Math worksheet for calculating mean, median, mode, and range.
Worksheet titled "Mean, Mode, Median, and Range" with ten problems requiring calculation of statistical measures for given number sets.
JPG
768×1024
79.8 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #271462
⭐
Show Answer Key & Explanations
Step-by-step solution for: Calculating The Mean Median Mode Worksheet | PDF | Theoretical ...
▼
Show Answer Key & Explanations
Step-by-step solution for: Calculating The Mean Median Mode Worksheet | PDF | Theoretical ...
To solve the problems involving Mean, Median, Mode, and Range, we will go through each set of numbers step by step. Let's break it down:
---
#### Set 1: \( 82, 23, 59, 94, 70, 26, 32, 83, 87, 94, 32 \)
- Mean: The mean is the average of the numbers.
\[
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total count of numbers}}
\]
Sum = \( 82 + 23 + 59 + 94 + 70 + 26 + 32 + 83 + 87 + 94 + 32 = 668 \)
Total count = 11
\[
\text{Mean} = \frac{668}{11} \approx 60.73
\]
- Median: The median is the middle number when the numbers are arranged in ascending order.
Arranged in ascending order: \( 23, 26, 32, 32, 59, 70, 82, 83, 87, 94, 94 \)
Since there are 11 numbers (odd count), the median is the 6th number.
\[
\text{Median} = 70
\]
- Mode: The mode is the number that appears most frequently.
From the ordered list: \( 23, 26, 32, 32, 59, 70, 82, 83, 87, 94, 94 \)
Both \( 32 \) and \( 94 \) appear twice, more than any other number.
\[
\text{Mode} = 32, 94
\]
- Range: The range is the difference between the largest and smallest numbers.
Largest number = 94, Smallest number = 23
\[
\text{Range} = 94 - 23 = 71
\]
Answer for Set 1:
\[
\boxed{60.73, 70, 32, 94, 71}
\]
---
#### Set 2: \( 83, 93, 77, 33, 62, 28, 23 \)
- Mean:
Sum = \( 83 + 93 + 77 + 33 + 62 + 28 + 23 = 399 \)
Total count = 7
\[
\text{Mean} = \frac{399}{7} = 57
\]
- Median:
Arranged in ascending order: \( 23, 28, 33, 62, 77, 83, 93 \)
Since there are 7 numbers (odd count), the median is the 4th number.
\[
\text{Median} = 62
\]
- Mode:
All numbers appear only once.
\[
\text{Mode} = \text{None}
\]
- Range:
Largest number = 93, Smallest number = 23
\[
\text{Range} = 93 - 23 = 70
\]
Answer for Set 2:
\[
\boxed{57, 62, \text{None}, 70}
\]
---
#### Set 3: \( 31, 92, 25, 69, 80, 31, 29 \)
- Mean:
Sum = \( 31 + 92 + 25 + 69 + 80 + 31 + 29 = 357 \)
Total count = 7
\[
\text{Mean} = \frac{357}{7} = 51
\]
- Median:
Arranged in ascending order: \( 25, 29, 31, 31, 69, 80, 92 \)
Since there are 7 numbers (odd count), the median is the 4th number.
\[
\text{Median} = 31
\]
- Mode:
The number \( 31 \) appears twice, more than any other number.
\[
\text{Mode} = 31
\]
- Range:
Largest number = 92, Smallest number = 25
\[
\text{Range} = 92 - 25 = 67
\]
Answer for Set 3:
\[
\boxed{51, 31, 31, 67}
\]
---
#### Set 4: \( 21, 62, 66, 66, 79, 28, 63, 48, 59, 94, 19 \)
- Mean:
Sum = \( 21 + 62 + 66 + 66 + 79 + 28 + 63 + 48 + 59 + 94 + 19 = 635 \)
Total count = 11
\[
\text{Mean} = \frac{635}{11} \approx 57.73
\]
- Median:
Arranged in ascending order: \( 19, 21, 28, 48, 59, 62, 63, 66, 66, 79, 94 \)
Since there are 11 numbers (odd count), the median is the 6th number.
\[
\text{Median} = 62
\]
- Mode:
The number \( 66 \) appears twice, more than any other number.
