Printable worksheet for finding mean, median, mode, and range of number sets.

To solve the problem, we need to calculate the mean, median, mode, and range for each set of numbers. Let's go through each set step by step.

Definitions:

1. Mean: The average of the numbers.
\[
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of values}}
\]

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

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

4. Range: The difference between the largest and smallest numbers.
\[
\text{Range} = \text{Largest number} - \text{Smallest number}
\]

---

Set 1: \( 24, 31, 12, 38, 12, 15 \)

#### Step 1: Mean
\[
\text{Sum} = 24 + 31 + 12 + 38 + 12 + 15 = 132
\]
\[
\text{Mean} = \frac{132}{6} = 22
\]

#### Step 2: Median
Arrange in ascending order: \( 12, 12, 15, 24, 31, 38 \)
Middle numbers: \( 15 \) and \( 24 \)
\[
\text{Median} = \frac{15 + 24}{2} = 19.5
\]

#### Step 3: Mode
The number that appears most frequently is \( 12 \).
\[
\text{Mode} = 12
\]

#### Step 4: Range
Largest number: \( 38 \)
Smallest number: \( 12 \)
\[
\text{Range} = 38 - 12 = 26
\]

Results for Set 1:
- Mean: \( 22 \)
- Median: \( 19.5 \)
- Mode: \( 12 \)
- Range: \( 26 \)

---

Set 2: \( 5, 28, 16, 32, 5, 16, 48, 29, 5, 35 \)

#### Step 1: Mean
\[
\text{Sum} = 5 + 28 + 16 + 32 + 5 + 16 + 48 + 29 + 5 + 35 = 227
\]
\[
\text{Mean} = \frac{227}{10} = 22.7
\]

#### Step 2: Median
Arrange in ascending order: \( 5, 5, 5, 16, 16, 28, 29, 32, 35, 48 \)
Middle numbers: \( 16 \) and \( 28 \)
\[
\text{Median} = \frac{16 + 28}{2} = 22
\]

#### Step 3: Mode
The number that appears most frequently is \( 5 \).
\[
\text{Mode} = 5
\]

#### Step 4: Range
Largest number: \( 48 \)
Smallest number: \( 5 \)
\[
\text{Range} = 48 - 5 = 43
\]

Results for Set 2:
- Mean: \( 22.7 \)
- Median: \( 22 \)
- Mode: \( 5 \)
- Range: \( 43 \)

---

Set 3: \( 53, 13, 34, 41, 26, 61, 34, 13, 69 \)

#### Step 1: Mean
\[
\text{Sum} = 53 + 13 + 34 + 41 + 26 + 61 + 34 + 13 + 69 = 344
\]
\[
\text{Mean} = \frac{344}{9} \approx 38.22
\]

#### Step 2: Median
Arrange in ascending order: \( 13, 13, 26, 34, 34, 41, 53, 61, 69 \)
Middle number: \( 34 \)
\[
\text{Median} = 34
\]

#### Step 3: Mode
The numbers \( 13 \) and \( 34 \) both appear twice.
\[
\text{Mode} = 13, 34
\]

#### Step 4: Range
Largest number: \( 69 \)
Smallest number: \( 13 \)
\[
\text{Range} = 69 - 13 = 56
\]

Results for Set 3:
- Mean: \( 38.22 \)
- Median: \( 34 \)
- Mode: \( 13, 34 \)
- Range: \( 56 \)

---

Set 4: \( 85, 58, 72, 85, 46, 93 \)

#### Step 1: Mean
\[
\text{Sum} = 85 + 58 + 72 + 85 + 46 + 93 = 439
\]
\[
\text{Mean} = \frac{439}{6} \approx 73.17
\]

#### Step 2: Median
Arrange in ascending order: \( 46, 58, 72, 85, 85, 93 \)
Middle numbers: \( 72 \) and \( 85 \)
\[
\text{Median} = \frac{72 + 85}{2} = 78.5
\]

