Mean, Median, Mode and Range worksheet - Free Printable

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

---

Set 1: \(2, 5, 5, 6, 9\)

#### Mean
The mean is the average of the numbers.
\[
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of values}}
\]
\[
\text{Sum} = 2 + 5 + 5 + 6 + 9 = 27
\]
\[
\text{Total number of values} = 5
\]
\[
\text{Mean} = \frac{27}{5} = 5.4
\]

#### Median
The median is the middle number when the data is arranged in ascending order.
\[
\text{Data in ascending order: } 2, 5, 5, 6, 9
\]
Since there are 5 numbers (odd count), the median is the middle number:
\[
\text{Median} = 5
\]

#### Mode
The mode is the number that appears most frequently.
\[
\text{Data: } 2, 5, 5, 6, 9
\]
The number \(5\) appears twice, which is more frequent than any other number.
\[
\text{Mode} = 5
\]

#### Range
The range is the difference between the largest and smallest numbers.
\[
\text{Largest number} = 9
\]
\[
\text{Smallest number} = 2
\]
\[
\text{Range} = 9 - 2 = 7
\]

#### Summary for Set 1
\[
\text{Mean} = 5.4, \quad \text{Median} = 5, \quad \text{Mode} = 5, \quad \text{Range} = 7
\]

---

Set 2: \(21, 32, 28, 19, 28\)

#### Mean
\[
\text{Sum} = 21 + 32 + 28 + 19 + 28 = 128
\]
\[
\text{Total number of values} = 5
\]
\[
\text{Mean} = \frac{128}{5} = 25.6
\]

#### Median
\[
\text{Data in ascending order: } 19, 21, 28, 28, 32
\]
The median is the middle number:
\[
\text{Median} = 28
\]

#### Mode
The number \(28\) appears twice, which is more frequent than any other number.
\[
\text{Mode} = 28
\]

#### Range
\[
\text{Largest number} = 32
\]
\[
\text{Smallest number} = 19
\]
\[
\text{Range} = 32 - 19 = 13
\]

#### Summary for Set 2
\[
\text{Mean} = 25.6, \quad \text{Median} = 28, \quad \text{Mode} = 28, \quad \text{Range} = 13
\]

---

Set 3: \(95, 93, 95, 95, 89, 93\)

#### Mean
\[
\text{Sum} = 95 + 93 + 95 + 95 + 89 + 93 = 560
\]
\[
\text{Total number of values} = 6
\]
\[
\text{Mean} = \frac{560}{6} \approx 93.33
\]

#### Median
\[
\text{Data in ascending order: } 89, 93, 93, 95, 95, 95
\]
Since there are 6 numbers (even count), the median is the average of the 3rd and 4th numbers:
\[
\text{Median} = \frac{93 + 95}{2} = 94
\]

#### Mode
The number \(95\) appears three times, which is more frequent than any other number.
\[
\text{Mode} = 95
\]

#### Range
\[
\text{Largest number} = 95
\]
\[
\text{Smallest number} = 89
\]
\[
\text{Range} = 95 - 89 = 6
\]

#### Summary for Set 3
\[
\text{Mean} \approx 93.33, \quad \text{Median} = 94, \quad \text{Mode} = 95, \quad \text{Range} = 6
\]

---

Set 4: \(343, 270, 221, 270\)

#### Mean
\[
\text{Sum} = 343 + 270 + 221 + 270 = 1104
\]
\[
\text{Total number of values} = 4
\]
\[
\text{Mean} = \frac{1104}{4} = 276
\]

#### Median
\[
\text{Data in ascending order: } 221, 270, 270, 343
\]
Since there are 4 numbers (even count), the median is the average of the 2nd and 3rd numbers:
\[
\text{Median} = \frac{270 + 270}{2} = 270
\]

#### Mode
The number \(270\) appears twice, which is more frequent than any other number.
\[
\text{Mode} = 270
\]

#### Range
\[
\text{Largest number} = 343
\]
\[
\text{Smallest number} = 221
\]
\[
\text{Range} = 343 - 221 = 122
\]

#### Summary for Set 4
\[
\text{Mean} = 276, \quad \text{Median} = 270, \quad \text{Mode} = 270, \quad \text{Range} = 122
\]

---

Set 5: \(7, 12, 17, 16, 18, 19, 17\)

#### Mean
\[
\text{Sum} = 7 + 12 + 17 + 16 + 18 + 19 + 17 = 106
\]
\[
\text{Total number of values} = 7
\]
\[
\text{Mean} = \frac{106}{7} \approx 15.14
\]

#### Median
\[
\text{Data in ascending order: } 7, 12, 16, 17, 17, 18, 19
\]
Since there are 7 numbers (odd count), the median is the middle number:
\[
\text{Median} = 17
\]

#### Mode
The number \(17\) appears twice, which is more frequent than any other number.
\[
\text{Mode} = 17
\]

#### Range
\[
\text{Largest number} = 19
\]
\[
\text{Smallest number} = 7
\]
\[
\text{Range} = 19 - 7 = 12
\]

#### Summary for Set 5
\[
\text{Mean} \approx 15.14, \quad \text{Median} = 17, \quad \text{Mode} = 17, \quad \text{Range} = 12
\]

---

Set 6: \(202, 211, 215, 275, 215\)

#### Mean
\[
\text{Sum} = 202 + 211 + 215 + 275 + 215 = 1118
\]
\[
\text{Total number of values} = 5
\]
\[
\text{Mean} = \frac{1118}{5} = 223.6
\]

#### Median
\[
\text{Data in ascending order: } 202, 211, 215, 215, 275
\]
Since there are 5 numbers (odd count), the median is the middle number:
\[
\text{Median} = 215
\]

#### Mode
The number \(215\) appears twice, which is more frequent than any other number.
\[
\text{Mode} = 215
\]

#### Range
\[
\text{Largest number} = 275
\]
\[
\text{Smallest number} = 202
\]
\[
\text{Range} = 275 - 202 = 73
\]

#### Summary for Set 6
\[
\text{Mean} = 223.6, \quad \text{Median} = 215, \quad \text{Mode} = 215, \quad \text{Range} = 73
\]

---

Final Answers

\[
\boxed{
\begin{array}{l}
\text{Set 1: Mean} = 5.4, \text{Median} = 5, \text{Mode} = 5, \text{Range} = 7 \\
\text{Set 2: Mean} = 25.6, \text{Median} = 28, \text{Mode} = 28, \text{Range} = 13 \\
\text{Set 3: Mean} \approx 93.33, \text{Median} = 94, \text{Mode} = 95, \text{Range} = 6 \\
\text{Set 4: Mean} = 276, \text{Median} = 270, \text{Mode} = 270, \text{Range} = 122 \\
\text{Set 5: Mean} \approx 15.14, \text{Median} = 17, \text{Mode} = 17, \text{Range} = 12 \\
\text{Set 6: Mean} = 223.6, \text{Median} = 215, \text{Mode} = 215, \text{Range} = 73 \\
\end{array}
}
\]