Math Worksheets | Dynamically Created Math Worksheets - Free Printable

To solve the problems involving Mean, Median, Mode, and Range, let's go through each set of numbers step by step. Here’s how to calculate each:

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. If multiple numbers repeat equally, there can be more than one mode.

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

---

Problem 1: \(7, 2, 5, 6, 4, 6\)

#### Step 1: Calculate the Mean
\[
\text{Mean} = \frac{7 + 2 + 5 + 6 + 4 + 6}{6} = \frac{30}{6} = 5
\]

#### Step 2: Calculate the Median
Arrange the numbers in ascending order: \(2, 4, 5, 6, 6, 7\).
Since there are 6 numbers (even), the median is the average of the 3rd and 4th numbers:
\[
\text{Median} = \frac{5 + 6}{2} = \frac{11}{2} = 5.5
\]

#### Step 3: Calculate the Mode
The number that appears most frequently is \(6\) (it appears twice).
\[
\text{Mode} = 6
\]

#### Step 4: Calculate the Range
\[
\text{Range} = 7 - 2 = 5
\]

Answer for Problem 1:
\[
\text{Mean} = 5, \quad \text{Median} = 5.5, \quad \text{Mode} = 6, \quad \text{Range} = 5
\]

---

Problem 2: \(9, 9, 7, 7, 7, 3\)

#### Step 1: Calculate the Mean
\[
\text{Mean} = \frac{9 + 9 + 7 + 7 + 7 + 3}{6} = \frac{42}{6} = 7
\]

#### Step 2: Calculate the Median
Arrange the numbers in ascending order: \(3, 7, 7, 7, 9, 9\).
Since there are 6 numbers (even), the median is the average of the 3rd and 4th numbers:
\[
\text{Median} = \frac{7 + 7}{2} = \frac{14}{2} = 7
\]

#### Step 3: Calculate the Mode
The number that appears most frequently is \(7\) (it appears three times).
\[
\text{Mode} = 7
\]

#### Step 4: Calculate the Range
\[
\text{Range} = 9 - 3 = 6
\]

Answer for Problem 2:
\[
\text{Mean} = 7, \quad \text{Median} = 7, \quad \text{Mode} = 7, \quad \text{Range} = 6
\]

---

Problem 3: \(6, 6, 2, 8, 6, 3, 2, 6, 6\)

#### Step 1: Calculate the Mean
\[
\text{Mean} = \frac{6 + 6 + 2 + 8 + 6 + 3 + 2 + 6 + 6}{9} = \frac{47}{9} \approx 5.22
\]

#### Step 2: Calculate the Median
Arrange the numbers in ascending order: \(2, 2, 3, 6, 6, 6, 6, 6, 8\).
Since there are 9 numbers (odd), the median is the 5th number:
\[
\text{Median} = 6
\]

#### Step 3: Calculate the Mode
The number that appears most frequently is \(6\) (it appears five times).
\[
\text{Mode} = 6
\]

#### Step 4: Calculate the Range
\[
\text{Range} = 8 - 2 = 6
\]

Answer for Problem 3:
\[
\text{Mean} \approx 5.22, \quad \text{Median} = 6, \quad \text{Mode} = 6, \quad \text{Range} = 6
\]

---

Problem 4: \(7, 8, 2, 8, 5\)

#### Step 1: Calculate the Mean
\[
\text{Mean} = \frac{7 + 8 + 2 + 8 + 5}{5} = \frac{30}{5} = 6
\]

#### Step 2: Calculate the Median
Arrange the numbers in ascending order: \(2, 5, 7, 8, 8\).
Since there are 5 numbers (odd), the median is the 3rd number:
\[
\text{Median} = 7
\]

#### Step 3: Calculate the Mode
The number that appears most frequently is \(8\) (it appears twice).
\[
\text{Mode} = 8
\]

#### Step 4: Calculate the Range
\[
\text{Range} = 8 - 2 = 6
\]

Answer for Problem 4:
\[
\text{Mean} = 6, \quad \text{Median} = 7, \quad \text{Mode} = 8, \quad \text{Range} = 6
\]

---

Problem 5: \(5, 5, 5, 4, 4, 3, 9\)

#### Step 1: Calculate the Mean
\[
\text{Mean} = \frac{5 + 5 + 5 + 4 + 4 + 3 + 9}{7} = \frac{35}{7} = 5
\]

#### Step 2: Calculate the Median
Arrange the numbers in ascending order: \(3, 4, 4, 5, 5, 5, 9\).
Since there are 7 numbers (odd), the median is the 4th number:
\[
\text{Median} = 5
\]

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

#### Step 4: Calculate the Range
\[
\text{Range} = 9 - 3 = 6
\]

Answer for Problem 5:
\[
\text{Mean} = 5, \quad \text{Median} = 5, \quad \text{Mode} = 5, \quad \text{Range} = 6
\]

---

Problem 6: \(2, 8, 7, 3, 4, 6, 6, 6, 3\)

#### Step 1: Calculate the Mean
\[
\text{Mean} = \frac{2 + 8 + 7 + 3 + 4 + 6 + 6 + 6 + 3}{9} = \frac{45}{9} = 5
\]

#### Step 2: Calculate the Median
Arrange the numbers in ascending order: \(2, 3, 3, 4, 6, 6, 6, 7, 8\).
Since there are 9 numbers (odd), the median is the 5th number:
\[
\text{Median} = 6
\]

#### Step 3: Calculate the Mode
The number that appears most frequently is \(6\) (it appears three times).
\[
\text{Mode} = 6
\]