\[
\text{Mode} = 66
\]
- Range:
Largest number = 94, Smallest number = 19
\[
\text{Range} = 94 - 19 = 75
\]
Answer for Set 4:
\[
\boxed{57.73, 62, 66, 75}
\]
---
#### Set 5: \( 83, 23, 24, 71, 52, 62, 63 \)
- Mean:
Sum = \( 83 + 23 + 24 + 71 + 52 + 62 + 63 = 378 \)
Total count = 7
\[
\text{Mean} = \frac{378}{7} = 54
\]
- Median:
Arranged in ascending order: \( 23, 24, 52, 62, 63, 71, 83 \)
Since there are 7 numbers (odd count), the median is the 4th number.
\[
\text{Median} = 62
\]
- Mode:
All numbers appear only once.
\[
\text{Mode} = \text{None}
\]
- Range:
Largest number = 83, Smallest number = 23
\[
\text{Range} = 83 - 23 = 60
\]
Answer for Set 5:
\[
\boxed{54, 62, \text{None}, 60}
\]
---
#### Set 6: \( 67, 70, 49, 95, 40, 97, 62, 54, 42 \)
- Mean:
Sum = \( 67 + 70 + 49 + 95 + 40 + 97 + 62 + 54 + 42 = 576 \)
Total count = 9
\[
\text{Mean} = \frac{576}{9} = 64
\]
- Median:
Arranged in ascending order: \( 40, 42, 49, 54, 62, 67, 70, 95, 97 \)
Since there are 9 numbers (odd count), the median is the 5th number.
\[
\text{Median} = 62
\]
- Mode:
All numbers appear only once.
\[
\text{Mode} = \text{None}
\]
- Range:
Largest number = 97, Smallest number = 40
\[
\text{Range} = 97 - 40 = 57
\]
Answer for Set 6:
\[
\boxed{64, 62, \text{None}, 57}
\]
---
#### Set 7: \( 86, 13, 60, 55, 61, 97, 30, 98, 79, 52, 18 \)
- Mean:
Sum = \( 86 + 13 + 60 + 55 + 61 + 97 + 30 + 98 + 79 + 52 + 18 = 659 \)
Total count = 11
\[
\text{Mean} = \frac{659}{11} \approx 59.91
\]
- Median:
Arranged in ascending order: \( 13, 18, 30, 52, 55, 60, 61, 79, 86, 97, 98 \)
Since there are 11 numbers (odd count), the median is the 6th number.
\[
\text{Median} = 60
\]
- Mode:
All numbers appear only once.
\[
\text{Mode} = \text{None}
\]
- Range:
Largest number = 98, Smallest number = 13
\[
\text{Range} = 98 - 13 = 85
\]
Answer for Set 7:
\[
\boxed{59.91, 60, \text{None}, 85}
\]
---
#### Set 8: \( 24, 22, 32, 59, 99, 59, 76, 83, 21, 95, 57 \)
- Mean:
Sum = \( 24 + 22 + 32 + 59 + 99 + 59 + 76 + 83 + 21 + 95 + 57 = 628 \)
Total count = 11
\[
\text{Mean} = \frac{628}{11} \approx 57.09
\]
- Median:
Arranged in ascending order: \( 21, 22, 24, 32, 57, 59, 59, 76, 83, 95, 99 \)
Since there are 11 numbers (odd count), the median is the 6th number.
\[
\text{Median} = 59
\]
- Mode:
The number \( 59 \) appears twice, more than any other number.
\[
\text{Mode} = 59
\]
- Range:
Largest number = 99, Smallest number = 21
\[
\text{Range} = 99 - 21 = 78
\]
Answer for Set 8:
\[
\boxed{57.09, 59, 59, 78}
\]
---
#### Set 9: \( 63, 25, 43, 28, 72, 61, 45, 46, 13 \)
- Mean:
Sum = \( 63 + 25 + 43 + 28 + 72 + 61 + 45 + 46 + 13 = 406 \)
Total count = 9
\[
\text{Mean} = \frac{406}{9} \approx 45.11
\]
- Median:
Arranged in ascending order: \( 13, 25, 28, 43, 45, 46, 61, 63, 72 \)
Since there are 9 numbers (odd count), the median is the 5th number.
