Mean (Average), Median, Mode, and Range Worksheets - Free Printable

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

---

Part a: 3, 4, 9, 7, 7

#### Mean
The mean is the average of the numbers. It is calculated as:
\[
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of values}}
\]
- Sum of the numbers: \(3 + 4 + 9 + 7 + 7 = 30\)
- Total number of values: 5
\[
\text{Mean} = \frac{30}{5} = 6
\]

#### Median
The median is the middle number when the numbers are arranged in ascending order.
- Arranged in ascending order: \(3, 4, 7, 7, 9\)
- Since there are 5 numbers (odd count), the median is the middle number: \(7\)

#### Mode
The mode is the number that appears most frequently.
- In the set \(3, 4, 9, 7, 7\), the number \(7\) appears twice, which is more frequent than any other number.
\[
\text{Mode} = 7
\]

#### Range
The range is the difference between the largest and smallest numbers.
- Largest number: \(9\)
- Smallest number: \(3\)
\[
\text{Range} = 9 - 3 = 6
\]

#### Final Answers for Part a:
\[
\text{Mean} = 6, \quad \text{Median} = 7, \quad \text{Mode} = 7, \quad \text{Range} = 6
\]

---

Part b: 15, 3, 3, 3

#### Mean
\[
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of values}}
\]
- Sum of the numbers: \(15 + 3 + 3 + 3 = 24\)
- Total number of values: 4
\[
\text{Mean} = \frac{24}{4} = 6
\]

#### Median
- Arranged in ascending order: \(3, 3, 3, 15\)
- Since there are 4 numbers (even count), the median is the average of the two middle numbers (\(3\) and \(3\)):
\[
\text{Median} = \frac{3 + 3}{2} = 3
\]

#### Mode
The number \(3\) appears three times, which is more frequent than any other number.
\[
\text{Mode} = 3
\]

#### Range
- Largest number: \(15\)
- Smallest number: \(3\)
\[
\text{Range} = 15 - 3 = 12
\]

#### Final Answers for Part b:
\[
\text{Mean} = 6, \quad \text{Median} = 3, \quad \text{Mode} = 3, \quad \text{Range} = 12
\]

---

Part c: 3, 0, 0, 2, 0

#### Mean
\[
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of values}}
\]
- Sum of the numbers: \(3 + 0 + 0 + 2 + 0 = 5\)
- Total number of values: 5
\[
\text{Mean} = \frac{5}{5} = 1
\]

#### Median
- Arranged in ascending order: \(0, 0, 0, 2, 3\)
- Since there are 5 numbers (odd count), the median is the middle number: \(0\)

#### Mode
The number \(0\) appears three times, which is more frequent than any other number.
\[
\text{Mode} = 0
\]

#### Range
- Largest number: \(3\)
- Smallest number: \(0\)
\[
\text{Range} = 3 - 0 = 3
\]

#### Final Answers for Part c:
\[
\text{Mean} = 1, \quad \text{Median} = 0, \quad \text{Mode} = 0, \quad \text{Range} = 3
\]

---

Part d: 5, 6, 5, 2, 4, 1

#### Mean
\[
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of values}}
\]
- Sum of the numbers: \(5 + 6 + 5 + 2 + 4 + 1 = 23\)
- Total number of values: 6
\[
\text{Mean} = \frac{23}{6} \approx 3.83
\]

#### Median
- Arranged in ascending order: \(1, 2, 4, 5, 5, 6\)
- Since there are 6 numbers (even count), the median is the average of the two middle numbers (\(4\) and \(5\)):
\[
\text{Median} = \frac{4 + 5}{2} = 4.5
\]

#### Mode
The number \(5\) appears twice, which is more frequent than any other number.
\[
\text{Mode} = 5
\]

#### Range
- Largest number: \(6\)
- Smallest number: \(1\)
\[
\text{Range} = 6 - 1 = 5
\]

#### Final Answers for Part d:
\[
\text{Mean} \approx 3.83, \quad \text{Median} = 4.5, \quad \text{Mode} = 5, \quad \text{Range} = 5
\]

---

Part e: 10, 6, 3, 10, 1

#### Mean
\[
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of values}}
\]
- Sum of the numbers: \(10 + 6 + 3 + 10 + 1 = 30\)
- Total number of values: 5
\[
\text{Mean} = \frac{30}{5} = 6
\]

#### Median
- Arranged in ascending order: \(1, 3, 6, 10, 10\)
- Since there are 5 numbers (odd count), the median is the middle number: \(6\)

#### Mode
The number \(10\) appears twice, which is more frequent than any other number.
\[
\text{Mode} = 10
\]

#### Range
- Largest number: \(10\)
- Smallest number: \(1\)
\[
\text{Range} = 10 - 1 = 9
\]

#### Final Answers for Part e:
\[
\text{Mean} = 6, \quad \text{Median} = 6, \quad \text{Mode} = 10, \quad \text{Range} = 9
\]

---

Part f: 4, 6, 2, 6, 9, 3, 5

#### Mean
\[
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of values}}
\]
- Sum of the numbers: \(4 + 6 + 2 + 6 + 9 + 3 + 5 = 35\)
- Total number of values: 7
\[
\text{Mean} = \frac{35}{7} = 5
\]

#### Median
- Arranged in ascending order: \(2, 3, 4, 5, 6, 6, 9\)
- Since there are 7 numbers (odd count), the median is the middle number: \(5\)

#### Mode
The number \(6\) appears twice, which is more frequent than any other number.
\[
\text{Mode} = 6
\]

#### Range
- Largest number: \(9\)
- Smallest number: \(2\)
\[
\text{Range} = 9 - 2 = 7
\]

#### Final Answers for Part f:
\[
\text{Mean} = 5, \quad \text{Median} = 5, \quad \text{Mode} = 6, \quad \text{Range} = 7
\]

---

Final Answer Summary:

\[
\boxed{
\begin{array}{l}
\text{a. Mean} = 6, \text{Median} = 7, \text{Mode} = 7, \text{Range} = 6 \\
\text{b. Mean} = 6, \text{Median} = 3, \text{Mode} = 3, \text{Range} = 12 \\
\text{c. Mean} = 1, \text{Median} = 0, \text{Mode} = 0, \text{Range} = 3 \\
\text{d. Mean} \approx 3.83, \text{Median} = 4.5, \text{Mode} = 5, \text{Range} = 5 \\
\text{e. Mean} = 6, \text{Median} = 6, \text{Mode} = 10, \text{Range} = 9 \\
\text{f. Mean} = 5, \text{Median} = 5, \text{Mode} = 6, \text{Range} = 7 \\
\end{array}
}
\]