Chapter 2 HW solutions

Chapter 2 1. Which types of graphs are used for quantitative data? Select all that apply. Histogram Stem-and-Leaf Plot Scatterplot 2. Which types of graphs are used for qualitative data? Select all that apply. Pie Chart Bar Graph 3. True or False: The bars for a histogram should always touch? True. (Unless, of course, there is an actual gap in the data.) 4. An instructor had the following grades recorded for an exam. 96 66 65 82 85 82 87 76 80 85 83 69 79 70 83 63 81 94 71 83 99 75 73 83 86 a) Create a stem-and-leaf plot. (Hint: You can copy and paste this data in to Calculator Soup as is.) Stem Leaf 6 3 5 6 9 7 0 1 3 5 6 9 8 0 1 2 2 3 3 3 3 5 5 6 7 9 4 6 9 b) Complete the following table. Class Frequency Relative Frequency 60-69 4 0.16 or 16% 70-79 6 0.24 or 24% 80-89 12 0.48 or 48% 90-99 3 0.12 or 12% Total 25 1 or 100% c) What should the relative frequencies always add up to? 100% d) What is the frequency for students that were in the C range of 70 – 79? 6

e) What is the relative frequency for students that were in the C range of 70 – 79? 0.24 or 24% f) Which is the modal class? 80-89 g) Which class has a relative frequency of 12%? 90-99 5. Eyeglassomatic manufactures eyeglasses for different retailers. The number of lenses for different activities is in table. Activity Number of lenses Grind 18872 Multi-coat 12105 Assemble 4333 Make Frames 25880 Receive Finished 26991 Unknown 1508 Grind means that they ground the lenses and put them in frames, multi-coat means that they put tinting or scratch resistance coatings on lenses and then put them in frames, assemble means that they receive frames and lenses from other sources and put them together, make frames means that they make the frames and put lenses in from other sources, receive finished means that they received glasses from other source, and unknown means they do not know where the lenses came from. a) Make a relative frequency table for the data. (Note: There are 89,688 pairs of glasses total in this data.) Activity Relative Frequency Grind 18872/89688 = 0.2104 Multi-coat 12105/89688 = 0.135 Assemble 4333/89688 = 0.0483 Make Frames 25880/89688 = 0.2886 Receive Finished 26991/89688 = 0.3009 Unknown 1508/89688 = 0.0168 b) How many eyeglasses did Eyeglassomatic assemble? 4,333 c) How many eyeglasses did Eyeglassomatic manufacturer all together? 89,688

6. The following table is from a sample of five hundred homes in Oregon asked the primary source of heating their residential home. Type of Heat Percent Electricity 33 Heating Oil 4 Natural Gas 50 Firewood 8 Other 5 a) How many of the households heat their home with firewood? 8 b) What percent of households heat their home with natural gas? 50/500=0.1 or 10% 7. The following table is from a sample of 50 undergraduate students from Central Michigan University. Class Relative Frequency Percent Freshman 18 Sophomore 13 Junior 23 Senior 46 a) What percent of students are below a senior class? 18%+13%+23%=54% b) What is the relative frequency of the junior class? 23% 8. A sample of heights of 20 people in cm is recorded below. 167 201 170 185 175 162 182 186 172 173 188 154 185 178 177 184 178 165 169 171 185 178 175 176 a. Make a stem-and-leaf plot. Stem Leaf 15 4 16 2 5 7 9 17 0 1 2 3 5 5 6 7 8 8 8 18 2 4 5 5 5 6 8 19 20 1

a) How many colleges were sampled? 50 b) What was the approximate value of the highest change in tuition? 78.9% 10. The following data represents the grades in a statistics course. Below is the frequency distribution and histogram. Class Limit Frequency Relative Frequency 40 – 49.9 2 0.08 50 – 59.9 1 0.04 60 – 69.9 7 0.28 70 – 79.9 6 0.24 80 – 89.9 7 0.28 90 – 99.9 2 0.04 a) How many students were in the class? 25 b) What was the approximate lowest and highest grade in the class? Lowest: 40% Highest: 99.9% c) What percent of students had a passing grade of 70% or higher? 15/25=0.60 or 60%

11. The following graph represents a random sample of car models driven by college students. What percent of college students drove a Nissan? 20% of college students drove a Nissan. 12. The following data represents the percent change in tuition levels at public, four-year colleges (inflation adjusted) from 2008 to 2013 (Weissmann, 2013). Use the frequency distribution to answer the following questions. Class Limits Cumulative Frequency 2.2 – 11.7 6 11.8 – 21.3 26 21.4 – 30.9 37 31.0 – 40.5 41 40.6 – 50.1 43 50.2 – 59.7 45 59.8 – 69.3 48 69.4 – 78.9 50 a) How many colleges were sampled? 296 colleges b) What class of percent changes had the most colleges in that range? class: 69.4-78.6 c) How many colleges had a percent change below 50.2% change in tuition? 43+41+37+26+6=153 colleges

15. A scatter plot for a random sample of 24 countries shows the average life expectancy and the average number of births per woman (fertility rate). What is the approximate fertility rate for a country that has a life expectancy of 76 years? (2013, October 14). Retrieved from http://data.worldbank.org/indicator/SP.DYN.TFRT.IN Expected fertility rate for a country with Life Expectancy of 76 years would have a fertility rate of about 2. 16. Why is this a misleading or poor graph? The frequency axis does not have labels.

17. Why is this a misleading or poor graph? The horizontal axis does not have any labels (and there is no title). We don’t even know what this graph is trying to tell us! 18. Why is this a misleading or poor graph? Retrieved from http://www.tradingeconomics.com/united-states/unemployment-rate The vertical axis does not start at 0 making the changes look larger than they are.