Practice Maths

Interpreting and Comparing Data — Solutions

  1. Comparing Pairs of Datasets

    Pair 1 — Daily steps

    1. Range: Friend A: 3  |  Friend B: 11 ▶ View Solution
    2. Min/Max: Friend A: min=7, max=10  |  Friend B: min=3, max=14 ▶ View Solution
    3. More consistent: Friend A — range of 3 vs Friend B’s range of 11 ▶ View Solution
    4. Comparison sentence: Friend A walks consistently 7 000–10 000 steps; Friend B varies widely from 3 000 to 14 000 ▶ View Solution

    Pair 2 — Maths scores

    1. Range: 7A: 37  |  7B: 18 ▶ View Solution
    2. Lowest score: 7A: 45%  |  7B: 60% ▶ View Solution
    3. More even spread: Class 7B — range of 18 ▶ View Solution
    4. Comparison: 7B more consistent (60–78%); 7A wider spread including some as low as 45% ▶ View Solution

    Pair 3 — Puzzle times

    1. Range: Adults: 7 min  |  Teenagers: 11 min ▶ View Solution
    2. Minimum times: Adults min = 8 min; fastest adult was 6 min faster than fastest teenager ▶ View Solution
    3. Faster group: Adults — all times (8–15 min) below most teenager times (14–25 min) ▶ View Solution
    4. Context sentence: Adults consistently faster (8–15 min) compared to teenagers (14–25 min) ▶ View Solution

  2. Outliers, Shape & Spread

    1. Outlier in house prices: $890 000 — over $500 000 above the next highest value ▶ View Solution
    2. Shape of data 12–17: Roughly symmetric and bell-shaped — clusters in the middle, fewer at extremes ▶ View Solution
    3. Dataset X (range 4) vs Dataset Y (range 30): X is tightly clustered; Y has values spread far apart with much greater variability ▶ View Solution
    4. Effect of outlier on range: Range increased from 4 to 27 — one extreme value can make range very misleading ▶ View Solution

  3. Are These Statements Supported by the Data?

    Year 7: 3, 5, 4, 7, 2, 6, 5, 8, 4, 5  |  Year 8: 6, 8, 7, 9, 5, 8, 10, 7, 6, 9

    1. “Year 8 reads more”: Supported — Year 8 values (5–10) generally higher than Year 7 (2–8) ▶ View Solution
    2. “No Year 7 student read more than 8 books”: Supported — maximum in Year 7 is 8 ▶ View Solution
    3. “Year 7 has wider variety”: Supported — Year 7 range = 6; Year 8 range = 5 ▶ View Solution
    4. “All Year 8 students read at least 5 books”: Supported — minimum in Year 8 is 5 ▶ View Solution

  4. Write a Comparison & Draw Conclusions

    Player 1: 8, 12, 15, 9, 11, 14, 10, 13, 12, 16  |  Player 2: 4, 20, 8, 18, 5, 22, 7, 19, 6, 21

    1. Range: Player 1: 8  |  Player 2: 18 ▶ View Solution
    2. Min/Max: Player 1: min=8, max=16  |  Player 2: min=4, max=22 ▶ View Solution
    3. Comparison paragraph: Player 1 scores consistently (8–16, range=8); Player 2 varies widely (4–22, range=18) — Player 1 is more reliable ▶ View Solution
    4. Coach’s choice: Player 1 — range of 8 shows consistency; reliability more valuable than occasional peaks ▶ View Solution
    5. Limitations: Range only shows extremes; need mean and median; game context unknown ▶ View Solution

  5. Calculate range from a dataset

    1. 14, 22, 9, 31, 17, 25 — min = 9, max = 31, range = 22 ▶ View Solution
    2. 55, 62, 48, 70, 53, 67, 59 — min = 48, max = 70, range = 22 ▶ View Solution
    3. 3, 3, 3, 7, 7, 7 — min = 3, max = 7, range = 4 ▶ View Solution
    4. 0, 15, 30, 45, 60 — min = 0, max = 60, range = 60 ▶ View Solution
    5. 101, 99, 105, 97, 103, 100 — min = 97, max = 105, range = 8 ▶ View Solution
    6. 8, 8, 8, 8, 8 — min = 8, max = 8, range = 0 (all values identical) ▶ View Solution

  6. Describe a single dataset

    Scores: 45, 52, 67, 71, 48, 55, 63, 70, 58, 49, 68, 72

    1. Range: 27 ▶ View Solution
    2. Describe the distribution: Clusters in 45–58 and 63–72; slight gap in mid-range ▶ View Solution
    3. Any clear outliers?: No — all values within the reasonable range of 45–72 ▶ View Solution
    4. Overall description: Wide range (27); two performance groups visible at lower 50s and upper 60s ▶ View Solution

  7. Dot plots and comparison

    Team Red: 5, 8, 6, 9, 7, 8, 7, 6, 8, 5  |  Team Blue: 2, 11, 4, 13, 3, 12, 5, 10, 6, 14

    1. Range: Team Red: 4  |  Team Blue: 12 ▶ View Solution
    2. Minimum: Team Red: 5  |  Team Blue: 2 ▶ View Solution
    3. Maximum: Team Red: 9  |  Team Blue: 14 ▶ View Solution
    4. More consistent: Team Red — range of 4 vs Team Blue’s range of 12 ▶ View Solution
    5. Same total, same performance?: No — same total hides very different consistency; Red scored steadily, Blue wildly ▶ View Solution

  8. Comparing using a stem-and-leaf plot

    1. Worker weights in order: A: 12, 15, 18, 21, 24, 27, 29, 33, 36, 45  |  B: 13, 16, 19, 20, 22, 25, 28, 31, 34 ▶ View Solution
    2. Range: Worker A: 33 kg  |  Worker B: 21 kg ▶ View Solution
    3. Parcel count: Worker A: 10  |  Worker B: 9 ▶ View Solution
    4. Comparison sentences: A has wider range (12–45 kg) with one outlier at 45 kg; B more evenly spread (13–34 kg) ▶ View Solution

  9. Real-world data comparison

    Week 1: $420, $385, $450, $310, $480  |  Week 2: $395, $410, $425, $405, $415

    1. Range: Week 1: $170  |  Week 2: $30 ▶ View Solution
    2. Min/Max: Week 1: min=$310, max=$480  |  Week 2: min=$395, max=$425 ▶ View Solution
    3. More consistent: Week 2 — range of only $30 vs Week 1’s $170 ▶ View Solution
    4. $310 as an outlier: $310 is $75 below the next lowest Week 1 value; something unusual likely happened that day ▶ View Solution
    5. What else is needed to assess improvement?: Mean sales per week; which days correspond to which figures to see the trend ▶ View Solution

  10. Identify misleading conclusions

    Student A: 6, 7, 6, 8, 7 (total=34)  |  Student B: 4, 10, 5, 9, 6 (total=34)

    1. Are they equally consistent?: No — same total hides different consistency (A range=2; B range=6) ▶ View Solution
    2. Is B a better performer because B had the fastest lap?: Not a fair conclusion — one fast lap does not mean overall better performance ▶ View Solution
    3. Who is more reliable?: Student A — range = 2 vs B’s range = 6 ▶ View Solution
    4. What does the larger range tell us about B?: Highly variable lap times — sometimes very fast, sometimes very slow ▶ View Solution
    5. Who would you recommend for a long-distance race?: Student A — consistent pacing (6–8 min) is crucial for distance racing ▶ View Solution