#### Step 3: Mode
The number that appears most frequently is \( 85 \).
\[
\text{Mode} = 85
\]

#### Step 4: Range
Largest number: \( 93 \)
Smallest number: \( 46 \)
\[
\text{Range} = 93 - 46 = 47
\]

Results for Set 4:
- Mean: \( 73.17 \)
- Median: \( 78.5 \)
- Mode: \( 85 \)
- Range: \( 47 \)

---

Set 5: \( 92, 63, 22, 80, 63, 71, 44, 35 \)

#### Step 1: Mean
\[
\text{Sum} = 92 + 63 + 22 + 80 + 63 + 71 + 44 + 35 = 470
\]
\[
\text{Mean} = \frac{470}{8} = 58.75
\]

#### Step 2: Median
Arrange in ascending order: \( 22, 35, 44, 63, 63, 71, 80, 92 \)
Middle numbers: \( 63 \) and \( 63 \)
\[
\text{Median} = \frac{63 + 63}{2} = 63
\]

#### Step 3: Mode
The number that appears most frequently is \( 63 \).
\[
\text{Mode} = 63
\]

#### Step 4: Range
Largest number: \( 92 \)
Smallest number: \( 22 \)
\[
\text{Range} = 92 - 22 = 70
\]

Results for Set 5:
- Mean: \( 58.75 \)
- Median: \( 63 \)
- Mode: \( 63 \)
- Range: \( 70 \)

---

Set 6: \( 39, 82, 74, 96, 64, 52, 74 \)

#### Step 1: Mean
\[
\text{Sum} = 39 + 82 + 74 + 96 + 64 + 52 + 74 = 481
\]
\[
\text{Mean} = \frac{481}{7} \approx 68.71
\]

#### Step 2: Median
Arrange in ascending order: \( 39, 52, 64, 74, 74, 82, 96 \)
Middle number: \( 74 \)
\[
\text{Median} = 74
\]

#### Step 3: Mode
The number that appears most frequently is \( 74 \).
\[
\text{Mode} = 74
\]

#### Step 4: Range
Largest number: \( 96 \)
Smallest number: \( 39 \)
\[
\text{Range} = 96 - 39 = 57
\]

Results for Set 6:
- Mean: \( 68.71 \)
- Median: \( 74 \)
- Mode: \( 74 \)
- Range: \( 57 \)

---

Set 7: \( 72, 43, 15, 66, 32, 72, 52, 19, 28, 81 \)

#### Step 1: Mean
\[
\text{Sum} = 72 + 43 + 15 + 66 + 32 + 72 + 52 + 19 + 28 + 81 = 480
\]
\[
\text{Mean} = \frac{480}{10} = 48
\]

#### Step 2: Median
Arrange in ascending order: \( 15, 19, 28, 32, 43, 52, 66, 72, 72, 81 \)
Middle numbers: \( 43 \) and \( 52 \)
\[
\text{Median} = \frac{43 + 52}{2} = 47.5
\]

#### Step 3: Mode
The number that appears most frequently is \( 72 \).
\[
\text{Mode} = 72
\]

#### Step 4: Range
Largest number: \( 81 \)
Smallest number: \( 15 \)
\[
\text{Range} = 81 - 15 = 66
\]

Results for Set 7:
- Mean: \( 48 \)
- Median: \( 47.5 \)
- Mode: \( 72 \)
- Range: \( 66 \)

---

Set 8: \( 40, 90, 36, 68, 90, 11, 88, 54 \)

#### Step 1: Mean
\[
\text{Sum} = 40 + 90 + 36 + 68 + 90 + 11 + 88 + 54 = 487
\]
\[
\text{Mean} = \frac{487}{8} = 60.875
\]

#### Step 2: Median
Arrange in ascending order: \( 11, 36, 40, 54, 68, 88, 90, 90 \)
Middle numbers: \( 54 \) and \( 68 \)
\[
\text{Median} = \frac{54 + 68}{2} = 61
\]

