6th Grade Math Worksheets | Mean, Median, Mode and Range - Free Printable

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.

Set 1: \(35, 56, 34, 44, 52, 12, 34, 45\)

#### Step 1: Mean
The mean is the average of the numbers. It is calculated as:
\[
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Number of values}}
\]
First, find the sum:
\[
35 + 56 + 34 + 44 + 52 + 12 + 34 + 45 = 312
\]
There are 8 numbers, so:
\[
\text{Mean} = \frac{312}{8} = 39
\]

#### Step 2: Median
The median is 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.
Arrange the numbers in ascending order:
\[
12, 34, 34, 35, 44, 45, 52, 56
\]
Since there are 8 numbers (even), the median is the average of the 4th and 5th numbers:
\[
\text{Median} = \frac{35 + 44}{2} = \frac{79}{2} = 39.5
\]

#### Step 3: Mode
The mode is the number that appears most frequently.
From the ordered list:
\[
12, 34, 34, 35, 44, 45, 52, 56
\]
The number 34 appears twice, more than any other number.
\[
\text{Mode} = 34
\]

#### Step 4: Range
The range is the difference between the largest and smallest numbers.
\[
\text{Range} = 56 - 12 = 44
\]

Final Answers for Set 1:

\[
\text{Mean} = 39, \quad \text{Median} = 39.5, \quad \text{Mode} = 34, \quad \text{Range} = 44
\]

---

Set 2: \(24, 34, 32, 16, 45, 38, 28\)

#### Step 1: Mean
Find the sum:
\[
24 + 34 + 32 + 16 + 45 + 38 + 28 = 217
\]
There are 7 numbers, so:
\[
\text{Mean} = \frac{217}{7} = 31
\]

#### Step 2: Median
Arrange the numbers in ascending order:
\[
16, 24, 28, 32, 34, 38, 45
\]
Since there are 7 numbers (odd), the median is the 4th number:
\[
\text{Median} = 32
\]

#### Step 3: Mode
From the ordered list:
\[
16, 24, 28, 32, 34, 38, 45
\]
No number appears more than once.
\[
\text{Mode} = \text{None}
\]

#### Step 4: Range
\[
\text{Range} = 45 - 16 = 29
\]

Final Answers for Set 2:

\[
\text{Mean} = 31, \quad \text{Median} = 32, \quad \text{Mode} = \text{None}, \quad \text{Range} = 29
\]

---

Set 3: \(86, 24, 65, 65, 24, 24\)

#### Step 1: Mean
Find the sum:
\[
86 + 24 + 65 + 65 + 24 + 24 = 288
\]
There are 6 numbers, so:
\[
\text{Mean} = \frac{288}{6} = 48
\]

#### Step 2: Median
Arrange the numbers in ascending order:
\[
24, 24, 24, 65, 65, 86
\]
Since there are 6 numbers (even), the median is the average of the 3rd and 4th numbers:
\[
\text{Median} = \frac{24 + 65}{2} = \frac{89}{2} = 44.5
\]

#### Step 3: Mode
From the ordered list:
\[
24, 24, 24, 65, 65, 86
\]
The number 24 appears three times, more than any other number.
\[
\text{Mode} = 24
\]

#### Step 4: Range
\[
\text{Range} = 86 - 24 = 62
\]

Final Answers for Set 3:

\[
\text{Mean} = 48, \quad \text{Median} = 44.5, \quad \text{Mode} = 24, \quad \text{Range} = 62
\]

---

Set 4: \(32, 23, 22, 33, 33, 23, 32, 23, 22\)

#### Step 1: Mean
Find the sum:
\[
32 + 23 + 22 + 33 + 33 + 23 + 32 + 23 + 22 = 245
\]
There are 9 numbers, so:
\[
\text{Mean} = \frac{245}{9} \approx 27.22
\]

#### Step 2: Median
Arrange the numbers in ascending order:
\[
22, 22, 23, 23, 23, 32, 32, 33, 33
\]
Since there are 9 numbers (odd), the median is the 5th number:
\[
\text{Median} = 23
\]

#### Step 3: Mode
From the ordered list:
\[
22, 22, 23, 23, 23, 32, 32, 33, 33
\]
The number 23 appears three times, more than any other number.
\[
\text{Mode} = 23
\]

#### Step 4: Range
\[
\text{Range} = 33 - 22 = 11
\]

Final Answers for Set 4:

\[
\text{Mean} \approx 27.22, \quad \text{Median} = 23, \quad \text{Mode} = 23, \quad \text{Range} = 11
\]

---

Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Set 1:} & \text{Mean} = 39, \text{Median} = 39.5, \text{Mode} = 34, \text{Range} = 44 \\
\text{Set 2:} & \text{Mean} = 31, \text{Median} = 32, \text{Mode} = \text{None}, \text{Range} = 29 \\
\text{Set 3:} & \text{Mean} = 48, \text{Median} = 44.5, \text{Mode} = 24, \text{Range} = 62 \\
\text{Set 4:} & \text{Mean} \approx 27.22, \text{Median} = 23, \text{Mode} = 23, \text{Range} = 11
\end{array}
}
\]