Mean, Median, Mode & Range Worksheets - Free Printable

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

---

Problem 1:

Set: \( 5, 65, 6, 9, 16, 78 \)

#### Mean:
The mean is the average of the numbers.
\[
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of values}}
\]
\[
\text{Sum} = 5 + 65 + 6 + 9 + 16 + 78 = 179
\]
\[
\text{Total number of values} = 6
\]
\[
\text{Mean} = \frac{179}{6} \approx 29.83
\]

#### Median:
The median is the middle value when the numbers are arranged in ascending order.
\[
\text{Ascending order: } 5, 6, 9, 16, 65, 78
\]
Since there are 6 numbers (an even count), the median is the average of the 3rd and 4th numbers:
\[
\text{Median} = \frac{9 + 16}{2} = \frac{25}{2} = 12.5
\]

#### Mode:
The mode is the number that appears most frequently. In this set, all numbers appear once, so there is no mode.
\[
\text{Mode} = \text{None}
\]

#### Range:
The range is the difference between the largest and smallest numbers.
\[
\text{Largest number} = 78, \quad \text{Smallest number} = 5
\]
\[
\text{Range} = 78 - 5 = 73
\]

Final Answer for Problem 1:
\[
\text{Mean} = 29.83, \quad \text{Median} = 12.5, \quad \text{Mode} = \text{None}, \quad \text{Range} = 73
\]

---

Problem 2:

Set: \( 9, 23, 19, 18, 53, 64, 5, 2 \)

#### Mean:
\[
\text{Sum} = 9 + 23 + 19 + 18 + 53 + 64 + 5 + 2 = 193
\]
\[
\text{Total number of values} = 8
\]
\[
\text{Mean} = \frac{193}{8} = 24.125
\]

#### Median:
\[
\text{Ascending order: } 2, 5, 9, 18, 19, 23, 53, 64
\]
Since there are 8 numbers (an even count), the median is the average of the 4th and 5th numbers:
\[
\text{Median} = \frac{18 + 19}{2} = \frac{37}{2} = 18.5
\]

#### Mode:
All numbers appear once, so there is no mode.
\[
\text{Mode} = \text{None}
\]

#### Range:
\[
\text{Largest number} = 64, \quad \text{Smallest number} = 2
\]
\[
\text{Range} = 64 - 2 = 62
\]

Final Answer for Problem 2:
\[
\text{Mean} = 24.125, \quad \text{Median} = 18.5, \quad \text{Mode} = \text{None}, \quad \text{Range} = 62
\]

---

Problem 3:

Set: \( 3, 9, 53, 35, 73, 6, 1, 21, 1 \)

#### Mean:
\[
\text{Sum} = 3 + 9 + 53 + 35 + 73 + 6 + 1 + 21 + 1 = 202
\]
\[
\text{Total number of values} = 9
\]
\[
\text{Mean} = \frac{202}{9} \approx 22.44
\]

#### Median:
\[
\text{Ascending order: } 1, 1, 3, 6, 9, 21, 35, 53, 73
\]
Since there are 9 numbers (an odd count), the median is the 5th number:
\[
\text{Median} = 9
\]

#### Mode:
The number that appears most frequently is \( 1 \) (appears twice).
\[
\text{Mode} = 1
\]

#### Range:
\[
\text{Largest number} = 73, \quad \text{Smallest number} = 1
\]
\[
\text{Range} = 73 - 1 = 72
\]

Final Answer for Problem 3:
\[
\text{Mean} = 22.44, \quad \text{Median} = 9, \quad \text{Mode} = 1, \quad \text{Range} = 72
\]

---

Problem 4:

Set: \( 12, 5, 9, 37, 69, 20, 7, 4 \)

#### Mean:
\[
\text{Sum} = 12 + 5 + 9 + 37 + 69 + 20 + 7 + 4 = 163
\]
\[
\text{Total number of values} = 8
\]
\[
\text{Mean} = \frac{163}{8} = 20.375
\]

#### Median:
\[
\text{Ascending order: } 4, 5, 7, 9, 12, 20, 37, 69
\]
Since there are 8 numbers (an even count), the median is the average of the 4th and 5th numbers:
\[
\text{Median} = \frac{9 + 12}{2} = \frac{21}{2} = 10.5
\]

