & 2.33 & 2.27 \end{array}\) a) Make a stem-and-leaf display of these gas prices. Use split stems; for example, use two \(2.2\) stems-one for prices between \(\$ 2.20\) and \(\$ 2.24\) and the other for prices from \(\$ 2.25\) to \(\$ 2.29 .\) b) Describe the shape, center, and spread of this distribution. c) What unusual feature do you see?
Problem 32
During his 20 seasons in the NHL, Wayne Gretzky scored \(50 \%\) more points than anyone who ever played professional hockey. He accomplished this amazing feat while playing in 280 fewer games than Gordie Howe, the previous record holder. Here are the number of games Gretzky played during each season: \(\begin{aligned} &79,80,80,80,74,80,80,79,64,78,73,78,74,45,81,48,80, \\ &82,82,70 \end{aligned}\) a) Create a stem-and-leaf display for these data, using split stems. b) Describe the shape of the distribution. c) Describe the center and spread of this distribution. d) What unusual feature do you see? What might explain this?
Problem 36
The Cornell Lab of Ornithology holds an annual Christmas Bird Count (www.birdsource.org), in which bird watchers at various locations around the country see how many different species of birds they can spot. Here are some of the counts reported from sites in Texas during the 1999 event: \(\begin{array}{lllllll} 228 & 178 & 186 & 162 & 206 & 166 & 163 \\ 183 & 181 & 206 & 177 & 175 & 167 & 162 \\ 160 & 160 & 157 & 156 & 153 & 153 & 152 \end{array}\) a) Create a stem-and-leaf display of these data. b) Write a brief description of the distribution. Be sure to discuss the overall shape as well as any unusual features.
Problem 37
The data below give the number of hurricanes classified as major hurricanes in the Atlantic Ocean each year from 1944 through 2006 , as reported by NOAA (www.nhc.noaa.gov): \(\begin{aligned} &3,2,1,2,4,3,7,2,3,3,2,5,2,2,4,2,2,6,0,2,5,1,3,1,0, \\ &3,2,1,0,1,2,3,2,1,2,2,2,3,1,1,1,3,0,1,3,2,1,2,1,1, \\ &0,5,6,1,3,5,3,3,2,3,6,7,2 \end{aligned}\) a) Create a dotplot of these data. b) Describe the distribution.
