#set document(title: "2.4 Chapter 2 Exercises", author: "Rachel Webb") #set page(width: 8.5in, height: auto, margin: 1in) #import "@preview/cetz:0.5.2" #set text(font: ("STIX Two Text", "Libertinus Serif", "New Computer Modern"), size: 10.5pt, lang: "en") #show math.equation: set text(font: ("STIX Two Math", "New Computer Modern Math")) #set par(justify: true, leading: 0.62em, spacing: 0.9em) #set enum(spacing: 1.1em) // room between list items so tall inline fractions don't collide #set list(spacing: 1.1em) #set table(stroke: 0.5pt + rgb("#c7ccd3")) #let BLUE = rgb("#183B6F") // brand navy — section bars + example/solution labels (white on navy 11.09:1) #let ORANGE = rgb("#A94509") // brand primary-700 — AA-safe deep orange for TEXT (5.93:1 on white; raw brand #F37021 is 2.94:1 and must never carry text) #let RED = rgb("#DC2626") // brand error-600 #let GREEN = rgb("#059669") // brand success-600 (decoration only; small green text uses green-text #007942) #show heading.where(level: 1): it => block(width: 100%, above: 0pt, below: 16pt, fill: gradient.linear(BLUE, rgb("#2C5AA0")), inset: (x: 14pt, y: 12pt), radius: 3pt, text(fill: white, weight: "bold", size: 19pt, it.body)) #show heading.where(level: 2): it => block(width: 100%, above: 18pt, below: 10pt, fill: BLUE, inset: (x: 10pt, y: 6pt), radius: 2pt, text(fill: white, weight: "bold", size: 12pt, it.body)) #show heading.where(level: 3): it => text(fill: ORANGE, weight: "bold", size: 12.5pt, it.body) #show heading.where(level: 4): it => text(fill: BLUE, weight: "bold", size: 10.5pt, it.body) #let examplebox(label, title, body) = block(width: 100%, breakable: true, fill: rgb("#EFF1F5"), stroke: 0.5pt + rgb("#CFDDF0"), radius: 4pt, inset: 10pt, above: 12pt, below: 12pt)[ #block(below: 6pt)[#box(fill: BLUE, inset: (x: 6pt, y: 2pt), radius: 2pt, text(fill: white, weight: "bold", size: 8.5pt, label)) #h(0.4em) #strong[#title]] #body] // rail = decorative left rule (raw brand token); labelcolor = AA-safe label text shade #let notebox(label, rail, labelcolor, tint, body) = block(width: 100%, breakable: true, fill: tint, stroke: (left: 3pt + rail), inset: (left: 10pt, rest: 8pt), radius: (right: 4pt), above: 11pt, below: 11pt)[ #text(fill: labelcolor, weight: "bold", size: 7.5pt, tracking: 0.5pt)[#upper(label)] #linebreak() #body] #let solutionbox(body) = block(above: 4pt, below: 8pt)[ #text(fill: BLUE, weight: "bold", size: 8.5pt)[Solution] #linebreak() #body] #let figph(msg) = block(width: 100%, height: 60pt, fill: rgb("#f6f7f9"), stroke: (paint: rgb("#c7ccd3"), dash: "dashed"), radius: 4pt, inset: 10pt)[ #align(center + horizon, text(fill: rgb("#889"), style: "italic", size: 9pt, msg))] // Standardize inlined figure sizes: measure the natural CeTZ canvas, then scale to a // consistent envelope (aspect-aware; see build_typst.py FIG_* constants). Unlike the // print preamble, dimensions are FLOORED: in an editor a user can trim a figure to a // degenerate 1-D shape (a bare line), and w/h or tw/w would then divide by zero. #let _STD_W = 3.5 #let _WIDE_W = 5.6 #let _MAX_H = 3.4 #let _ASPECT_WIDE = 2.2 #let _UPSCALE_MAX = 1.15 #let stdfig(body) = context { let m = measure(body) let w = calc.max(m.width / 1in, 0.01) let h = calc.max(m.height / 1in, 0.01) let tw = if w / h > _ASPECT_WIDE { _WIDE_W } else { _STD_W } let s = calc.min(tw / w, _MAX_H / h, _UPSCALE_MAX) align(center, box(scale(x: s * 100%, y: s * 100%, reflow: true, body))) } #show figure: set block(breakable: false) #set figure(gap: 8pt) #show figure.caption: set text(size: 8.5pt, fill: rgb("#555")) == 2.4#h(0.6em)Chapter 2 Exercises #notebox("Your Turn", rgb("#8a94a6"), rgb("#556666"), rgb("#f7f8fa"))[ #emph[Chapter 2 Exercises] 1. Which types of graphs are used for quantitative data? Select all that apply. a) Ogive b) Pie Chart c) Histogram d) Stem-and-Leaf Plot e) Bar Graph 2. Which types of graphs are used for qualitative data? Select all that apply. a) Pareto Chart b) Pie Chart c) Dotplot d) Stem-and-Leaf Plot e) Bar Graph f) Time Series Plot 3. The bars for a histogram should always touch, true or false? 