#### Step 4: Calculate the Range
\[
\text{Range} = 8 - 2 = 6
\]

Answer for Problem 6:
\[
\text{Mean} = 5, \quad \text{Median} = 6, \quad \text{Mode} = 6, \quad \text{Range} = 6
\]

---

Problem 7: \(9, 3, 9, 2, 2, 6, 7, 2\)

#### Step 1: Calculate the Mean
\[
\text{Mean} = \frac{9 + 3 + 9 + 2 + 2 + 6 + 7 + 2}{8} = \frac{40}{8} = 5
\]

#### Step 2: Calculate the Median
Arrange the numbers in ascending order: \(2, 2, 2, 3, 6, 7, 9, 9\).
Since there are 8 numbers (even), the median is the average of the 4th and 5th numbers:
\[
\text{Median} = \frac{3 + 6}{2} = \frac{9}{2} = 4.5
\]

#### Step 3: Calculate the Mode
The number that appears most frequently is \(2\) (it appears three times).
\[
\text{Mode} = 2
\]

#### Step 4: Calculate the Range
\[
\text{Range} = 9 - 2 = 7
\]

Answer for Problem 7:
\[
\text{Mean} = 5, \quad \text{Median} = 4.5, \quad \text{Mode} = 2, \quad \text{Range} = 7
\]

---

Problem 8: \(9, 2, 2, 5, 8, 4, 5\)

#### Step 1: Calculate the Mean
\[
\text{Mean} = \frac{9 + 2 + 2 + 5 + 8 + 4 + 5}{7} = \frac{35}{7} = 5
\]

#### Step 2: Calculate the Median
Arrange the numbers in ascending order: \(2, 2, 4, 5, 5, 8, 9\).
Since there are 7 numbers (odd), the median is the 4th number:
\[
\text{Median} = 5
\]

#### Step 3: Calculate the Mode
The numbers \(2\) and \(5\) both appear twice, so there are two modes.
\[
\text{Mode} = 2 \text{ and } 5
\]

#### Step 4: Calculate the Range
\[
\text{Range} = 9 - 2 = 7
\]

Answer for Problem 8:
\[
\text{Mean} = 5, \quad \text{Median} = 5, \quad \text{Mode} = 2 \text{ and } 5, \quad \text{Range} = 7
\]

---

Problem 9: \(8, 7, 4, 7, 5, 5, 6\)

#### Step 1: Calculate the Mean
\[
\text{Mean} = \frac{8 + 7 + 4 + 7 + 5 + 5 + 6}{7} = \frac{42}{7} = 6
\]

#### Step 2: Calculate the Median
Arrange the numbers in ascending order: \(4, 5, 5, 6, 7, 7, 8\).
Since there are 7 numbers (odd), the median is the 4th number:
\[
\text{Median} = 6
\]

#### Step 3: Calculate the Mode
The numbers \(5\) and \(7\) both appear twice, so there are two modes.
\[
\text{Mode} = 5 \text{ and } 7
\]

#### Step 4: Calculate the Range
\[
\text{Range} = 8 - 4 = 4
\]

Answer for Problem 9:
\[
\text{Mean} = 6, \quad \text{Median} = 6, \quad \text{Mode} = 5 \text{ and } 7, \quad \text{Range} = 4
\]

---

Problem 10: \(6, 9, 9, 7, 2, 4, 5\)

#### Step 1: Calculate the Mean
\[
\text{Mean} = \frac{6 + 9 + 9 + 7 + 2 + 4 + 5}{7} = \frac{42}{7} = 6
\]

#### Step 2: Calculate the Median
Arrange the numbers in ascending order: \(2, 4, 5, 6, 7, 9, 9\).
Since there are 7 numbers (odd), the median is the 4th number:
\[
\text{Median} = 6
\]

#### Step 3: Calculate the Mode
The number that appears most frequently is \(9\) (it appears twice).
\[
\text{Mode} = 9
\]

#### Step 4: Calculate the Range
\[
\text{Range} = 9 - 2 = 7
\]

Answer for Problem 10:
\[
\text{Mean} = 6, \quad \text{Median} = 6, \quad \text{Mode} = 9, \quad \text{Range} = 7
\]

---

Final Answers:

\[
\boxed{
\begin{array}{llll}
1) & \text{Mean} = 5, & \text{Median} = 5.5, & \text{Mode} = 6, & \text{Range} = 5 \\
2) & \text{Mean} = 7, & \text{Median} = 7, & \text{Mode} = 7, & \text{Range} = 6 \\
3) & \text{Mean} \approx 5.22, & \text{Median} = 6, & \text{Mode} = 6, & \text{Range} = 6 \\
4) & \text{Mean} = 6, & \text{Median} = 7, & \text{Mode} = 8, & \text{Range} = 6 \\
5) & \text{Mean} = 5, & \text{Median} = 5, & \text{Mode} = 5, & \text{Range} = 6 \\
6) & \text{Mean} = 5, & \text{Median} = 6, & \text{Mode} = 6, & \text{Range} = 6 \\
7) & \text{Mean} = 5, & \text{Median} = 4.5, & \text{Mode} = 2, & \text{Range} = 7 \\
8) & \text{Mean} = 5, & \text{Median} = 5, & \text{Mode} = 2 \text{ and } 5, & \text{Range} = 7 \\
9) & \text{Mean} = 6, & \text{Median} = 6, & \text{Mode} = 5 \text{ and } 7, & \text{Range} = 4 \\
10) & \text{Mean} = 6, & \text{Median} = 6, & \text{Mode} = 9, & \text{Range} = 7 \\
\end{array}
}
\]