Practice Maths

Connecting Displays and Measures — Solutions

  1. Calculate All Four Measures

    1. {8, 12, 15, 9, 11, 12, 14, 10}: Mean = 11.375, Median = 11.5, Mode = 12, Range = 7 ▶ View Solution
    2. {3, 7, 3, 9, 5, 3, 8, 6, 4, 7}: Mean = 5.5, Median = 5.5, Mode = 3, Range = 6 ▶ View Solution
    3. {45, 52, 48, 61, 45, 58, 52, 49, 45, 60}: Mean = 51.5, Median = 50.5, Mode = 45, Range = 16 ▶ View Solution

  2. Measures from a Stem-and-Leaf Plot

    1. Values in order: 16, 18, 19, 21, 24, 24, 27, 32, 35, 38, 40, 43, 51 ▶ View Solution
    2. All four measures: Mean ≈29.8, Median = 27, Mode = 24, Range = 35 ▶ View Solution
    3. Summary: Typical age around 27–30; median 27 suggests most volunteers in their 20s–30s; range 35 shows wide variety from teens to 50s ▶ View Solution

  3. What Does Each Measure Tell You?

    1. Mean $650k vs Median $480k: Right-skewed — luxury outliers inflate mean; use median for typical home price ▶ View Solution
    2. Range of 0: All values are identical ▶ View Solution
    3. {5, 5, 5, 5, 100}: Mean = 24, Median = 5, Mode = 5, Range = 95 — mode and median best describe data; outlier 100 makes mean misleading ▶ View Solution

  4. Compare Two Classes

    7C sorted: 54, 58, 61, 63, 65, 68, 70, 71, 72, 74  |  7D sorted: 42, 46, 50, 59, 65, 75, 78, 82, 88, 90

    1. All measures: 7C: Mean 65.6, Median 66.5, Range 20  |  7D: Mean 67.5, Median 70, Range 48 ▶ View Solution
    2. Better and more consistent: 7D slightly better overall (mean 67.5 vs 65.6); 7C far more consistent (range 20 vs 48) ▶ View Solution
    3. Fairness of “highest score” argument: Not fair — one high score doesn’t represent the class; means differ by only 1.9 points; 7D also has the lowest score ▶ View Solution

  5. Complete the Measures Table

    1. {4, 6, 6, 8, 10}: Mean = 6.8, Median = 6, Mode = 6 (given), Range = 6 ▶ View Solution
    2. {1, 3, 3, 5, 7, 9}: Mean ≈4.67 (given), Median = 4, Mode = 3, Range = 8 ▶ View Solution
    3. {20, 20, 20, 20}: Mean = 20, Median = 20, Mode = 20, Range = 0 (given) ▶ View Solution

  6. True or False?

    1. Mean = median means perfectly symmetric: False — common indicator of symmetry but not a guarantee ▶ View Solution
    2. Mode most useful for numeric data with no repeats: False — if all values appear once there is no mode ▶ View Solution
    3. Range from stem-and-leaf without listing all values: True — only need largest and smallest leaves ▶ View Solution
    4. Two datasets can share same mean, median, range: True — e.g. {3, 5, 7} and {4, 5, 6} ▶ View Solution
    5. Mean > median implies right skew: True — large values on the right pull mean above median ▶ View Solution

  7. Spot the Error

    1. Error: Missed the second 40 — stem 4 has leaves 0, 0, 6 (three values: 40, 40, 46) ▶ View Solution
    2. Correct values and measures: Values: 23, 25, 28, 31, 34, 40, 40, 46 — Mean = 33.375, Median = 32.5, Mode = 40, Range = 23 ▶ View Solution

  8. Choose the Best Measure

    1. Typical weekly wage: Median (reason given) — wages skewed by high earners; median gives fairer picture ▶ View Solution
    2. Most popular car colour: Mode (given) — categorical data; mean and median don’t apply ▶ View Solution
    3. Class test results, no outliers: Mean — no outliers; uses all scores for a precise summary ▶ View Solution
    4. Property prices with one mansion: Median — mansion outlier would inflate mean far above typical price ▶ View Solution

  9. Reading from a Dot Plot

    1. Data values: 1, 2, 2, 3, 3, 3, 4, 4, 5, 6, 6, 7 ▶ View Solution
    2. All four measures: Mean ≈3.83, Median = 3.5, Mode = 3, Range = 6 ▶ View Solution
    3. What mode tells us: Most students read 3 books — most common reading total for the term ▶ View Solution

  10. Extended Comparison

    1. All measures: Morning: Mean 9.625, Median 9.5, Mode 8/9/10, Range 4  |  Evening: Mean 10.0, Median 10.0, no mode, Range 10 ▶ View Solution
    2. More consistent: Morning — range of 4 vs evening’s range of 10 ▶ View Solution
    3. Short report: Evening group averaged slightly more laps (10.0 vs 9.6) but varied far more (range 10 vs 4); morning group more reliable; choice depends on whether consistency or peak performance matters more ▶ View Solution