Practice Maths

Measures Using Technology — Solutions

  1. Calculate All Four Measures

    1. Dataset A: Mean = 25.2, Median = 25, no mode, Range = 18 ▶ View Solution
    2. Dataset B: Mean = 10.4, Median = 10, Mode = 8, Range = 7 ▶ View Solution
    3. Dataset C: Mean = 103.6, Median = 103, no mode, Range = 20 ▶ View Solution
    4. Dataset D: Mean = 3.95, Median = 3.9, no mode, Range = 3.0 ▶ View Solution

  2. Identifying Technology Errors

    1. Mean of 142: Likely extra zero typed (e.g. 140 instead of 14); correct mean = 17.5 ▶ View Solution
    2. Mean of 7.2 for data 40–60: Possible decimal entry error (e.g. 4.5 instead of 45) or formula range including empty cells read as zeros ▶ View Solution
    3. Why estimate first: Quickly spots obvious errors — if all data is 50–70 but result is 5.8, you know to re-check immediately ▶ View Solution
    4. Mean of 103.5 out of 100: Not possible — mean cannot exceed maximum score; indicates a data entry error ▶ View Solution

  3. Applied Statistical Problems

    1. Canteen sales:
      1. Measures: Mean = 37.3, Median = 38, no mode, Range = 17 ▶ View Solution
      2. Best measure for ordering: Mean — accounts for all days, gives typical daily demand (~37 sandwiches) ▶ View Solution
      3. Outlier day effect: Low day (28) pulls mean down; removing it gives mean = 38.0; range drops from 17 to 16 ▶ View Solution
    2. Basketball player:
      1. Measures (12 games): Mean = 22.0, Median = 21.5, no mode, Range = 17 ▶ View Solution
      2. Including 0s (14 games): Mean drops to 18.9; range increases to 31 ▶ View Solution
      3. Include or exclude 0s?: Exclude — represent injury absences, not playing performance ▶ View Solution
    3. Comparing two teams:
      1. Mean and range: Team A: Mean 60.0, Range 26  |  Team B: Mean 63.0, Range 4 ▶ View Solution
      2. Which to manage?: Team B — higher average (63 vs 60) and far more consistent (range 4 vs 26) ▶ View Solution

  4. Spreadsheet Formulas

    1. Mean: =AVERAGE(A1:A20) ▶ View Solution
    2. Median: =MEDIAN(A1:A20) ▶ View Solution
    3. Mode: =MODE(A1:A20) ▶ View Solution
    4. Range: =MAX(A1:A20)−MIN(A1:A20) ▶ View Solution

  5. Estimate and Check

    1. {50, 52, 48, 51, 49, 53, 47, 50}: Mean = 50.0 — matched estimate ▶ View Solution
    2. {200, 250, 180, 230, 210, 190, 220, 240}: Mean = 215.0 — matched estimate ▶ View Solution
    3. {1.1, 1.3, 0.9, 1.2, 1.0, 1.4, 0.8, 1.1}: Mean = 1.1 ▶ View Solution
    4. {72, 68, 75, 71, 69, 74, 70, 73}: Mean = 71.5 ▶ View Solution

  6. Choosing and Interpreting Measures

    1. Mean much higher than median: Data likely contains large outliers pulling mean upward; median more representative of typical value ▶ View Solution
    2. All four measures equal to 10: Yes — e.g. {5, 10, 10, 15}: mean = 10, median = 10, mode = 10, range = 10 ▶ View Solution
    3. Same mean, different range: Same typical value (mean 50); X tightly clustered (range 5), Y highly variable (range 40) ▶ View Solution
    4. Mean alone insufficient: Mean only gives average, not spread; also report range and median for a full picture ▶ View Solution

  7. Missing Values Problems

    1. Fifth number (mean 14, four known): 12 ▶ View Solution
    2. Sixth test score (mean 72): 74 ▶ View Solution
    3. Seventh value (mean 30, sum of 6 = 185): 25 ▶ View Solution
    4. Largest value (range 24, smallest 13): 37 ▶ View Solution

  8. Using Technology to Detect and Correct Errors

    1. Temperature data with error 260:
      1. Mean with 260: 41.9°C — not reasonable; most values are 22–28°C ▶ View Solution
      2. Identify and correct error: 260 is a data entry error — likely 26 with an extra zero; correct value = 26 ▶ View Solution
      3. Corrected measures: Mean = 25.2°C, Median = 25.5°C, Range = 6°C ▶ View Solution
    2. Mean of 15.3 for ages 11–14: Likely a value entered as 150+ or formula including non-age cells; check each cell for outliers and verify formula range ▶ View Solution
    3. Adding value of 62 to dataset:
      1. Effect on mean and range: Mean increases from 45.2 to 46.5; range increases from 18 to ~26 (62 becomes new maximum) ▶ View Solution

  9. Statistics in Context — Football Goals

    1. Measures for both teams: Eagles: Mean 3.2, Median 3.0, Mode 2, Range 5  |  Tigers: Mean 3.3, Median 3.0, Mode 3, Range 1 ▶ View Solution
    2. Higher average: Tigers — 3.3 vs 3.2 ▶ View Solution
    3. More consistent: Tigers — range of 1 vs Eagles’ range of 5 ▶ View Solution
    4. Spreadsheet formula for Eagles: =AVERAGE(B2:K2) ▶ View Solution

  10. Extended Technology Investigation — Homework Time

    1. Estimate the mean: ≈52–55 minutes (values range 30–90, most between 40–65) ▶ View Solution
    2. Measures: Mean = 55.6 min, Median = 52.5 min, Mode = 45 min, Range = 60 min ▶ View Solution
    3. Spreadsheet formulas: =AVERAGE(A1:A18)  /  =MEDIAN(A1:A18)  /  =MODE(A1:A18)  /  =MAX(A1:A18)−MIN(A1:A18) ▶ View Solution
    4. Does data support “about an hour” claim?: Not strongly — mean 55.6 min but mode is 45 min; “about 50–55 minutes” more accurate ▶ View Solution