\[
\text{Median} = 45
\]
- Mode:
All numbers appear only once.
\[
\text{Mode} = \text{None}
\]
- Range:
Largest number = 72, Smallest number = 13
\[
\text{Range} = 72 - 13 = 59
\]
Answer for Set 9:
\[
\boxed{45.11, 45, \text{None}, 59}
\]
---
#### Set 10: \( 53, 44, 10, 45, 59, 97, 77 \)
- Mean:
Sum = \( 53 + 44 + 10 + 45 + 59 + 97 + 77 = 385 \)
Total count = 7
\[
\text{Mean} = \frac{385}{7} = 55
\]
- Median:
Arranged in ascending order: \( 10, 44, 45, 53, 59, 77, 97 \)
Since there are 7 numbers (odd count), the median is the 4th number.
\[
\text{Median} = 53
\]
- Mode:
All numbers appear only once.
\[
\text{Mode} = \text{None}
\]
- Range:
Largest number = 97, Smallest number = 10
\[
\text{Range} = 97 - 10 = 87
\]
Answer for Set 10:
\[
\boxed{55, 53, \text{None}, 87}
\]
---
1. \( \boxed{60.73, 70, 32, 94, 71} \)
2. \( \boxed{57, 62, \text{None}, 70} \)
3. \( \boxed{51, 31, 31, 67} \)
4. \( \boxed{57.73, 62, 66, 75} \)
5. \( \boxed{54, 62, \text{None}, 60} \)
6. \( \boxed{64, 62, \text{None}, 57} \)
7. \( \boxed{59.91, 60, \text{None}, 85} \)
8. \( \boxed{57.09, 59, 59, 78} \)
9. \( \boxed{45.11, 45, \text{None}, 59} \)
10. \( \boxed{55, 53, \text{None}, 87} \)
Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. 60.73, 70, 32, 94, 71 \\
2. 57, 62, \text{None}, 70 \\
3. 51, 31, 31, 67 \\
4. 57.73, 62, 66, 75 \\
5. 54, 62, \text{None}, 60 \\
6. 64, 62, \text{None}, 57 \\
7. 59.91, 60, \text{None}, 85 \\
8. 57.09, 59, 59, 78 \\
9. 45.11, 45, \text{None}, 59 \\
10. 55, 53, \text{None}, 87 \\
\end{array}
}
\]
---
1. Mean, Median, Mode, and Range
#### Set 1: \( 82, 23, 59, 94, 70, 26, 32, 83, 87, 94, 32 \)
- Mean: The mean is the average of the numbers.
\[
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total count of numbers}}
\]
Sum = \( 82 + 23 + 59 + 94 + 70 + 26 + 32 + 83 + 87 + 94 + 32 = 668 \)
Total count = 11
\[
\text{Mean} = \frac{668}{11} \approx 60.73
\]
- Median: The median is the middle number when the numbers are arranged in ascending order.
Arranged in ascending order: \( 23, 26, 32, 32, 59, 70, 82, 83, 87, 94, 94 \)
Since there are 11 numbers (odd count), the median is the 6th number.
\[
\text{Median} = 70
\]
- Mode: The mode is the number that appears most frequently.
From the ordered list: \( 23, 26, 32, 32, 59, 70, 82, 83, 87, 94, 94 \)
Both \( 32 \) and \( 94 \) appear twice, more than any other number.
\[
\text{Mode} = 32, 94
\]
- Range: The range is the difference between the largest and smallest numbers.
Largest number = 94, Smallest number = 23
\[
\text{Range} = 94 - 23 = 71
\]
Answer for Set 1:
\[
\boxed{60.73, 70, 32, 94, 71}
\]
---
#### Set 2: \( 83, 93, 77, 33, 62, 28, 23 \)
- Mean:
Sum = \( 83 + 93 + 77 + 33 + 62 + 28 + 23 = 399 \)
Total count = 7
\[
\text{Mean} = \frac{399}{7} = 57
\]
- Median:
Arranged in ascending order: \( 23, 28, 33, 62, 77, 83, 93 \)
Since there are 7 numbers (odd count), the median is the 4th number.