4. A sample of rents found the smallest rent to be \$600 and the largest rent was \$2,500. What is the recommended class width for a frequency table with 7 classes? 5. An instructor had the following grades recorded for an exam. #notebox("Note", rgb("#8a94a6"), rgb("#556666"), rgb("#f7f8fa"))[ #emph[Check your Exercise 5 table] The 25 exam grades load into L1, and a histogram with Class width 10 starting at 60 (the panel's own suggestion) tallies 4, 6, 12, 3 - so the 70-79 class has frequency 6 with relative frequency 6/25 = 0.24, the modal class is 80-89, and the cumulative frequency through 80-89 is 4 + 6 + 12 = 22. The frequency table under the chart fills in the rest of part (b). - Histogram of the 25 grades: bars 4, 6, 12, 3 ] #figure(table( columns: 5, align: left, inset: 6pt, table.header([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. b) Complete the following table. #figure(table( columns: 5, align: left, inset: 6pt, table.header([#strong[Class]], [#strong[Frequency]], [#strong[Cumulative Frequency]], [#strong[Relative Frequency]], [#strong[Cumulative Relative Frequency]]), [60 – 69], [], [], [], [], [70 – 79], [], [], [], [], [80 – 89], [], [], [], [], [90 – 99], [], [], [], [], [#strong[Total]], [#strong[25]], [], [], [], )) c) What should the relative frequencies always add up to? d) What should the last value always be in the cumulative frequency column? e) What is the frequency for students that were in the C range of 70-79? f) What is the relative frequency for students that were in the C range of 70-79? g) Which is the modal class? h) Which class has a relative frequency of 12%? i) What is the cumulative frequency for students that were in the B range of 80-89? j) Which class has a cumulative relative frequency of 40%? 6. Eyeglassomatic manufactures eyeglasses for different retailers. The number of lenses for different activities is in table. #figure(table( columns: 7, align: left, inset: 6pt, table.header([Activity], [Grind], [Multi-coat], [Assemble], [Make Frames], [Receive Finished], [Unknown]), [Number of lenses], [18,872], [12,105], [4,333], [25,880], [26,991], [1,508], )) 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 another source, and unknown means they do not know where the lenses came from. a) Make a relative frequency table for the data. b) How many of the eyeglasses did Eyeglassomatic assemble? c) How many of the eyeglasses did Eyeglassomatic manufacture all together? d) What is the relative frequency for the assemble category? e) What percent of eyeglasses did Eyeglassomatic grind? 7. The following table is from a sample of five hundred homes in Oregon asked the primary source of heating in their residential homes. #figure(table( columns: 2, align: left, inset: 6pt, table.header([#strong[Type of Heat]], [#strong[Percent]]), [Electricity], [33], [Heating Oil], [4], [Natural Gas], [50], [Firewood], [8], [Other], [5], )) a) How many of the households heat their home with firewood? b) What percent of households heat their home with natural gas? 8. The following table is from a sample of 50 undergraduate PSU students. #figure(table( columns: 2, align: left, inset: 6pt, table.header([#strong[Class]], [#strong[Relative Frequency Percent]]), [Freshman], [18], [Sophomore], [13], [Junior], [23], [Senior], [46], )) a) What percent of students are below a senior class? b) What is the cumulative frequency of the junior class? 