Types of Data Displays — Solutions

1. Match Data to Display

   1. Goals scored by 10 players: Dot plot ▶ View Solution
   2. Favourite colour of students: Bar/column graph ▶ View Solution
   3. Temperature each day for a month: Line graph ▶ View Solution
   4. School budget split across areas: Pie chart ▶ View Solution
   5. Heights of 20 students (140–175 cm): Stem-and-leaf plot ▶ View Solution
   6. Books read by 8 students: Dot plot ▶ View Solution
   7. Family weekly income split: Pie chart ▶ View Solution
   8. Monthly rainfall over one year: Bar graph or line graph ▶ View Solution

2. Reading Values from Graphs

   Graph A — Absences

   1. Most absences: Wednesday ▶ View Solution
   2. Fewest absences: Tuesday ▶ View Solution
   3. Total absences: 55 ▶ View Solution
   4. Wednesday minus Tuesday: 7 more absences ▶ View Solution

   Graph B — Plant height

   1. Height at end of Week 3: 11 cm ▶ View Solution
   2. Most growth between two weeks: Week 2 to Week 3 ▶ View Solution
   3. No growth: Week 4 to Week 5 ▶ View Solution
   4. Total growth Week 1 to Week 6: 14 cm ▶ View Solution

   Graph C — Dot plot: pets owned

   1. Students with exactly 2 pets: 4 students ▶ View Solution
   2. Most common number of pets: 2 pets ▶ View Solution
   3. Students with 3 or more pets: 3 students ▶ View Solution
   4. Range: 5 ▶ View Solution

3. Why Does the Display Choice Matter?

   1. Why line graph for temperature but not favourite colours?: Temp is continuous over time; colours are categories with no order — connecting them is meaningless ▶ View Solution
   2. Is “sandwiches outsell pies by nearly double” correct? What’s misleading?: No — difference is only 7; y-axis starting at 80 exaggerates the gap ▶ View Solution
   3. Why line graph better than pie for test results over a semester?: Pie shows proportions at one moment; line graph shows change across tests ▶ View Solution
   4. What must every good graph include?: Title, axis labels with units, clear scale, consistent intervals, legend if needed ▶ View Solution

4. Choose, Justify & Interpret

   1. Dot plot or stem-and-leaf for 25 teenagers’ sleep hours?: Stem-and-leaf plot — less crowded for 25 values, shows distribution clearly ▶ View Solution
   2. Best display for library budget breakdown?: Pie chart — shows proportions of the total ▶ View Solution
   3. Bar or line graph for daily step counts over 2 weeks?: Line graph — continuous data over time shows the trend ▶ View Solution
   4. Misleading conclusion from ice cream sales graph with truncated axis?: April (60) was still half of February (120); truncated axis makes the drop look more dramatic ▶ View Solution

5. Identify the display type

   1. Circular graph divided into sectors: Pie chart ▶ View Solution
   2. Each data value shown as a dot above a number line: Dot plot ▶ View Solution
   3. Tens digit on the left, units as leaves on the right: Stem-and-leaf plot ▶ View Solution
   4. Rectangles comparing categories by height: Bar/column graph ▶ View Solution
   5. Points connected by a line showing change over time: Line graph ▶ View Solution
   6. Two datasets sharing a central stem, leaves going opposite directions: Back-to-back stem-and-leaf plot ▶ View Solution

6. Describe what each graph shows

   1. Most popular and least popular subject: Maths (8 students); Art (4 students) ▶ View Solution
   2. Maths as percentage of 30 students: 26.7% ▶ View Solution
   3. Bar graph or pie chart for favourite subject?: Either works; bar is easier for comparing exact values, pie for proportions ▶ View Solution
   4. Can subjects be shown on a line graph?: No — subjects are categories with no order; connecting implies a trend that doesn’t exist ▶ View Solution

7. Graph features and scale

   1. Students in the tallest bar: 25 students ▶ View Solution
   2. Temperature increase Monday to Friday: 8°C ▶ View Solution
   3. Two problems with missing title and axis labels: Cannot identify what is being measured; cannot tell what units are used ▶ View Solution
   4. Fraction not using bus or walking: 14 ▶ View Solution

8. Comparing and selecting displays

   1. Best display for Queensland annual rainfall over 20 years: Line graph — shows how values change year by year; reveals trends ▶ View Solution
   2. Bar graph vs line graph for cereal brand popularity: Bar graph works; line graph doesn’t (brands are categories with no order) ▶ View Solution
   3. Dot plot or bar graph for 15 students owning 0–6 pets: Dot plot — shows individual data points, easy to see clustering ▶ View Solution
   4. Dot plot or stem-and-leaf for finding the median quickly: Stem-and-leaf — values already ordered ▶ View Solution

9. Reading a pie chart

   1. Students travelling by bus (40% of 40): 16 students ▶ View Solution
   2. Students walking (25% of 40): 10 students ▶ View Solution
   3. Most common travel method: Bus (40%) ▶ View Solution
   4. More students by car than bike: 10 students ▶ View Solution
   5. Do all percentages add to 100%?: Yes — 40 + 25 + 30 + 5 = 100% ▶ View Solution

10. Real-world data investigation

    1. Best display for sprint times over 8 sessions: Line graph — shows improvement trend over sessions; x-axis: session (1–8), y-axis: time (seconds) ▶ View Solution
    2. Dot plot advantage and disadvantage for sprint data: Advantage: shows individual times; disadvantage: doesn’t show time order, so trend is invisible ▶ View Solution
    3. Appropriate y-axis for rubbish data (8%–45%): 0 to 50% in steps of 10 ▶ View Solution
    4. Best display for student ratings 1–5: Bar graph with ratings on x-axis, number of students on y-axis ▶ View Solution