Practice sheet with four word problems to help students calculate the mean, median, mode, and range of different data sets.

Let's solve each problem step by step and explain the solution.

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Problem 1: Spelling Test Scores

Scores: 13, 17, 12, 19, 20, 13, 11

#### Step 1: Order the numbers
Arrange in ascending order:
11, 12, 13, 13, 17, 19, 20

#### Mean:
Sum of scores ÷ number of scores
Sum = 11 + 12 + 13 + 13 + 17 + 19 + 20 = 105
Number of scores = 7
Mean = 105 ÷ 7 = 15

#### Median:
Middle value in ordered list (7 values → 4th value)
Ordered: 11, 12, 13, 13, 17, 19, 20
Median = 13

#### Mode:
Most frequent value
13 appears twice; others appear once → Mode = 13

#### Range:
Largest − Smallest = 20 − 11 = 9

✔ Answer:
- Mean: 15
- Median: 13
- Mode: 13
- Range: 9

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Problem 2: Salamander Fishing Catches

Catches: Captain 15, Sally 12, Quadra 18, Tyger 8, Frazer 22, Quadra 18

So the data is: 15, 12, 18, 8, 22, 18

#### Step 1: Order the numbers
8, 12, 15, 18, 18, 22

#### Mean:
Sum = 8 + 12 + 15 + 18 + 18 + 22 = 93
Number of values = 6
Mean = 93 ÷ 6 = 15.5

#### Median:
Even number of values → average of 3rd and 4th values
3rd = 15, 4th = 18
Median = (15 + 18) ÷ 2 = 16.5

#### Mode:
18 appears twice; others once → Mode = 18

#### Range:
22 − 8 = 14

✔ Answer:
- Mean: 15.5
- Median: 16.5
- Mode: 18
- Range: 14

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Problem 3: Runners' Laps

Laps: 15, 12, 8, 26, 14, 11, 8, 15, 9, 10, 15

#### Step 1: Order the numbers
8, 8, 9, 10, 11, 12, 14, 15, 15, 15, 26

#### Mean:
Sum = 8 + 8 + 9 + 10 + 11 + 12 + 14 + 15 + 15 + 15 + 26 = 133
Number of runners = 11
Mean = 133 ÷ 11 ≈ 12.09 (rounded to two decimal places)

#### Median:
11 values → middle is 6th value
Ordered: 8, 8, 9, 10, 11, 12, 14, 15, 15, 15, 26
Median = 12

#### Mode:
15 appears three times → most frequent → Mode = 15

#### Range:
26 − 8 = 18

✔ Answer:
- Mean: 12.09
- Median: 12
- Mode: 15
- Range: 18

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Problem 4: Ice-Cream Sales Over Two Weeks

Week 1: 87, 75, 95, 102, 109, 61, 85
Week 2: 77, 103, 102, 79, 82, 63, 70

First, combine all sales for 2 weeks:

All sales:
87, 75, 95, 102, 109, 61, 85, 77, 103, 102, 79, 82, 63, 70

Total = 14 values

#### Step 1: Order the numbers
61, 63, 70, 75, 77, 79, 82, 85, 87, 95, 102, 102, 103, 109

#### Mean:
Sum = 61 + 63 + 70 + 75 + 77 + 79 + 82 + 85 + 87 + 95 + 102 + 102 + 103 + 109
Let’s compute step-by-step:

Grouping:
- 61 + 63 = 124
- 70 + 75 = 145 → total = 124 + 145 = 269
- 77 + 79 = 156 → 269 + 156 = 425
- 82 + 85 = 167 → 425 + 167 = 592
- 87 + 95 = 182 → 592 + 182 = 774
- 102 + 102 = 204 → 774 + 204 = 978
- 103 + 109 = 212 → 978 + 212 = 1190

Sum = 1190
Number of values = 14
Mean = 1190 ÷ 14 = 85

#### Median:
14 values → average of 7th and 8th values
Ordered list:
1. 61
2. 63
3. 70
4. 75
5. 77
6. 79
7. 82
8. 85
9. 87
10. 95
11. 102
12. 102
13. 103
14. 109

Median = (82 + 85) ÷ 2 = 83.5

#### Mode:
102 appears twice; all others once → Mode = 102

#### Range:
Largest − Smallest = 109 − 61 = 48

✔ Answer:
- Mean: 85
- Median: 83.5
- Mode: 102
- Range: 48

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✔ Final Answers Summary:

| Problem | Mean | Median | Mode | Range |
|--------|----------|----------|--------|-------|
| 1 | 15 | 13 | 13 | 9 |
| 2 | 15.5 | 16.5 | 18 | 14 |
| 3 | 12.09 | 12 | 15 | 18 |
| 4 | 85 | 83.5 | 102 | 48 |

Let me know if you'd like this formatted as a printable answer sheet!