Mean Median Mode Range Worksheets - Free Printable

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

---

Set 1: {61, 57, 49, 60, 45, 51, 57, 60, 53, 57, 55, 48, 65, 52}

#### Step 1: Order the data
{45, 48, 49, 51, 52, 53, 55, 57, 57, 57, 60, 60, 61, 65}

#### Step 2: Calculate the Mean
The mean is the sum of all the numbers divided by the total count.
\[
\text{Sum} = 45 + 48 + 49 + 51 + 52 + 53 + 55 + 57 + 57 + 57 + 60 + 60 + 61 + 65 = 780
\]
\[
\text{Count} = 14
\]
\[
\text{Mean} = \frac{780}{14} = 55.71
\]

#### Step 3: Calculate the Median
The median is the middle value in an ordered list. Since there are 14 numbers (even count), the median is the average of the 7th and 8th values.
\[
\text{7th value} = 55, \quad \text{8th value} = 57
\]
\[
\text{Median} = \frac{55 + 57}{2} = 56
\]

#### Step 4: Calculate the Mode
The mode is the number that appears most frequently.
\[
\text{Mode} = 57 \quad (\text{appears 3 times})
\]

#### Step 5: Calculate the Range
The range is the difference between the largest and smallest numbers.
\[
\text{Range} = 65 - 45 = 20
\]

#### Final Answers for Set 1
\[
\text{Mean} = 55.71, \quad \text{Median} = 56, \quad \text{Mode} = 57, \quad \text{Range} = 20
\]

---

Set 2: {129, 113, 110, 123, 112, 115, 110, 124, 121, 113, 115, 121, 115}

#### Step 1: Order the data
{110, 110, 112, 113, 113, 115, 115, 115, 121, 121, 123, 124, 129}

#### Step 2: Calculate the Mean
\[
\text{Sum} = 110 + 110 + 112 + 113 + 113 + 115 + 115 + 115 + 121 + 121 + 123 + 124 + 129 = 1451
\]
\[
\text{Count} = 13
\]
\[
\text{Mean} = \frac{1451}{13} = 111.62
\]

#### Step 3: Calculate the Median
The median is the middle value in an ordered list. Since there are 13 numbers (odd count), the median is the 7th value.
\[
\text{Median} = 115
\]

#### Step 4: Calculate the Mode
The mode is the number that appears most frequently.
\[
\text{Mode} = 115 \quad (\text{appears 3 times})
\]

#### Step 5: Calculate the Range
\[
\text{Range} = 129 - 110 = 19
\]

#### Final Answers for Set 2
\[
\text{Mean} = 111.62, \quad \text{Median} = 115, \quad \text{Mode} = 115, \quad \text{Range} = 19
\]

---

Set 3: {-4, 7, 4, -8, 13, 4, -2, -5, 7, -6, 5, 15, -2, 1, 7}

#### Step 1: Order the data
{-8, -6, -5, -4, -2, -2, 1, 4, 4, 5, 7, 7, 7, 13, 15}

#### Step 2: Calculate the Mean
\[
\text{Sum} = -8 + (-6) + (-5) + (-4) + (-2) + (-2) + 1 + 4 + 4 + 5 + 7 + 7 + 7 + 13 + 15 = 45
\]
\[
\text{Count} = 15
\]
\[
\text{Mean} = \frac{45}{15} = 3
\]

#### Step 3: Calculate the Median
The median is the middle value in an ordered list. Since there are 15 numbers (odd count), the median is the 8th value.
\[
\text{Median} = 4
\]

#### Step 4: Calculate the Mode
The mode is the number that appears most frequently.
\[
\text{Mode} = 7 \quad (\text{appears 3 times})
\]

#### Step 5: Calculate the Range
\[
\text{Range} = 15 - (-8) = 23
\]

#### Final Answers for Set 3
\[
\text{Mean} = 3, \quad \text{Median} = 4, \quad \text{Mode} = 7, \quad \text{Range} = 23
\]

---

Set 4: {83, 77, 81, 79, 85, 77, 76, 72, 87, 81, 77, 91, 81, 77}

#### Step 1: Order the data
{72, 76, 77, 77, 77, 77, 79, 81, 81, 81, 83, 85, 87, 91}

#### Step 2: Calculate the Mean
\[
\text{Sum} = 72 + 76 + 77 + 77 + 77 + 77 + 79 + 81 + 81 + 81 + 83 + 85 + 87 + 91 = 1134
\]
\[
\text{Count} = 14
\]
\[
\text{Mean} = \frac{1134}{14} = 81
\]

