Practice Maths

Stem-and-Leaf Plots — Solutions

  1. Create Stem-and-Leaf Plots

    1. Dataset A — Key: 2 | 7 = 27
      Stem|Leaves
      2|7   7   9
      3|3   4   5   8   9
      4|1   2   6
      5|1
      ▶ View Solution
    2. Dataset B — Key: 1 | 2 = 12
      Stem|Leaves
      0|6   7   8   9
      1|1   2   3   4   5   6   8   9
      2|0
      ▶ View Solution
    3. Dataset C — Key: 6 | 2 = 62
      Stem|Leaves
      6|2   5   8   9
      7|1   2   4   6   9
      8|1   3   4   8
      ▶ View Solution

  2. Reading Stem-and-Leaf Plots

    Plot 1 — Temperatures

    1. Days recorded: 12 days ▶ View Solution
    2. Highest temperature: 34°C ▶ View Solution
    3. Days in the 20s: 7 days ▶ View Solution
    4. Mode: 25°C ▶ View Solution

    Plot 2 — Spelling test scores

    1. Lowest score: 24 ▶ View Solution
    2. Students scoring 40 or above: 6 students ▶ View Solution
    3. Most common score (mode): 33 and 45 (bimodal) ▶ View Solution
    4. Range: 26 ▶ View Solution

    Plot 3 — Ages at event

    1. Total people: 14 people ▶ View Solution
    2. Most common age group: Teens and 30s (both have 4 values) ▶ View Solution
    3. Ages in the 30s: 30, 35, 35, 36 ▶ View Solution
    4. Range: 41 years ▶ View Solution

  3. Understanding the Plot Structure

    1. Dataset A values in order: 27, 27, 29, 33, 34, 35, 38, 39, 41, 42, 46, 51 ▶ View Solution
    2. Stem-and-leaf vs plain ordered list — what’s the advantage?: Stems group values by decade; shows distribution and clustering at a glance ▶ View Solution
    3. What error do unordered leaves cause?: Median cannot be reliably identified by counting to the middle position ▶ View Solution
    4. Dataset B most common stem: Stem 1 — 8 out of 13 values fall in 10–19 ▶ View Solution

  4. Back-to-Back Stem-and-Leaf Plot

    1. Class A scores in order: 52, 56, 59, 61, 63, 65, 68, 72, 74, 77, 80, 85
      Class B scores in order: 53, 57, 58, 60, 62, 65, 69, 71, 74, 76, 78, 82, 86
      Back-to-back stem-and-leaf plot — Key: Class A: 5 | 2 = 52  |  Class B: 5 | 3 = 53
      Class A (leaves)StemClass B (leaves)
      9   6   253   7   8
      8   5   3   160   2   5   9
      7   4   271   4   6   8
      5   082   6
      ▶ View Solution
    2. Highest score each class: Class A: 85  |  Class B: 86 ▶ View Solution
    3. Highest score each class: Class A: 85  |  Class B: 86 ▶ View Solution
    4. Scores in the 70s: Class A: 3 students  |  Class B: 4 students ▶ View Solution
    5. Range: Class A: 33  |  Class B: 33 ▶ View Solution

  5. Interpret in Context

    1. Quiz scores (11–20) — Key: 1 | 1 = 11; mode at 14–18 (each ×2); max 20; 8 students scored >15
      Stem|Leaves
      1|1   2   3   4   4   5   5   6   6   7   7   8   8   9
      2|0
      ▶ View Solution
    2. Basketball players' heights — Key: 16 | 2 = 162 cm; most values in 170s and 180s
      Stem|Leaves
      16|2   8
      17|2   5   6   9
      18|3   5   8
      19|1
      ▶ View Solution
    3. Median from stem-and-leaf plot: 74 ▶ View Solution

  6. Read the key and decode values

    1. All values: 32, 35, 38, 40, 41, 44, 47, 49, 52, 53, 56, 60, 65 ▶ View Solution
    2. Total count: 13 values ▶ View Solution
    3. Minimum: 32 ▶ View Solution
    4. Maximum: 65 ▶ View Solution
    5. Range: 33 ▶ View Solution
    6. Stem with most values: Stem 4 (five values) ▶ View Solution
    7. Median: 47 ▶ View Solution

  7. Errors in stem-and-leaf plots

    1. Missing value: 22 is missing from stem 2 (leaves should be 2, 4, 6) ▶ View Solution
    2. Other error: Leaves in stems 3 and 4 are not in ascending order ▶ View Solution
    3. Corrected plot — Key: 2 | 2 = 22
      Stem|Leaves
      2|2   4   6
      3|1   5   8   9
      4|1   2   8
      ▶ View Solution
    4. Median of corrected dataset: 36.5 ▶ View Solution

  8. Create a back-to-back plot

    1. Back-to-back plot for 7X and 7Y — Key: 7X: 1 | 2 = 12 min  |  7Y: 1 | 4 = 14 min
      7X (leaves)Stem7Y (leaves)
      8   7   5   214   9
      8   5   2   020   3   5   7   8
      5   031   2   6
      ▶ View Solution
    2. Which class read longer: Class 7Y — most values in 20s and 30s; 7X has more values in teens ▶ View Solution
    3. Range: 7X: 23 min  |  7Y: 22 min ▶ View Solution
    4. 7X students reading 20 minutes or more: 6 students ▶ View Solution

  9. Stem-and-leaf to measures

    1. Plant growth data — Key: 3 | 8 = 38 days
      Stem|Leaves
      3|8
      4|1   3   4   5   7   9
      5|0   2   3   5   6   8
      6|1   3
      ▶ View Solution
    2. Median: 50 days ▶ View Solution
    3. Mode and range: No mode; range = 25 days ▶ View Solution
    4. Do 80% of values fall between 40 and 59 days?: Yes — 12 of 15 values (80%) ▶ View Solution
    5. New median after adding values 28 and 71: 50 days (unchanged) ▶ View Solution

  10. Comparing datasets with back-to-back plots

    1. Back-to-back plot: adults vs teenagers (screen time, hours/week) — Key: Adults: 1 | 5 = 15 hr  |  Teens: 3 | 1 = 31 hr
      Adults (leaves)StemTeenagers (leaves)
      9   8   51 
      8   5   3   2   12 
      7   031   3   5   6   8
       40   2   4   5   8
      ▶ View Solution
    2. Range: Adults: 15 hr  |  Teenagers: 17 hr ▶ View Solution
    3. Two comparison observations: All teen values (31–48 hr) exceed all adult values (15–30 hr); both groups have similar range sizes ▶ View Solution
    4. Is “teens spend double the time” fully supported?: Not fully — adult max (30) vs teen min (31) is barely different; ratio is not consistently 2:1 ▶ View Solution