Practice sheet featuring four real-world scenarios to help students master finding the mean, median, mode, and range.

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 when ordered. Since there are 7 values (odd), the median is the 4th value:
13

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

#### Range:
Highest – Lowest = 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 (6), so average of 3rd and 4th values:
(15 + 18) ÷ 2 = 16.5

#### Mode:
18 appears twice → 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:
Odd number of values (11), so middle (6th) value:
12

#### Mode:
15 appears three times (most frequent) → 15

#### Range:
26 – 8 = 18

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

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Problem 4: Ice-Cream Sales

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

#### Step 1: Combine all sales
List all values:
87, 75, 95, 102, 109, 61, 85, 77, 103, 102, 79, 82, 63, 70

Total = 14 values

#### Step 2: Order them
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 add step by step:

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

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

#### Median:
Even number (14), so average of 7th and 8th values:
7th = 82, 8th = 85
Median = (82 + 85) ÷ 2 = 83.5

#### Mode:
102 appears twice; others appear once → 102

#### Range:
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 |

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