\[
\text{Median} = 62
\]
- Mode:
All numbers appear only once.
\[
\text{Mode} = \text{None}
\]
- Range:
Largest number = 93, Smallest number = 23
\[
\text{Range} = 93 - 23 = 70
\]
Answer for Set 2:
\[
\boxed{57, 62, \text{None}, 70}
\]
---
#### Set 3: \( 31, 92, 25, 69, 80, 31, 29 \)
- Mean:
Sum = \( 31 + 92 + 25 + 69 + 80 + 31 + 29 = 357 \)
Total count = 7
\[
\text{Mean} = \frac{357}{7} = 51
\]
- Median:
Arranged in ascending order: \( 25, 29, 31, 31, 69, 80, 92 \)
Since there are 7 numbers (odd count), the median is the 4th number.
\[
\text{Median} = 31
\]
- Mode:
The number \( 31 \) appears twice, more than any other number.
\[
\text{Mode} = 31
\]
- Range:
Largest number = 92, Smallest number = 25
\[
\text{Range} = 92 - 25 = 67
\]
Answer for Set 3:
\[
\boxed{51, 31, 31, 67}
\]
---
#### Set 4: \( 21, 62, 66, 66, 79, 28, 63, 48, 59, 94, 19 \)
- Mean:
Sum = \( 21 + 62 + 66 + 66 + 79 + 28 + 63 + 48 + 59 + 94 + 19 = 635 \)
Total count = 11
\[
\text{Mean} = \frac{635}{11} \approx 57.73
\]
- Median:
Arranged in ascending order: \( 19, 21, 28, 48, 59, 62, 63, 66, 66, 79, 94 \)
Since there are 11 numbers (odd count), the median is the 6th number.
\[
\text{Median} = 62
\]
- Mode:
The number \( 66 \) appears twice, more than any other number.
\[
\text{Mode} = 66
\]
- Range:
Largest number = 94, Smallest number = 19
\[
\text{Range} = 94 - 19 = 75
\]
Answer for Set 4:
\[
\boxed{57.73, 62, 66, 75}
\]
---
#### Set 5: \( 83, 23, 24, 71, 52, 62, 63 \)
- Mean:
Sum = \( 83 + 23 + 24 + 71 + 52 + 62 + 63 = 378 \)
Total count = 7
\[
\text{Mean} = \frac{378}{7} = 54
\]
- Median:
Arranged in ascending order: \( 23, 24, 52, 62, 63, 71, 83 \)
Since there are 7 numbers (odd count), the median is the 4th number.
\[
\text{Median} = 62
\]
- Mode:
All numbers appear only once.
\[
\text{Mode} = \text{None}
\]
- Range:
Largest number = 83, Smallest number = 23
\[
\text{Range} = 83 - 23 = 60
\]
Answer for Set 5:
\[
\boxed{54, 62, \text{None}, 60}
\]
---
#### Set 6: \( 67, 70, 49, 95, 40, 97, 62, 54, 42 \)
- Mean:
Sum = \( 67 + 70 + 49 + 95 + 40 + 97 + 62 + 54 + 42 = 576 \)
Total count = 9
\[
\text{Mean} = \frac{576}{9} = 64
\]
- Median:
Arranged in ascending order: \( 40, 42, 49, 54, 62, 67, 70, 95, 97 \)
Since there are 9 numbers (odd count), the median is the 5th number.
\[
\text{Median} = 62
\]
- Mode:
All numbers appear only once.
\[
\text{Mode} = \text{None}
\]
- Range:
Largest number = 97, Smallest number = 40
\[
\text{Range} = 97 - 40 = 57
\]
Answer for Set 6:
\[
\boxed{64, 62, \text{None}, 57}
\]
---
#### Set 7: \( 86, 13, 60, 55, 61, 97, 30, 98, 79, 52, 18 \)
- Mean:
Sum = \( 86 + 13 + 60 + 55 + 61 + 97 + 30 + 98 + 79 + 52 + 18 = 659 \)
Total count = 11
\[
\text{Mean} = \frac{659}{11} \approx 59.91
\]
- Median:
Arranged in ascending order: \( 13, 18, 30, 52, 55, 60, 61, 79, 86, 97, 98 \)
Since there are 11 numbers (odd count), the median is the 6th number.