9. A sample of heights of 20 people in cm is recorded below. Make a stem-and-leaf plot. #notebox("Note", rgb("#8a94a6"), rgb("#556666"), rgb("#f7f8fa"))[ #emph[See the tall outlier on a dot plot] Opens the plots panel with the Exercise 9 heights in L1. Choose Dot Plot: the dots pile up through the 170s and one stands alone at 201, mirroring the answer key's stemplot where the 19 row is empty; switch to Histogram (width 10, first class 150) and the bars 1, 4, 11, 7, 0, 1 are the stemplot's row counts. - Dot plot of the heights: one dot alone at 201 ] #figure(table( columns: 6, align: left, inset: 6pt, [Height (cm)], [], [], [], [], [], [167], [201], [170], [185], [175], [162], [182], [186], [172], [173], [188], [154], [185], [178], [177], [184], [178], [165], [169], [171], [185], [178], [175], [176], )) 10. The stem-and-leaf plot below is for pulse rates before and after exercise. #figure(figph[Back-to-back stem-and-leaf plot of pulse rates with stems 6 through 12 in the center; before-exercise leaves on the left span 62 to 104, and after-exercise leaves on the right span 85 to 128, showing higher rates after exercise.], alt: "Back-to-back stem-and-leaf plot of pulse rates with stems 6 through 12 in the center; before-exercise leaves on the left span 62 to 104, and after-exercise leaves on the right span 85 to 128, showing higher rates after exercise.", caption: none) a) Was pulse rate higher on average before or after exercise? b) What was the fastest pulse rate of the before exercise group? c) What was the slowest pulse rate of the after-exercise group? 11. The following data represents the percent change in tuition levels at public, four-year colleges (inflation adjusted) from 2008 to 2013 (Weissmann, 2013). Below is the frequency distribution and histogram. #figure(table( columns: 4, align: left, inset: 6pt, table.header([Class Limits], [Class Midpoint], [Frequency], [Relative Frequency]), [2.2 – 11.7], [6.95], [6], [0.12], [11.8 – 21.3], [16.55], [20], [0.40], [21.4 – 30.9], [26.15], [11], [0.22], [31.0 – 40.5], [35.75], [4], [0.08], [40.6 – 50.1], [45.35], [2], [0.04], [50.2 – 59.7], [54.95], [2], [0.04], [59.8 – 69.3], [64.55], [3], [0.06], [69.4 – 78.9], [74.15], [2], [0.04], )) #figure(figph[Histogram titled Percentage Change in Tuition Levels (Inflation Adjusted) 2008 to 2013: percentage change from about 0 to 80 on the horizontal axis and frequency up to 25 on the vertical; bar heights are 6, 20, 11, 4, 2, 2, 3, and 2, peaking for changes between about 10% and 20% and skewed right.], alt: "Histogram titled Percentage Change in Tuition Levels (Inflation Adjusted) 2008 to 2013: percentage change from about 0 to 80 on the horizontal axis and frequency up to 25 on the vertical; bar heights are 6, 20, 11, 4, 2, 2, 3, and 2, peaking for changes between about 10% and 20% and skewed right.", caption: none) a) How many colleges were sampled? b) What was the approximate value of the highest change in tuition? c) What was the approximate value of the most frequent change in tuition? 12. The following data and graph represent the grades in a statistics course. #figure(table( columns: 4, align: left, inset: 6pt, table.header([Class Limits], [Class Midpoint], [Frequency], [Relative Frequency]), [40 – 49.9], [45], [2], [0.08], [50 – 59.9], [55], [1], [0.04], [60 – 69.9], [65], [7], [0.28], [70 – 79.9], [75], [6], [0.24], [80 – 89.9], [85], [7], [0.28], [90 – 99.9], [95], [2], [0.04], )) #figure(figph[Histogram titled Grades for Statistics Class: percentage grades from 40 to 100 on the horizontal axis and frequency from 0 to 8 on the vertical; bar heights are 2 for the 40s, 1 for the 50s, 7 for the 60s, 6 for the 70s, 7 for the 80s, and 2 for the 90s.], alt: "Histogram titled Grades for Statistics Class: percentage grades from 40 to 100 on the horizontal axis and frequency from 0 to 8 on the vertical; bar heights are 2 for the 40s, 1 for the 50s, 7 for the 60s, 6 for the 70s, 7 for the 80s, and 2 for the 90s.", caption: none) a) How many students were in the class? b) What was the approximate lowest and highest grade in the class? c) What percent of students had a passing grade of 70% or higher? 