#### Step 3: Calculate the Median
The median is the middle value in an ordered list. Since there are 14 numbers (even count), the median is the average of the 7th and 8th values.
\[
\text{7th value} = 77, \quad \text{8th value} = 81
\]
\[
\text{Median} = \frac{77 + 81}{2} = 79
\]

#### Step 4: Calculate the Mode
The mode is the number that appears most frequently.
\[
\text{Mode} = 77 \quad (\text{appears 4 times})
\]

#### Step 5: Calculate the Range
\[
\text{Range} = 91 - 72 = 19
\]

#### Final Answers for Set 4
\[
\text{Mean} = 81, \quad \text{Median} = 79, \quad \text{Mode} = 77, \quad \text{Range} = 19
\]

---

Set 5: {0.7, 0.2, 0.9, 1.2, 1.5, 0.4, 0.6, 0.2, 1.1, 0.3, 0.7, 0.2, 1.1}

#### Step 1: Order the data
{0.2, 0.2, 0.2, 0.3, 0.4, 0.6, 0.7, 0.7, 0.9, 1.1, 1.1, 1.2, 1.5}

#### Step 2: Calculate the Mean
\[
\text{Sum} = 0.2 + 0.2 + 0.2 + 0.3 + 0.4 + 0.6 + 0.7 + 0.7 + 0.9 + 1.1 + 1.1 + 1.2 + 1.5 = 9.2
\]
\[
\text{Count} = 13
\]
\[
\text{Mean} = \frac{9.2}{13} \approx 0.71
\]

#### Step 3: Calculate the Median
The median is the middle value in an ordered list. Since there are 13 numbers (odd count), the median is the 7th value.
\[
\text{Median} = 0.7
\]

#### Step 4: Calculate the Mode
The mode is the number that appears most frequently.
\[
\text{Mode} = 0.2 \quad (\text{appears 3 times})
\]

#### Step 5: Calculate the Range
\[
\text{Range} = 1.5 - 0.2 = 1.3
\]

#### Final Answers for Set 5
\[
\text{Mean} \approx 0.71, \quad \text{Median} = 0.7, \quad \text{Mode} = 0.2, \quad \text{Range} = 1.3
\]

---

Set 6: {6.2, 5.6, 4.9, 5.1, 6.2, 5.7, 5.1, 4.7, 5.4, 6.2, 4.5, 6.4}

#### Step 1: Order the data
{4.5, 4.7, 4.9, 5.1, 5.1, 5.4, 5.6, 5.7, 6.2, 6.2, 6.2, 6.4}

#### Step 2: Calculate the Mean
\[
\text{Sum} = 4.5 + 4.7 + 4.9 + 5.1 + 5.1 + 5.4 + 5.6 + 5.7 + 6.2 + 6.2 + 6.2 + 6.4 = 64.6
\]
\[
\text{Count} = 12
\]
\[
\text{Mean} = \frac{64.6}{12} \approx 5.38
\]

#### Step 3: Calculate the Median
The median is the middle value in an ordered list. Since there are 12 numbers (even count), the median is the average of the 6th and 7th values.
\[
\text{6th value} = 5.4, \quad \text{7th value} = 5.6
\]
\[
\text{Median} = \frac{5.4 + 5.6}{2} = 5.5
\]

#### Step 4: Calculate the Mode
The mode is the number that appears most frequently.
\[
\text{Mode} = 6.2 \quad (\text{appears 3 times})
\]

#### Step 5: Calculate the Range
\[
\text{Range} = 6.4 - 4.5 = 1.9
\]

#### Final Answers for Set 6
\[
\text{Mean} \approx 5.38, \quad \text{Median} = 5.5, \quad \text{Mode} = 6.2, \quad \text{Range} = 1.9
\]

---

Final Answer Summary

\[
\boxed{
\begin{array}{|c|c|c|c|c|}
\hline
\text{Set} & \text{Mean} & \text{Median} & \text{Mode} & \text{Range} \\
\hline
1 & 55.71 & 56 & 57 & 20 \\
2 & 111.62 & 115 & 115 & 19 \\
3 & 3 & 4 & 7 & 23 \\
4 & 81 & 79 & 77 & 19 \\
5 & 0.71 & 0.7 & 0.2 & 1.3 \\
6 & 5.38 & 5.5 & 6.2 & 1.9 \\
\hline
\end{array}
}
\]