\[
\text{Median} = 60
\]
- Mode:
All numbers appear only once.
\[
\text{Mode} = \text{None}
\]
- Range:
Largest number = 98, Smallest number = 13
\[
\text{Range} = 98 - 13 = 85
\]
Answer for Set 7:
\[
\boxed{59.91, 60, \text{None}, 85}
\]
---
#### Set 8: \( 24, 22, 32, 59, 99, 59, 76, 83, 21, 95, 57 \)
- Mean:
Sum = \( 24 + 22 + 32 + 59 + 99 + 59 + 76 + 83 + 21 + 95 + 57 = 628 \)
Total count = 11
\[
\text{Mean} = \frac{628}{11} \approx 57.09
\]
- Median:
Arranged in ascending order: \( 21, 22, 24, 32, 57, 59, 59, 76, 83, 95, 99 \)
Since there are 11 numbers (odd count), the median is the 6th number.
\[
\text{Median} = 59
\]
- Mode:
The number \( 59 \) appears twice, more than any other number.
\[
\text{Mode} = 59
\]
- Range:
Largest number = 99, Smallest number = 21
\[
\text{Range} = 99 - 21 = 78
\]
Answer for Set 8:
\[
\boxed{57.09, 59, 59, 78}
\]
---
#### Set 9: \( 63, 25, 43, 28, 72, 61, 45, 46, 13 \)
- Mean:
Sum = \( 63 + 25 + 43 + 28 + 72 + 61 + 45 + 46 + 13 = 406 \)
Total count = 9
\[
\text{Mean} = \frac{406}{9} \approx 45.11
\]
- Median:
Arranged in ascending order: \( 13, 25, 28, 43, 45, 46, 61, 63, 72 \)
Since there are 9 numbers (odd count), the median is the 5th number.
\[
\text{Median} = 45
\]
- Mode:
All numbers appear only once.
\[
\text{Mode} = \text{None}
\]
- Range:
Largest number = 72, Smallest number = 13
\[
\text{Range} = 72 - 13 = 59
\]
Answer for Set 9:
\[
\boxed{45.11, 45, \text{None}, 59}
\]
---
#### Set 10: \( 53, 44, 10, 45, 59, 97, 77 \)
- Mean:
Sum = \( 53 + 44 + 10 + 45 + 59 + 97 + 77 = 385 \)
Total count = 7
\[
\text{Mean} = \frac{385}{7} = 55
\]
- Median:
Arranged in ascending order: \( 10, 44, 45, 53, 59, 77, 97 \)
Since there are 7 numbers (odd count), the median is the 4th number.
\[
\text{Median} = 53
\]
- Mode:
All numbers appear only once.
\[
\text{Mode} = \text{None}
\]
- Range:
Largest number = 97, Smallest number = 10
\[
\text{Range} = 97 - 10 = 87
\]
Answer for Set 10:
\[
\boxed{55, 53, \text{None}, 87}
\]
---
Final Answers:
1. \( \boxed{60.73, 70, 32, 94, 71} \)
2. \( \boxed{57, 62, \text{None}, 70} \)
3. \( \boxed{51, 31, 31, 67} \)
4. \( \boxed{57.73, 62, 66, 75} \)
5. \( \boxed{54, 62, \text{None}, 60} \)
6. \( \boxed{64, 62, \text{None}, 57} \)
7. \( \boxed{59.91, 60, \text{None}, 85} \)
8. \( \boxed{57.09, 59, 59, 78} \)
9. \( \boxed{45.11, 45, \text{None}, 59} \)
10. \( \boxed{55, 53, \text{None}, 87} \)
Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. 60.73, 70, 32, 94, 71 \\
2. 57, 62, \text{None}, 70 \\
3. 51, 31, 31, 67 \\
4. 57.73, 62, 66, 75 \\
5. 54, 62, \text{None}, 60 \\
6. 64, 62, \text{None}, 57 \\
7. 59.91, 60, \text{None}, 85 \\
8. 57.09, 59, 59, 78 \\
9. 45.11, 45, \text{None}, 59 \\
10. 55, 53, \text{None}, 87 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of mean mode median worksheet.
