Practice Maths

Topic Review — Displaying Data — Solutions

  1. Choose the right display

    1. Test scores of 25 students (42–98): Stem-and-leaf plot (shows numerical distribution while retaining all values) ▶ View Solution
    2. Household budget across 6 categories: Pie chart (shows proportions of a whole) ▶ View Solution
    3. Rainy days each month: Bar graph or line graph (monthly counts over time) ▶ View Solution
    4. Laps swum by 10 swimmers (values 4–9): Dot plot (small dataset, discrete values) ▶ View Solution
    5. A student's marks in 5 subjects: Bar/column graph (categorical data — each subject is a category) ▶ View Solution

  2. Create a stem-and-leaf plot

    Heights: 152, 167, 145, 173, 158, 162, 149, 165, 171, 154, 168, 147, 163, 176, 155

    1. Stem-and-leaf plot (leaves in order): ▶ View Solution
      Stem Leaves
      145   7   9
      152   4   5   8
      162   3   5   7   8
      171   3   6

      Key: 16 | 2 = 162 cm

    2. Tallest height: 176 cm ▶ View Solution
    3. Students in the 160s: 5 students (162, 163, 165, 167, 168) ▶ View Solution
    4. Range: 176 − 145 = 31 cm ▶ View Solution

  3. Read and interpret a stem-and-leaf plot

    1. Sessions recorded: 13 sessions (3 + 5 + 3 + 2 leaves) ▶ View Solution
    2. Min and Max: Min = 24 laps  |  Max = 52 laps ▶ View Solution
    3. Mode: 35 laps (appears twice in the 30s stem) ▶ View Solution
    4. Most sessions: Stem 3 (30s) with 5 sessions ▶ View Solution

  4. Identify misleading graph features

    1. Truncated y-axis: The claim is incorrect. Product A = 82, Product B = 78, so Product A sells 82 ÷ 78 ≈ 1.05 times more — about 5% more, not double. The y-axis starting at 75 makes the 4-unit difference look enormous visually. Starting at 0 would show the bars are nearly the same height. ▶ View Solution
    2. Uneven intervals: Uneven intervals mean equal changes in temperature appear as different sizes on the graph. For example, a 5° rise from 5 to 10 looks the same as a 10° rise from 10 to 20. This distorts the slope of the line and can make changes look bigger or smaller than they actually are. ▶ View Solution
    3. Three required features: Title (what the graph is about), axis labels with units, and a consistent scale. A legend is also required if there are multiple datasets. ▶ View Solution

  5. Compare two datasets

    Athlete A: 11.2–11.6 s  |  Athlete B: 10.8–12.4 s

    1. Range: Athlete A: 11.6 − 11.2 = 0.4 s  |  Athlete B: 12.4 − 10.8 = 1.6 s ▶ View Solution
    2. More consistent: Athlete A — range of only 0.4 s means times vary very little. Athlete B's range of 1.6 s is four times larger, showing much less consistency. ▶ View Solution
    3. Fastest single time: Athlete B with 10.8 s ▶ View Solution
    4. Two-sentence comparison: Athlete A is highly consistent, always running between 11.2 and 11.6 seconds, making them reliable in competition. Athlete B can run faster (10.8 s) but also much slower (12.4 s), making their performance unpredictable. ▶ View Solution

  6. Interpret data in context

    1. Bird counts: Pattern 1: Counts peak from month 4 to 7 (34–41 birds) — this could be breeding season or migration arrival, when birds are most active or present. Pattern 2: Counts are lowest from month 11 to month 2 (9–14 birds) — this could be winter when migratory birds have left or birds are less visible. ▶ View Solution
    2. Outlier effect: Without the outlier (52): data is symmetric, clustered around 7–8, range = 9 − 5 = 4. With the outlier: range = 52 − 5 = 47 — the spread appears enormous. The outlier completely changes the description of spread even though 9 out of 10 values are tightly grouped. ▶ View Solution
    3. Homework distribution: The data is right-skewed: most values are low (0–25 minutes) with one outlier at 60 minutes. The range is 60 − 0 = 60 minutes. Most students spent 0–30 minutes, but there are two students who did no homework. The outlier (60 min) is the single most extreme value. This suggests most students do little or moderate homework, with one student doing significantly more. ▶ View Solution

  7. Describe graphs

    1. Two features a pie chart can show that a stem-and-leaf plot cannot: proportions/percentages of a whole; which category takes the largest or smallest share ▶ View Solution
    2. One advantage of a stem-and-leaf plot over a bar chart: Shows every individual data value — exact values are retained and you can find the median directly by counting ▶ View Solution
    3. Bar chart vs histogram: A bar chart shows separate categories with gaps between bars; a histogram shows continuous numerical data grouped into equal intervals with no gaps ▶ View Solution
    4. True — a pie chart can display daily activities in hours as proportions of a 24-hour day (e.g. sleep 8 h = 13 of the circle) ▶ View Solution

  8. Dot plot — quiz scores

    Scores: 5, 7, 6, 8, 7, 9, 7, 6, 8, 7, 5, 10, 8, 7, 6

    1. Dot plot (5: 2 dots  |  6: 3 dots  |  7: 5 dots  |  8: 3 dots  |  9: 1 dot  |  10: 1 dot): ▶ View Solution 5 6 7 8 9 10 Quiz Score
    2. Mode: 7 (appears 5 times) ▶ View Solution
    3. Students scoring 8 or above: 5 students (3 scored 8, 1 scored 9, 1 scored 10) ▶ View Solution
    4. Fraction below 7: 13 — 5 students scored 5 or 6 out of 15 total  (5 ÷ 15 = 13) ▶ View Solution

  9. Book survey

    Data: 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 7, 8, 12

    1. Best display: Dot plot — small discrete values, shows distribution clearly while retaining every individual data point ▶ View Solution
    2. Frequency table: 0–2: 9 students  |  3–5: 7 students  |  6–8: 3 students  |  9+: 1 student ▶ View Solution
    3. Effect of outlier on mean: Sum = 71; mean = 71 ÷ 20 = 3.55. Without 12: sum = 59, mean = 59 ÷ 19 ≈ 3.1. Most students read 0–5 books, so the outlier pulls the mean above what is typical — median would be more representative here ▶ View Solution

  10. Design a survey and display

    1. Two survey questions: (1) “How do you travel to school?” with options Walk / Bike / Car / Bus / Other; (2) “How many minutes does your journey take?” ▶ View Solution
    2. Best display for “how do you get to school?”: Bar/column graph or pie chart — travel method is categorical data. Bar graph is better for comparing exact counts; pie chart shows what fraction of students use each method ▶ View Solution
    3. Bias and fix: Survey could be biased if conducted near one entrance (e.g. the bus stop) — students who walk or are driven would be under-represented. Fix: randomly select students from different homerooms so all travel types have an equal chance of being included ▶ View Solution