Mean Median Mode Range Worksheets - Math Monks - Free Printable

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.
$$
\text{Range} = \text{Maximum} - \text{Minimum}
$$

---

1. 10, 39, 71, 39, 76, 38, 25

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

- Mean:
$$
\frac{10 + 25 + 38 + 39 + 39 + 71 + 76}{7} = \frac{298}{7} \approx 42.57
$$

- Median: Middle number (4th) → 39

- Mode: 39 appears twice → 39

- Range: $76 - 10 = 66$

✔ Answer:
Mean: 42.57, Median: 39, Mode: 39, Range: 66

---

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 (3rd) → 33

- Mode: 18 appears twice → 18

- Range: $54 - 18 = 36$

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

---

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 all appear twice → No unique mode (or multimodal)

But typically, if multiple values tie for most frequent, we say "no mode" or list all modes. Here, since all appear twice, no mode (or modes: 2, 3, 8, 9). But standard answer often says no mode.

- Range: $9 - 1 = 8$

✔ Answer:
Mean: 4.78, Median: 3, Mode: No mode, Range: 8

---

4. 31, 31, 31, 34, 60

Sorted: 31, 31, 31, 34, 60

- Mean:
$$
\frac{31+31+31+34+60}{5} = \frac{227}{5} = 45.4
$$

- Median: 3rd number → 31

- Mode: 31 appears 3 times → 31

- Range: $60 - 31 = 29$

✔ Answer:
Mean: 45.4, Median: 31, Mode: 31, Range: 29

---

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 3 times → 4

- Range: $7 - 3 = 4$

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

---

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 → No unique mode (bimodal: 3 and 5)

- Range: $9 - 1 = 8$

✔ Answer:
Mean: 4, Median: 3, Mode: 3 and 5 (or no mode), Range: 8

---

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 3 times → 8

- Range: $8 - 4 = 4$

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

---

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 → 75

- Range: $90 - 34 = 56$

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

---

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 3 times → 4

- Range: $9 - 4 = 5$

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

---

10. 67, 70, 49, 95, 40, 97, 62, 54, 62

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

- Mean:
$$
\frac{40+49+54+62+62+67+70+95+97}{9} = \frac{606}{9} = 67.33\overline{3}
$$

- Median: 5th number → 62

- Mode: 62 appears twice → 62

- Range: $97 - 40 = 57$

✔ Answer:
Mean: 67.33, Median: 62, Mode: 62, Range: 57

---

## ✔ Final Answers:

| # | Mean | Median | Mode | Range |
|---|----------|--------|------------|-------|
| 1 | 42.57 | 39 | 39 | 66 |
| 2 | 31.4 | 33 | 18 | 36 |
| 3 | 4.78 | 3 | No mode | 8 |
| 4 | 45.4 | 31 | 31 | 29 |
| 5 | 4.29 | 4 | 4 | 4 |
| 6 | 4 | 3 | 3, 5 (or no mode) | 8 |
| 7 | 6.75 | 7 | 8 | 4 |
| 8 | 68.5 | 75 | 75 | 56 |
| 9 | 5.625 | 6 | 4 | 5 |
|10 | 67.33 | 62 | 62 | 57 |

> Note: For #3, #6, and others with multiple modes, you can write "No mode" or list the modes. In many schools, they expect "No mode" unless specified otherwise.

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