13. The following graph represents a random sample of car models driven by college students. What percent of college students drove a Nissan? #figure(figph[Pie chart titled Car Models Owned by College Students: Chevy 24%, Toyota 24%, Nissan 20%, Honda 12%, Ford 10%, and Other 10%.], alt: "Pie chart titled Car Models Owned by College Students: Chevy 24%, Toyota 24%, Nissan 20%, Honda 12%, Ford 10%, and Other 10%.", caption: none) 14. The following graph and data represent the percent change in tuition levels at public, four-year colleges (inflation adjusted) from 2008 to 2013 (Weissmann, 2013). #figure(figph[Ogive titled Percentage Change in Tuition Levels (Inflation Adjusted) 2008 to 2013: cumulative frequency rises from 0 at about a 2% change to 26 near 21% and 37 near 31%, then levels off to reach 50 by about a 79% change.], alt: "Ogive titled Percentage Change in Tuition Levels (Inflation Adjusted) 2008 to 2013: cumulative frequency rises from 0 at about a 2% change to 26 near 21% and 37 near 31%, then levels off to reach 50 by about a 79% change.", caption: none) #figure(table( columns: 2, align: left, inset: 6pt, table.header([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? b) What class of percent changes had the most colleges in that range? c) How many colleges had a percent change below 50.2% change in tuition? d) What is the cumulative relative frequency for the 50.2% – 59.7% change in tuition class? 15. Eyeglassomatic manufactures eyeglasses for different retailers. The number of lenses for different activities is in table. #figure(table( columns: 7, align: left, inset: 6pt, table.header([Activity], [Grind], [Multi-coat], [Assemble], [Make Frames], [Receive Finished], [Unknown]), [Number of lenses], [18,872], [12,105], [4,333], [25,880], [26,991], [1,508], )) a) Make a pie chart. b) Make a bar chart. c) Make a Pareto chart. 16. The daily sales using different sales strategies is shown in the graph below. #figure(figph[Grouped bar chart titled Sales Strategy Comparison showing daily sales in dollars for Products A through D under seven strategies; Strategies 1, 3, and 7 top \$200 for at least one product, while Strategy 2 is lowest, near or below \$100 for all four.], alt: "Grouped bar chart titled Sales Strategy Comparison showing daily sales in dollars for Products A through D under seven strategies; Strategies 1, 3, and 7 top $200 for at least one product, while Strategy 2 is lowest, near or below $100 for all four.", caption: none) a) Which strategy generated the most sales? b) Was there a particular strategy that worked well for one product, but not for another product? 17. The following graph represents a random sample of car models driven by college students. What was the most common car model? #figure(figph[Bar chart titled Car Models Owned by College Students showing percentages: Chevy 24, Ford 10, Honda 12, Nissan 20, Toyota 24, and Other 10, with Chevy and Toyota tied as most common.], alt: "Bar chart titled Car Models Owned by College Students showing percentages: Chevy 24, Ford 10, Honda 12, Nissan 20, Toyota 24, and Other 10, with Chevy and Toyota tied as most common.", caption: none) 18. The Australian Institute of Criminology gathered data on the number of deaths (per 100,000 people) due to firearms during the period 1983 to 1997. The data is in table below. Create a time-series plot of the data. What is the overall trend over time? (2013, September 26). Retrieved from #link("http://www.statsci.org/data/oz/firearms.html")[http://www.statsci.org/data/oz/firearms.html]. #notebox("Note", rgb("#8a94a6"), rgb("#556666"), rgb("#f7f8fa"))[ #emph[Trace the firearm-death trend] The years 1983-1997 load into L1 and the death rates into L2. Crunch draws no connect-the-dots time series, so choose Scatter Plot with X = L1 and Y = L2 and read the points left to right: the rate rises to 4.52 per 100,000 in 1985, then falls steadily to 2.30 by 1997. - Death rate vs year: high of 4.52 (1985) down to 2.30 (1997) ] #figure(table( columns: 2, align: left, inset: 6pt, table.header([Year], [Rate]), [1983], [4.31], [1984], [4.42], [1985], [4.52], [1986], [4.35], [1987], [4.39], [1988], [4.21], [1989], [3.4], [1990], [3.61], [1991], [3.67], [1992], [3.61], [1993], [2.98], [1994], [2.95], [1995], [2.72], [1996], [2.95], [1997], [2.3], )) 19. 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? #figure(figph[Scatterplot of fertility rate versus life expectancy: fertility falls from about 7 births per woman near 54 years of life expectancy to under 2 near 76 to 82 years, showing a negative association.], alt: "Scatterplot of fertility rate versus life expectancy: fertility falls from about 7 births per woman near 54 years of life expectancy to under 2 near 76 to 82 years, showing a negative association.", caption: none) (2013, October 14). Retrieved from #link("http://data.worldbank.org/indicator/SP.DYN.TFRT.IN")[http://data.worldbank.org/indicator/SP.DYN.TFRT.IN]. 20. The Australian Institute of Criminology gathered data on the number of deaths (per 100,000 people) due to firearms during the period 1983 to 1997. The time-series plot is below. What year had the highest rate of deaths? #figure(figph[Time-series graph titled Deaths From Firearms showing deaths per 100,000 people from 1983 to 1997: the rate stays near 4.3 to 4.5 through 1988, then declines to about 2.3 by 1997.], alt: "Time-series graph titled Deaths From Firearms showing deaths per 100,000 people from 1983 to 1997: the rate stays near 4.3 to 4.5 through 1988, then declines to about 2.3 by 1997.", caption: none) (2013, September 26). Retrieved from #link("http://www.statsci.org/data/oz/firearms.html")[http://www.statsci.org/data/oz/firearms.html]. 21. A survey by the Pew Research Center, conducted in 16 countries among 20,132 respondents from April 4 to May 29, 2016, before the United Kingdom’s Brexit referendum to exit the EU. The following is a time series graph for the proportion of survey respondents by country that responded that the current economic situation is their country was good. #figure(figph[Pew Research Center line graph titled Some European publics view economy on the rebound, but others remain negative, tracking the percent saying the current economic situation is good from 2007 to 2016; by 2016 Germany reaches 75%, Poland 49%, UK 47%, Italy 33%, Spain 13%, France 12%, and Greece 2%.], alt: "Pew Research Center line graph titled Some European publics view economy on the rebound, but others remain negative, tracking the percent saying the current economic situation is good from 2007 to 2016; by 2016 Germany reaches 75%, Poland 49%, UK 47%, Italy 33%, Spain 13%, France 12%, and Greece 2%.", caption: none) #link("http://www.pewglobal.org/2016/08/09/views-on-national-economies-mixed-as-many-countries-continue-to-struggle/")[http://www.pewglobal.org/2016/08/09/views-on-national-economies-mixed-as-many-countries-continue-to-struggle/] a) Which country had the most favorable outlook of their country’s economic situation in 2010? b) Which country had the least favorable outlook of their country’s economic situation in 2016? 