Educational worksheet on stem and leaf plots covering range, mode, median, and mean calculations, with exercises for data representation and comparison.

Let's solve each section of this Stem and Leaf Plots (B) worksheet step by step.

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✔ Section A: Analyze the given stem-and-leaf plots

#### Plot 1
Key: `9 | 3` means 93

Data:
```
9 | 4 5 7 → 94, 95, 97
10 | 0 6 6 7 9 → 100, 106, 106, 107, 109
11 | 1 3 4 8 → 111, 113, 114, 118
12 | 2 6 → 122, 126
```

List in order:
94, 95, 97, 100, 106, 106, 107, 109, 111, 113, 114, 118, 122, 126

Total numbers = 14

- Range = Max – Min = 126 – 94 = 32
- Mode = Most frequent value = 106 (appears twice)
- Median: Middle value. Since 14 values, median is average of 7th and 8th:
- 7th = 107, 8th = 109 → Median = (107 + 109)/2 = 108
- Mean:
Sum = 94+95+97+100+106+106+107+109+111+113+114+118+122+126
Let's compute:
- 94+95=189; +97=286; +100=386; +106=492; +106=598; +107=705; +109=814; +111=925; +113=1038; +114=1152; +118=1270; +122=1392; +126=1518
- Sum = 1518
- Mean = 1518 / 14 ≈ 108.43

✔ Answers for Plot 1:
- Range = 32
- Mode = 106
- Median = 108
- Mean = 108.43

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#### Plot 2
Key: `7 | 8` means 7.8

Data:
```
7 | 1 1 → 7.1, 7.1
8 | 2 2 2 5 → 8.2, 8.2, 8.2, 8.5
9 | 0 9 → 9.0, 9.9
10 | 3 8 8 9 → 10.3, 10.8, 10.8, 10.9
```

List in order:
7.1, 7.1, 8.2, 8.2, 8.2, 8.5, 9.0, 9.9, 10.3, 10.8, 10.8, 10.9

Total numbers = 12

- Range = 10.9 – 7.1 = 3.8
- Mode = 8.2 (appears 3 times) → 8.2
- Median: Average of 6th and 7th values:
- 6th = 8.5, 7th = 9.0 → Median = (8.5 + 9.0)/2 = 8.75
- Mean:
Sum = 7.1+7.1 = 14.2
+8.2×3 = 24.6 → total = 38.8
+8.5 = 47.3
+9.0 = 56.3
+9.9 = 66.2
+10.3 = 76.5
+10.8×2 = 10.8+10.8=21.6 → 98.1
+10.9 = 109.0
Mean = 109.0 / 12 ≈ 9.08

✔ Answers for Plot 2:
- Range = 3.8
- Mode = 8.2
- Median = 8.75
- Mean = 9.08

---

✔ Section B: Create stem-and-leaf plots from data

#### Left Box: Data = 12.6, 9.9, 10.2, 12.0, 9.5, 10.7, 12.4, 9.6, 12.8, 10.1, 12.4

Sort data:
9.5, 9.6, 9.9, 10.1, 10.2, 10.7, 12.0, 12.4, 12.4, 12.6, 12.8

Stems: 9, 10, 12

| Stem | Leaves |
|------|--------|
| 9 | 5 6 9 |
| 10 | 1 2 7 |
| 12 | 0 4 4 6 8 |

Key: `9 | 5` means 9.5

---

#### Right Box: Data = 2.55, 2.41, 2.58, 2.45, 2.40, 2.56, 2.63, 2.49, 2.58, 2.44, 2.47

Sort:
2.40, 2.41, 2.44, 2.45, 2.47, 2.49, 2.55, 2.56, 2.58, 2.58, 2.63

Stems: 2.4, 2.5, 2.6

We’ll use tenths as stems, hundredths as leaves

| Stem | Leaves |
|------|--------|
| 2.4 | 0 1 4 5 7 9 |
| 2.5 | 5 6 8 8 |
| 2.6 | 3 |

Key: `2.4 | 0` means 2.40

---

✔ Section C: Back-to-back stem-and-leaf plot for weights

Anisa’s class:
30, 32, 36, 36, 39, 42, 42, 44, 46, 48, 48, 51, 55, 57
Sorted: 30, 32, 36, 36, 39, 42, 42, 44, 46, 48, 48, 51, 55, 57

Jo’s class:
24, 29, 30, 32, 33, 34, 35, 38, 40, 41, 44, 46, 47, 48
Sorted: 24, 29, 30, 32, 33, 34, 35, 38, 40, 41, 44, 46, 47, 48

Now create back-to-back plot with stems = tens digit, leaves = units digit

| Stem | Anisa's Class | | Jo's Class |
|------|---------------|---|------------|
| 2 | | | 4 9 |
| 3 | 0 2 6 6 9 | | 0 2 3 4 5 8 |
| 4 | 2 2 4 6 8 8 | | 0 1 4 6 7 8 |
| 5 | 1 5 7 | | |

