Practice Maths

Mixed Data Analysis — Solutions

  1. Calculate All Four Measures

    1. Dataset A — Goals: Mean = 3.6, Median = 3.5, Mode = 5, Range = 5 ▶ View Solution
    2. Dataset B — Heights: Mean = 156 cm, Median = 153.5 cm, Mode = 152 cm, Range = 24 cm ▶ View Solution
    3. Dataset C — Puzzle time: Mean = 10.1 min, Median = 9.5 min, Mode = 8 min, Range = 9 min ▶ View Solution

  2. Choose the Best Display Type

    1. Pets per student: Column graph — shows frequency of each discrete value clearly ▶ View Solution
    2. Favourite sport percentages: Pie chart or divided bar — shows parts of a whole ▶ View Solution
    3. Heights of 30 students: Stem-and-leaf plot or histogram — shows shape of distribution and spread ▶ View Solution
    4. Hourly temperature over 24 hours: Line graph — shows how a quantity changes continuously over time ▶ View Solution

  3. Full Analysis

    1. Stem-and-leaf plot: 0 | 1 2 3 3 4 4 5 5 6 6 7 7 7 8 9    Key: 0|1 = 1 ▶ View Solution
    2. All four measures: Mean = 5.1, Median = 5, Mode = 7, Range = 8 ▶ View Solution
    3. Three conclusions: 1. Typical student read about 5 books. 2. Mode of 7 suggests a group of keen readers. 3. Range of 8 shows considerable variation (1 to 9 books) ▶ View Solution

  4. Sort and Calculate

    1. Dataset D — Daily steps: Mean = 7 525, Median = 7 750, Mode = 8 400, Range = 3 100 ▶ View Solution
    2. Dataset E — Spelling tests: Mean = 16.8, Median = 16.5, Mode = 14, Range = 6 ▶ View Solution
    3. Dataset F — Chess club ages: Mean = 13.5, Median = 13.5, Mode = 12, Range = 4 ▶ View Solution

  5. Which Measure of Centre?

    1. House prices with outlier: Median — $1 800 000 outlier inflates mean far above typical price ▶ View Solution
    2. Shoe sizes in class: Mode — most common size for practical decisions; mean may not be a real shoe size ▶ View Solution
    3. 1 km run times: Mean — tightly clustered data with no extreme outliers ▶ View Solution
    4. Number of siblings: Median or mode — outlier of 4 siblings would inflate the mean ▶ View Solution

  6. Outliers and Their Effect

    1. Dataset with outlier 50: Mean most affected (9.8 with vs 5.3 without); median barely changes (5.5 vs 5) ▶ View Solution
    2. Student test with score of 3: Mean drops by about 8.5 marks (from 71.3 to 62.75) when the score of 3 is included ▶ View Solution
    3. Why median is preferred: Median depends only on position; one extreme value can’t shift it significantly. Mean uses every value, so an outlier directly changes the result ▶ View Solution
    4. Real-world example: CEO salary — mean salary far above what typical employees earn; median better reflects a worker’s pay ▶ View Solution

  7. Stem-and-Leaf Plots

    1. Stem-and-leaf for given dataset: 2 | 6 7 9  /  3 | 1 3 4 7 8  /  4 | 1 4 5 8  /  5 | 0 2 6    Key: 2|6 = 26 ▶ View Solution
    2. Median and mode from plot: Median = 38, no mode ▶ View Solution
    3. Mean and range: Mean = 39.4, Range = 30 ▶ View Solution
    4. Stem with most values: Stem 3 — five values (31, 33, 34, 37, 38) ▶ View Solution
    5. List data from given plot: 21, 24, 28, 30, 33, 35, 39, 42, 46, 51, 57 ▶ View Solution
    6. Median, mode, range from plot in (e): Median = 35, no mode, Range = 36 ▶ View Solution

  8. Compare Two Classes

    1. List all scores: Class A: 22, 25, 28, 29, 31, 34, 36, 37, 40, 43, 45, 48, 52  |  Class B: 23, 26, 31, 34, 35, 38, 42, 44, 47, 50 ▶ View Solution
    2. Mean and range for each class: Class A: Mean 36.2, Range 30  |  Class B: Mean 37.0, Range 27 ▶ View Solution
    3. Median for each class: Class A: 36  |  Class B: 36.5 ▶ View Solution
    4. Which class performed better?: Class B — higher mean (37.0 vs 36.2) and higher median (36.5 vs 36) ▶ View Solution
    5. More spread: Class A — range 30 vs Class B’s 27 ▶ View Solution

  9. Interpreting a Column Graph

    1. Total students: 140 students ▶ View Solution
    2. Percentage by bus: 32.1% ▶ View Solution
    3. Fraction by car or walk: 1328 ▶ View Solution
    4. Two methods accounting for more than half: Bus + Car = 82 of 140 (58.6%) ▶ View Solution
    5. Mode is “Bus”: Yes — bus has the highest frequency (45 students) ▶ View Solution
    6. Two conclusions: 1. Bus most common (32.1%) — public transport important for Year 7. 2. Only 8.6% cycle — minority choice, possibly due to distance or safety ▶ View Solution

  10. Full Statistical Investigation

    1. Stem-and-leaf plot: 0 | 0 0 0  /  1 | 0 0 5 5 5  /  2 | 0 0 0 5 5  /  3 | 0 0 0  /  4 | 0 5 5  /  5 |  /  6 | 0    Key: 1|0 = 10 minutes ▶ View Solution
    2. All four measures: Mean = 22.75 min, Median = 20 min, Mode = 0/15/20/30 (multimodal), Range = 60 min ▶ View Solution
    3. Does the data support the claim?: No — 17 of 20 students read some amount; mean 22.75 min and median 20 min show most students do read for pleasure ▶ View Solution
    4. Potential outliers and effect on mean: 60 min is a potential outlier; removing it drops mean from 22.75 to 20.8 min ▶ View Solution
    5. Brief report: Average of ~23 min/day; median 20 min; most read 15–30 min daily; range of 60 min shows wide variation; most students in this group do engage in daily pleasure reading ▶ View Solution