#### Mode:
All numbers appear once, so there is no mode.
\[
\text{Mode} = \text{None}
\]

#### Range:
\[
\text{Largest number} = 69, \quad \text{Smallest number} = 4
\]
\[
\text{Range} = 69 - 4 = 65
\]

Final Answer for Problem 4:
\[
\text{Mean} = 20.375, \quad \text{Median} = 10.5, \quad \text{Mode} = \text{None}, \quad \text{Range} = 65
\]

---

Problem 5:

Set: \( 5, 78, 6, 3, 8, 37, 60, 71 \)

#### Mean:
\[
\text{Sum} = 5 + 78 + 6 + 3 + 8 + 37 + 60 + 71 = 268
\]
\[
\text{Total number of values} = 8
\]
\[
\text{Mean} = \frac{268}{8} = 33.5
\]

#### Median:
\[
\text{Ascending order: } 3, 5, 6, 8, 37, 60, 71, 78
\]
Since there are 8 numbers (an even count), the median is the average of the 4th and 5th numbers:
\[
\text{Median} = \frac{8 + 37}{2} = \frac{45}{2} = 22.5
\]

#### Mode:
All numbers appear once, so there is no mode.
\[
\text{Mode} = \text{None}
\]

#### Range:
\[
\text{Largest number} = 78, \quad \text{Smallest number} = 3
\]
\[
\text{Range} = 78 - 3 = 75
\]

Final Answer for Problem 5:
\[
\text{Mean} = 33.5, \quad \text{Median} = 22.5, \quad \text{Mode} = \text{None}, \quad \text{Range} = 75
\]

---

Problem 6:

Set: \( 2, 26, 9, 33, 2, 95 \)

#### Mean:
\[
\text{Sum} = 2 + 26 + 9 + 33 + 2 + 95 = 167
\]
\[
\text{Total number of values} = 6
\]
\[
\text{Mean} = \frac{167}{6} \approx 27.83
\]

#### Median:
\[
\text{Ascending order: } 2, 2, 9, 26, 33, 95
\]
Since there are 6 numbers (an even count), the median is the average of the 3rd and 4th numbers:
\[
\text{Median} = \frac{9 + 26}{2} = \frac{35}{2} = 17.5
\]

#### Mode:
The number that appears most frequently is \( 2 \) (appears twice).
\[
\text{Mode} = 2
\]

#### Range:
\[
\text{Largest number} = 95, \quad \text{Smallest number} = 2
\]
\[
\text{Range} = 95 - 2 = 93
\]

Final Answer for Problem 6:
\[
\text{Mean} = 27.83, \quad \text{Median} = 17.5, \quad \text{Mode} = 2, \quad \text{Range} = 93
\]

---

Problem 7:

Set: \( 68, 5, 9, 36, 5, 16, 74, 4, 5 \)

#### Mean:
\[
\text{Sum} = 68 + 5 + 9 + 36 + 5 + 16 + 74 + 4 + 5 = 222
\]
\[
\text{Total number of values} = 9
\]
\[
\text{Mean} = \frac{222}{9} = 24.67
\]

#### Median:
\[
\text{Ascending order: } 4, 5, 5, 5, 9, 16, 36, 68, 74
\]
Since there are 9 numbers (an odd count), the median is the 5th number:
\[
\text{Median} = 9
\]

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

#### Range:
\[
\text{Largest number} = 74, \quad \text{Smallest number} = 4
\]
\[
\text{Range} = 74 - 4 = 70
\]

Final Answer for Problem 7:
\[
\text{Mean} = 24.67, \quad \text{Median} = 9, \quad \text{Mode} = 5, \quad \text{Range} = 70
\]

---

Problem 8:

Set: \( 2, 96, 26, 28, 5, 6 \)

#### Mean:
\[
\text{Sum} = 2 + 96 + 26 + 28 + 5 + 6 = 163
\]
\[
\text{Total number of values} = 6
\]
\[
\text{Mean} = \frac{163}{6} \approx 27.17
\]

#### Median:
\[
\text{Ascending order: } 2, 5, 6, 26, 28, 96
\]
Since there are 6 numbers (an even count), the median is the average of the 3rd and 4th numbers:
\[
\text{Median} = \frac{6 + 26}{2} = \frac{32}{2} = 16
\]