#### Step 3: Mode
The number that appears most frequently is \( 90 \).
\[
\text{Mode} = 90
\]

#### Step 4: Range
Largest number: \( 90 \)
Smallest number: \( 11 \)
\[
\text{Range} = 90 - 11 = 79
\]

Results for Set 8:
- Mean: \( 60.875 \)
- Median: \( 61 \)
- Mode: \( 90 \)
- Range: \( 79 \)

---

Set 9: \( 12, 46, 32, 18, 26, 41, 46 \)

#### Step 1: Mean
\[
\text{Sum} = 12 + 46 + 32 + 18 + 26 + 41 + 46 = 221
\]
\[
\text{Mean} = \frac{221}{7} \approx 31.57
\]

#### Step 2: Median
Arrange in ascending order: \( 12, 18, 26, 32, 41, 46, 46 \)
Middle number: \( 32 \)
\[
\text{Median} = 32
\]

#### Step 3: Mode
The number that appears most frequently is \( 46 \).
\[
\text{Mode} = 46
\]

#### Step 4: Range
Largest number: \( 46 \)
Smallest number: \( 12 \)
\[
\text{Range} = 46 - 12 = 34
\]

Results for Set 9:
- Mean: \( 31.57 \)
- Median: \( 32 \)
- Mode: \( 46 \)
- Range: \( 34 \)

---

Set 10: \( 63, 40, 51, 70, 36, 21, 51, 28, 19 \)

#### Step 1: Mean
\[
\text{Sum} = 63 + 40 + 51 + 70 + 36 + 21 + 51 + 28 + 19 = 389
\]
\[
\text{Mean} = \frac{389}{9} \approx 43.22
\]

#### Step 2: Median
Arrange in ascending order: \( 19, 21, 28, 36, 40, 51, 51, 63, 70 \)
Middle number: \( 40 \)
\[
\text{Median} = 40
\]

#### Step 3: Mode
The number that appears most frequently is \( 51 \).
\[
\text{Mode} = 51
\]

#### Step 4: Range
Largest number: \( 70 \)
Smallest number: \( 19 \)
\[
\text{Range} = 70 - 19 = 51
\]

Results for Set 10:
- Mean: \( 43.22 \)
- Median: \( 40 \)
- Mode: \( 51 \)
- Range: \( 51 \)

---

Final Answers:

\[
\boxed{
\begin{array}{cccc}
\text{Set 1:} & \text{Mean: } 22 & \text{Median: } 19.5 & \text{Mode: } 12 & \text{Range: } 26 \\
\text{Set 2:} & \text{Mean: } 22.7 & \text{Median: } 22 & \text{Mode: } 5 & \text{Range: } 43 \\
\text{Set 3:} & \text{Mean: } 38.22 & \text{Median: } 34 & \text{Mode: } 13, 34 & \text{Range: } 56 \\
\text{Set 4:} & \text{Mean: } 73.17 & \text{Median: } 78.5 & \text{Mode: } 85 & \text{Range: } 47 \\
\text{Set 5:} & \text{Mean: } 58.75 & \text{Median: } 63 & \text{Mode: } 63 & \text{Range: } 70 \\
\text{Set 6:} & \text{Mean: } 68.71 & \text{Median: } 74 & \text{Mode: } 74 & \text{Range: } 57 \\
\text{Set 7:} & \text{Mean: } 48 & \text{Median: } 47.5 & \text{Mode: } 72 & \text{Range: } 66 \\
\text{Set 8:} & \text{Mean: } 60.875 & \text{Median: } 61 & \text{Mode: } 90 & \text{Range: } 79 \\
\text{Set 9:} & \text{Mean: } 31.57 & \text{Median: } 32 & \text{Mode: } 46 & \text{Range: } 34 \\
\text{Set 10:} & \text{Mean: } 43.22 & \text{Median: } 40 & \text{Mode: } 51 & \text{Range: } 51 \\
\end{array}
}
\]