22. Why is this a misleading or poor graph? #figure(figph[Bar chart titled Favorite Drinks showing frequency by drink type for colas, lemon flavored, root beer, teas, coffee, and other; coffee has the tallest bar and colas the next tallest, but the frequency axis has no numbers.], alt: "Bar chart titled Favorite Drinks showing frequency by drink type for colas, lemon flavored, root beer, teas, coffee, and other; coffee has the tallest bar and colas the next tallest, but the frequency axis has no numbers.", caption: none) 23. Why is this a misleading or poor graph? #figure(figph[Bar chart with no title, axis labels, or category names: eight bars rise irregularly from about 45,000 to about 165,000 on a vertical scale marked 0 to 180,000.], alt: "Bar chart with no title, axis labels, or category names: eight bars rise irregularly from about 45,000 to about 165,000 on a vertical scale marked 0 to 180,000.", caption: none) 24. Why is this a misleading or poor graph? #figure(figph[Bar chart titled United States Unemployment Rate, percentage of the labor force, with monthly bars falling from 9 to 7.3 between late 2011 and late 2013; the vertical axis is truncated, running only from 7 to 9.5.], alt: "Bar chart titled United States Unemployment Rate, percentage of the labor force, with monthly bars falling from 9 to 7.3 between late 2011 and late 2013; the vertical axis is truncated, running only from 7 to 9.5.", caption: none) #emph[United States unemployment.] (2013, October 14). Retrieved from #link("http://www.tradingeconomics.com/united-states/unemployment-rate")[http://www.tradingeconomics.com/united-states/unemployment-rate] 25. The Australian Institute of Criminology gathered data on the number of deaths (per 100,000 people) due to firearms during the period 1983 to 1997. Why is this a misleading or poor graph? #figure(figph[Line graph titled Deaths From Firearms (per 100,000) for 1983 to 1997 with the vertical axis reversed, running from 2 at the top to 5 at the bottom, so the death rate falling from about 4.7 to about 2.3 is drawn as a rising line.], alt: "Line graph titled Deaths From Firearms (per 100,000) for 1983 to 1997 with the vertical axis reversed, running from 2 at the top to 5 at the bottom, so the death rate falling from about 4.7 to about 2.3 is drawn as a rising line.", caption: none) (2013, September 26). Retrieved from #link("http://www.statsci.org/data/oz/firearms.html")[http://www.statsci.org/data/oz/firearms.html]. 26. Why is this a misleading or poor graph? #figure(figph[Bar chart titled Profit During First Half of Year with profits in dollars by month: January 4230, February 3760, March 2670, April labeled -1320 but drawn as a positive red bar, May 750, and June 1560.], alt: "Bar chart titled Profit During First Half of Year with profits in dollars by month: January 4230, February 3760, March 2670, April labeled -1320 but drawn as a positive red bar, May 750, and June 1560.", caption: none) Answer to Odd Numbered Exercises 1) a, c, 3) True 5) a) \\(\\begin{array}{l|llllllllllll} #linebreak() 6 & 3 & 5 & 6 & 9 \\\\ #linebreak() 7 & 0 & 1 & 3 & 5 & 6 & 9 \\\\ #linebreak() 8 & 0 & 1 & 2 & 2 & 3 & 3 & 3 & 3 & 5 & 5 & 6 & 7 \\\\ #linebreak() 9 & 4 & 6 & 9 \\\\ #linebreak() \\end{array}\\) b) c) 1 d) The sample size #emph[n]. e) 6 f) 0.24 g) 80-89 h) 90-99 i) 22 j) 70-79 7) a) 40 b) 50% 9) \\(\\begin{array}{l|lllllllllll} #linebreak() 15 & 4 & & & & & & & & & \\\\ #linebreak() 16 & 2 & 5 & 7 & 9 & & & & & & & \\\\ #linebreak() 17 & 0 & 1 & 2 & 3 & 5 & 5 & 6 & 7 & 8 & 8 & 8 \\\\ #linebreak() 18 & 2 & 4 & 5 & 5 & 5 & 6 & 8 & & & \\\\ #linebreak() 19 & & & & & & & & & & & \\\\ #linebreak() 20 & 1 & & & & & & & & & #linebreak() \\end{array}\\) 11) a) 50 b) 78 c) 16.55 13) 20% 15) a) b) c) 17) Chevy & Toyota 19) 1.5 21) a) Poland b) Greece 23) There are no labels for both axis or categories. 25) The vertical axis is reversed, making the graph appear to increase when it is actually decreasing. There are no labels for both axes. ]