#### Mode:
All numbers appear once, so there is no mode.
\[
\text{Mode} = \text{None}
\]

#### Range:
\[
\text{Largest number} = 96, \quad \text{Smallest number} = 2
\]
\[
\text{Range} = 96 - 2 = 94
\]

Final Answer for Problem 8:
\[
\text{Mean} = 27.17, \quad \text{Median} = 16, \quad \text{Mode} = \text{None}, \quad \text{Range} = 94
\]

---

Problem 9:

Set: \( 14, 46, 75, 4, 9, 49 \)

#### Mean:
\[
\text{Sum} = 14 + 46 + 75 + 4 + 9 + 49 = 197
\]
\[
\text{Total number of values} = 6
\]
\[
\text{Mean} = \frac{197}{6} \approx 32.83
\]

#### Median:
\[
\text{Ascending order: } 4, 9, 14, 46, 49, 75
\]
Since there are 6 numbers (an even count), the median is the average of the 3rd and 4th numbers:
\[
\text{Median} = \frac{14 + 46}{2} = \frac{60}{2} = 30
\]

#### Mode:
All numbers appear once, so there is no mode.
\[
\text{Mode} = \text{None}
\]

#### Range:
\[
\text{Largest number} = 75, \quad \text{Smallest number} = 4
\]
\[
\text{Range} = 75 - 4 = 71
\]

Final Answer for Problem 9:
\[
\text{Mean} = 32.83, \quad \text{Median} = 30, \quad \text{Mode} = \text{None}, \quad \text{Range} = 71
\]

---

Problem 10:

Set: \( 9, 7, 49, 63, 7, 54 \)

#### Mean:
\[
\text{Sum} = 9 + 7 + 49 + 63 + 7 + 54 = 189
\]
\[
\text{Total number of values} = 6
\]
\[
\text{Mean} = \frac{189}{6} = 31.5
\]

#### Median:
\[
\text{Ascending order: } 7, 7, 9, 49, 54, 63
\]
Since there are 6 numbers (an even count), the median is the average of the 3rd and 4th numbers:
\[
\text{Median} = \frac{9 + 49}{2} = \frac{58}{2} = 29
\]

#### Mode:
The number that appears most frequently is \( 7 \) (appears twice).
\[
\text{Mode} = 7
\]

#### Range:
\[
\text{Largest number} = 63, \quad \text{Smallest number} = 7
\]
\[
\text{Range} = 63 - 7 = 56
\]

Final Answer for Problem 10:
\[
\text{Mean} = 31.5, \quad \text{Median} = 29, \quad \text{Mode} = 7, \quad \text{Range} = 56
\]

---

Final Answers:

\[
\boxed{
\begin{array}{llll}
\text{Problem 1:} & \text{Mean} = 29.83, & \text{Median} = 12.5, & \text{Mode} = \text{None}, & \text{Range} = 73 \\
\text{Problem 2:} & \text{Mean} = 24.125, & \text{Median} = 18.5, & \text{Mode} = \text{None}, & \text{Range} = 62 \\
\text{Problem 3:} & \text{Mean} = 22.44, & \text{Median} = 9, & \text{Mode} = 1, & \text{Range} = 72 \\
\text{Problem 4:} & \text{Mean} = 20.375, & \text{Median} = 10.5, & \text{Mode} = \text{None}, & \text{Range} = 65 \\
\text{Problem 5:} & \text{Mean} = 33.5, & \text{Median} = 22.5, & \text{Mode} = \text{None}, & \text{Range} = 75 \\
\text{Problem 6:} & \text{Mean} = 27.83, & \text{Median} = 17.5, & \text{Mode} = 2, & \text{Range} = 93 \\
\text{Problem 7:} & \text{Mean} = 24.67, & \text{Median} = 9, & \text{Mode} = 5, & \text{Range} = 70 \\
\text{Problem 8:} & \text{Mean} = 27.17, & \text{Median} = 16, & \text{Mode} = \text{None}, & \text{Range} = 94 \\
\text{Problem 9:} & \text{Mean} = 32.83, & \text{Median} = 30, & \text{Mode} = \text{None}, & \text{Range} = 71 \\
\text{Problem 10:} & \text{Mean} = 31.5, & \text{Median} = 29, & \text{Mode} = 7, & \text{Range} = 56 \\
\end{array}
}
\]