Key: `3 | 6` means 36 kg

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✔ Section D: Back-to-back stem-and-leaf for heights (boys vs girls)

Boys:
1.33, 1.35, 1.39, 1.42, 1.44, 1.46, 1.46, 1.47, 1.49, 1.50, 1.51, 1.52, 1.58, 1.61

Girls:
1.28, 1.31, 1.31, 1.32, 1.34, 1.38, 1.39, 1.45, 1.45, 1.45, 1.52, 1.54, 1.59, 1.65

Use stem = first two digits (e.g., 1.3), leaf = last two digits (e.g., 33)

So we can use tenths as stem, hundredths as leaf

For example: 1.33 → stem = 1.3, leaf = 3

But better to use decimal stems:

| Stem | Boys (left) | | Girls (right) |
|------|-------------|---|----------------|
| 1.2 | | | 8 |
| 1.3 | 3 5 9 | | 1 1 2 4 8 9 |
| 1.4 | 2 4 6 6 7 9 | | 5 5 5 |
| 1.5 | 0 1 2 | | 2 4 9 |
| 1.6 | 1 | | 5 |

Key: `1.3 | 3` means 1.33 m

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🔍 Comment and compare boys' and girls' heights:

- Boys: Heights range from 1.33 m to 1.61 m
- Girls: Heights range from 1.28 m to 1.65 m
- Both groups have similar spread, but:
- Girls have a taller maximum height (1.65 vs 1.61)
- Boys are generally taller on average — more boys above 1.45 m
- Girls have more variability at lower end (more under 1.40 m)
- Girls have more students at 1.45 m (3 vs 0), but boys have higher values overall
- Median comparison:
- Boys: 14 values → median between 7th and 8th: 1.46 and 1.47 → ~1.465
- Girls: 14 values → 7th and 8th: both 1.45 → median = 1.45
→ Boys are slightly taller on average

✔ Conclusion: The boys tend to be taller than the girls, with a higher median and upper range. However, one girl is the tallest (1.65 m), while the tallest boy is 1.61 m.

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✔ Extension: Percentage of Anisa’s class weighing more than the mean

From earlier:
Anisa’s class weights:
30, 32, 36, 36, 39, 42, 42, 44, 46, 48, 48, 51, 55, 57

Sum =
30+32=62; +36=98; +36=134; +39=173; +42=215; +42=257; +44=301; +46=347; +48=395; +48=443; +51=494; +55=549; +57=606

Sum = 606
Number = 14
Mean = 606 / 14 ≈ 43.29 kg

Now count how many weigh more than 43.29 kg:

Values > 43.29:
44, 46, 48, 48, 51, 55, 57 → 7 values

Percentage = (7 / 14) × 100 = 50%

✔ Answer: 50% of Anisa’s class weigh more than the mean.

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✔ Final Summary of Answers

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#### Section A

Plot 1:
- Range = 32
- Mode = 106
- Median = 108
- Mean = 108.43

Plot 2:
- Range = 3.8
- Mode = 8.2
- Median = 8.75
- Mean = 9.08

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#### Section B

Left Plot:
| Stem | Leaves |
|------|--------|
| 9 | 5 6 9 |
| 10 | 1 2 7 |
| 12 | 0 4 4 6 8 |

Key: `9 | 5` means 9.5

Right Plot:
| Stem | Leaves |
|------|--------|
| 2.4 | 0 1 4 5 7 9 |
| 2.5 | 5 6 8 8 |
| 2.6 | 3 |

Key: `2.4 | 0` means 2.40

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#### Section C: Back-to-back (weights)

| Stem | Anisa's | | Jo's |
|------|---------|---|------|
| 2 | | | 4 9 |
| 3 | 0 2 6 6 9 | | 0 2 3 4 5 8 |
| 4 | 2 2 4 6 8 8 | | 0 1 4 6 7 8 |
| 5 | 1 5 7 | | |

Key: `3 | 6` means 36 kg

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#### Section D: Back-to-back (heights)

| Stem | Boys | | Girls |
|------|------|---|-------|
| 1.2 | | | 8 |
| 1.3 | 3 5 9 | | 1 1 2 4 8 9 |
| 1.4 | 2 4 6 6 7 9 | | 5 5 5 |
| 1.5 | 0 1 2 | | 2 4 9 |
| 1.6 | 1 | | 5 |

Key: `1.3 | 3` means 1.33 m

Comment: Boys are generally taller with a higher median (~1.465 m vs 1.45 m). Girls have a taller maximum (1.65 m), but more concentration around 1.45 m. Overall, boys are slightly taller on average.

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#### Extension:
Percentage of Anisa’s class weighing more than the mean: 50%

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✔ All problems solved! Let me know if you'd like this formatted as a printable answer sheet.