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

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

- Mean: The average of the numbers.
$$
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Number of values}}
$$

- Median: The middle number when the numbers are arranged in order. If there is an even number of values, the median is the average of the two middle numbers.

- Mode: The number that appears most frequently. If no number repeats, there is no mode.

- Range: The difference between the largest and smallest numbers.
$$
\text{Range} = \text{Maximum} - \text{Minimum}
$$

---

Problem 1: 10, 39, 71, 39, 76, 38, 25

Step 1: Sort the numbers
10, 25, 38, 39, 39, 71, 76

Mean:
$$
\frac{10 + 25 + 38 + 39 + 39 + 71 + 76}{7} = \frac{299}{7} \approx 42.71
$$

Median: Middle number (7th number) → 39

Mode: 39 (appears twice)

Range: 76 - 10 = 66

✔ Answer:
- Mean: 42.71
- Median: 39
- Mode: 39
- Range: 66

---

Problem 2: 18, 18, 33, 34, 54

Sorted: 18, 18, 33, 34, 54

Mean:
$$
\frac{18 + 18 + 33 + 34 + 54}{5} = \frac{157}{5} = 31.4
$$

Median: Middle number (3rd) → 33

Mode: 18 (appears twice)

Range: 54 - 18 = 36

✔ Answer:
- Mean: 31.4
- Median: 33
- Mode: 18
- Range: 36

---

Problem 3: 8, 9, 9, 8, 2, 3, 2, 3, 1

Sorted: 1, 2, 2, 3, 3, 8, 8, 9, 9

Mean:
$$
\frac{1+2+2+3+3+8+8+9+9}{9} = \frac{43}{9} \approx 4.78
$$

Median: 5th number → 3

Mode: 2, 3, 8, 9 (each appear twice) → No unique mode, or multimodal with multiple modes.

But usually, if more than one number has the highest frequency, we list them all. So mode: 2, 3, 8, 9

Range: 9 - 1 = 8

✔ Answer:
- Mean: 4.78
- Median: 3
- Mode: 2, 3, 8, 9
- Range: 8

---

Problem 4: 31, 31, 31, 34, 60

Sorted: 31, 31, 31, 34, 60

Mean:
$$
\frac{31+31+31+34+60}{5} = \frac{187}{5} = 37.4
$$

Median: 3rd number → 31

Mode: 31 (appears three times)

Range: 60 - 31 = 29

✔ Answer:
- Mean: 37.4
- Median: 31
- Mode: 31
- Range: 29

---

Problem 5: 3, 3, 4, 4, 4, 5, 7

Sorted: 3, 3, 4, 4, 4, 5, 7

Mean:
$$
\frac{3+3+4+4+4+5+7}{7} = \frac{30}{7} \approx 4.29
$$

Median: 4th number → 4

Mode: 4 (appears three times)

Range: 7 - 3 = 4

✔ Answer:
- Mean: 4.29
- Median: 4
- Mode: 4
- Range: 4

---

Problem 6: 1, 2, 3, 3, 5, 5, 9

Sorted: 1, 2, 3, 3, 5, 5, 9

Mean:
$$
\frac{1+2+3+3+5+5+9}{7} = \frac{28}{7} = 4
$$

Median: 4th number → 3

Mode: 3 and 5 (both appear twice) → Bimodal: 3 and 5

Range: 9 - 1 = 8

✔ Answer:
- Mean: 4
- Median: 3
- Mode: 3, 5
- Range: 8

---

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

Sorted: 4, 6, 6, 7, 7, 8, 8, 8

Mean:
$$
\frac{4+6+6+7+7+8+8+8}{8} = \frac{54}{8} = 6.75
$$

Median: Average of 4th and 5th → (7 + 7)/2 = 7

Mode: 8 (appears three times)

Range: 8 - 4 = 4

✔ Answer:
- Mean: 6.75
- Median: 7
- Mode: 8
- Range: 4

---

Problem 8: 34, 52, 75, 75, 85, 90

Sorted: 34, 52, 75, 75, 85, 90

Mean:
$$
\frac{34+52+75+75+85+90}{6} = \frac{411}{6} = 68.5
$$

Median: Average of 3rd and 4th → (75 + 75)/2 = 75

Mode: 75 (appears twice)

Range: 90 - 34 = 56

✔ Answer:
- Mean: 68.5
- Median: 75
- Mode: 75
- Range: 56

---

Problem 9: 4, 4, 6, 6, 8, 4, 8, 9

Sorted: 4, 4, 4, 6, 6, 8, 8, 9

Mean:
$$
\frac{4+4+4+6+6+8+8+9}{8} = \frac{45}{8} = 5.625
$$

Median: Average of 4th and 5th → (6 + 6)/2 = 6

Mode: 4 (appears three times)

Range: 9 - 4 = 5

✔ Answer:
- Mean: 5.625
- Median: 6
- Mode: 4
- Range: 5

---

Problem 10: 67, 70, 49, 95, 40, 97, 62, 54, 62

Sorted: 40, 49, 54, 62, 62, 67, 70, 95, 97

Mean:
$$
\frac{40+49+54+62+62+67+70+95+97}{9} = \frac{596}{9} \approx 66.22
$$

Median: 5th number → 62

Mode: 62 (appears twice)

Range: 97 - 40 = 57

✔ Answer:
- Mean: 66.22
- Median: 62
- Mode: 62
- Range: 57

---

✔ Final Answers Summary:

| Problem | Mean | Median | Mode | Range |
|--------|------------|--------|-------------|-------|
| 1 | 42.71 | 39 | 39 | 66 |
| 2 | 31.4 | 33 | 18 | 36 |
| 3 | 4.78 | 3 | 2, 3, 8, 9 | 8 |
| 4 | 37.4 | 31 | 31 | 29 |
| 5 | 4.29 | 4 | 4 | 4 |
| 6 | 4 | 3 | 3, 5 | 8 |
| 7 | 6.75 | 7 | 8 | 4 |
| 8 | 68.5 | 75 | 75 | 56 |
| 9 | 5.625 | 6 | 4 | 5 |
| 10 | 66.22 | 62 | 62 | 57 |

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