Math worksheet for calculating mean, median, and mode of number sets.

Let's solve each problem step by step. For each set of numbers, we will calculate:

- Mean: The average of the numbers = (Sum of all numbers) ÷ (Number of values)
- Median: The middle number when the numbers are arranged in order. If there is an even number of values, it's the average of the two middle numbers.
- Mode: The number that appears most frequently. If no number repeats, there is no mode.

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Problem 1: 32, 33, 22, 85, 58

Step 1: Order the numbers:
22, 32, 33, 58, 85

Mean:
(22 + 32 + 33 + 58 + 85) ÷ 5 = 230 ÷ 5 = 46

Median:
Middle number (3rd in ordered list): 33

Mode:
No number repeats → No mode

✔ Answer: Mean: 46, Median: 33, Mode: No mode

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Problem 2: 18, 18, 26, 36, 64

Order: 18, 18, 26, 36, 64

Mean:
(18 + 18 + 26 + 36 + 64) ÷ 5 = 162 ÷ 5 = 32.4

Median:
Middle number: 26

Mode:
18 appears twice → 18

✔ Answer: Mean: 32.4, Median: 26, Mode: 18

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Problem 3: 58, 84, 90, 90, 97

Order: 58, 84, 90, 90, 97

Mean:
(58 + 84 + 90 + 90 + 97) ÷ 5 = 419 ÷ 5 = 83.8

Median:
Middle number: 90

Mode:
90 appears twice → 90

✔ Answer: Mean: 83.8, Median: 90, Mode: 90

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Problem 4: 9, 15, 28, 10, 8

Order: 8, 9, 10, 15, 28

Mean:
(8 + 9 + 10 + 15 + 28) ÷ 5 = 70 ÷ 5 = 14

Median:
Middle number: 10

Mode:
All numbers appear once → No mode

✔ Answer: Mean: 14, Median: 10, Mode: No mode

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Problem 5: 21, 15, 16, 25, 13, 18

Order: 13, 15, 16, 18, 21, 25

Mean:
(13 + 15 + 16 + 18 + 21 + 25) ÷ 6 = 108 ÷ 6 = 18

Median:
Even count → average of 3rd and 4th: (16 + 18) ÷ 2 = 17

Mode:
All numbers appear once → No mode

✔ Answer: Mean: 18, Median: 17, Mode: No mode

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Problem 6: 53, 44, 10, 45, 59, 97, 77

Order: 10, 44, 45, 53, 59, 77, 97

Mean:
(10 + 44 + 45 + 53 + 59 + 77 + 97) ÷ 7 = 435 ÷ 7 ≈ 62.14

Median:
Middle number (4th): 53

Mode:
All unique → No mode

✔ Answer: Mean: ~62.14, Median: 53, Mode: No mode

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Problem 7: 5, 3, 2, 6, 5, 2, 5

Order: 2, 2, 3, 5, 5, 5, 6

Mean:
(2 + 2 + 3 + 5 + 5 + 5 + 6) ÷ 7 = 28 ÷ 7 = 4

Median:
Middle number (4th): 5

Mode:
5 appears 3 times → 5

✔ Answer: Mean: 4, Median: 5, Mode: 5

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Problem 8: 6, 6, 6, 7, 7, 5, 4

Order: 4, 5, 6, 6, 6, 7, 7

Mean:
(4 + 5 + 6 + 6 + 6 + 7 + 7) ÷ 7 = 41 ÷ 7 ≈ 5.86

Median:
Middle number (4th): 6

Mode:
6 appears 3 times → 6

✔ Answer: Mean: ~5.86, Median: 6, Mode: 6

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Problem 9: 9, 19, 16, 9, 16, 2, 14, 8, 2

Order: 2, 2, 8, 9, 9, 14, 16, 16, 19

Mean:
(2 + 2 + 8 + 9 + 9 + 14 + 16 + 16 + 19) ÷ 9 = 95 ÷ 9 ≈ 10.56

Median:
Middle number (5th): 9

Mode:
2, 9, 16 each appear twice → No single mode (bimodal or multimodal). But if only one mode is expected, write No mode or list multiple modes.

But typically, if more than one value has the highest frequency, we say "no mode" unless specified otherwise.

Here: 2, 9, 16 — all appear twice → No mode

✔ Answer: Mean: ~10.56, Median: 9, Mode: No mode

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Problem 10: 19, 5, 9, 12, 10, 5

Order: 5, 5, 9, 10, 12, 19

Mean:
(5 + 5 + 9 + 10 + 12 + 19) ÷ 6 = 60 ÷ 6 = 10

Median:
Even count → average of 3rd and 4th: (9 + 10) ÷ 2 = 9.5

Mode:
5 appears twice → 5

✔ Answer: Mean: 10, Median: 9.5, Mode: 5

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✔ Final Answers:

| Problem | Mean | Median | Mode |
|--------|------------|----------|----------|
| 1 | 46 | 33 | No mode |
| 2 | 32.4 | 26 | 18 |
| 3 | 83.8 | 90 | 90 |
| 4 | 14 | 10 | No mode |
| 5 | 18 | 17 | No mode |
| 6 | 62.14 | 53 | No mode |
| 7 | 4 | 5 | 5 |
| 8 | 5.86 | 6 | 6 |
| 9 | 10.56 | 9 | No mode |
| 10 | 10 | 9.5 | 5 |

> ⚠️ Note: Some decimals are rounded to two decimal places for clarity.

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