Mean Median Mode Range Practice Problems

Understanding mean, median, mode, and range is fundamental in statistics, providing essential tools for data analysis. Mastering these concepts allows you to describe and interpret data sets effectively. This article provides practice problems to help you solidify your understanding of these measures.

Mean, Median, Mode, and Range: A Quick Review

Before diving into practice problems, let's briefly recap the definitions of mean, median, mode, and range.

• Mean: The average of a set of numbers. Calculated by adding all the numbers and dividing by the count of numbers.
• Median: The middle value in a data set ordered from least to greatest. If there are two middle numbers, the median is the average of those two.
• Mode: The number that appears most frequently in a data set. A data set can have no mode, one mode, or multiple modes.
• Range: The difference between the highest and lowest values in a data set.

Practice Problems: Level 1 - Basic Calculations

These problems will help you get comfortable with the basic calculations for mean, median, mode, and range.

Problem 1:

Find the mean, median, mode, and range of the following data set: 4, 7, 2, 9, 4

Solution:

• Mean: (4 + 7 + 2 + 9 + 4) / 5 = 26 / 5 = 5.2
• Median: First, order the data: 2, 4, 4, 7, 9. The middle number is 4. So, the median is 4.
• Mode: The number 4 appears twice, which is more than any other number. So, the mode is 4.
• Range: 9 - 2 = 7

Problem 2:

Calculate the mean, median, mode, and range for this data set: 12, 15, 18, 12, 13

Solution:

• Mean: (12 + 15 + 18 + 12 + 13) / 5 = 70 / 5 = 14
• Median: Order the data: 12, 12, 13, 15, 18. The middle number is 13. So, the median is 13.
• Mode: The number 12 appears twice, which is more than any other number. So, the mode is 12.
• Range: 18 - 12 = 6

Problem 3:

Determine the mean, median, mode, and range of the following: 25, 30, 25, 32, 28

Solution:

• Mean: (25 + 30 + 25 + 32 + 28) / 5 = 140 / 5 = 28
• Median: Order the data: 25, 25, 28, 30, 32. The middle number is 28. So, the median is 28.
• Mode: The number 25 appears twice, which is more than any other number. So, the mode is 25.
• Range: 32 - 25 = 7

Problem 4:

Find the mean, median, mode, and range of this set: 1, 1, 2, 3, 5, 8, 13

Solution:

• Mean: (1 + 1 + 2 + 3 + 5 + 8 + 13) / 7 = 33 / 7 = 4.71 (approximately)
• Median: The data is already ordered. The middle number is 3. So, the median is 3.
• Mode: The number 1 appears twice, which is more than any other number. So, the mode is 1.
• Range: 13 - 1 = 12

Problem 5:

Calculate the mean, median, mode, and range for the following: 10, 10, 10, 20, 20

Solution:

• Mean: (10 + 10 + 10 + 20 + 20) / 5 = 70 / 5 = 14
• Median: Order the data: 10, 10, 10, 20, 20. The middle number is 10. So, the median is 10.
• Mode: The number 10 appears three times, which is more than any other number. So, the mode is 10.
• Range: 20 - 10 = 10

Practice Problems: Level 2 - Dealing with Even Numbers and Larger Sets

These problems introduce data sets with an even number of values and slightly larger sets to increase complexity.

Problem 6:

Find the mean, median, mode, and range of the following data set: 6, 8, 3, 9, 10, 4

Solution:

• Mean: (6 + 8 + 3 + 9 + 10 + 4) / 6 = 40 / 6 = 6.67 (approximately)
• Median: First, order the data: 3, 4, 6, 8, 9, 10. Since there are an even number of values, the median is the average of the two middle numbers (6 and 8). So, the median is (6 + 8) / 2 = 7.
• Mode: There is no number that appears more than once. So, there is no mode.
• Range: 10 - 3 = 7

Problem 7:

Calculate the mean, median, mode, and range for this data set: 11, 15, 12, 18, 20, 14

Solution:

• Mean: (11 + 15 + 12 + 18 + 20 + 14) / 6 = 90 / 6 = 15
• Median: Order the data: 11, 12, 14, 15, 18, 20. Since there are an even number of values, the median is the average of the two middle numbers (14 and 15). So, the median is (14 + 15) / 2 = 14.5.
• Mode: There is no number that appears more than once. So, there is no mode.
• Range: 20 - 11 = 9

Problem 8:

Determine the mean, median, mode, and range of the following: 22, 28, 24, 30, 22, 26

Solution:

• Mean: (22 + 28 + 24 + 30 + 22 + 26) / 6 = 152 / 6 = 25.33 (approximately)
• Median: Order the data: 22, 22, 24, 26, 28, 30. Since there are an even number of values, the median is the average of the two middle numbers (24 and 26). So, the median is (24 + 26) / 2 = 25.
• Mode: The number 22 appears twice, which is more than any other number. So, the mode is 22.
• Range: 30 - 22 = 8

Problem 9:

Find the mean, median, mode, and range of this set: 5, 10, 5, 10, 15, 20, 25, 30

Solution:

• Mean: (5 + 10 + 5 + 10 + 15 + 20 + 25 + 30) / 8 = 120 / 8 = 15
• Median: Order the data: 5, 5, 10, 10, 15, 20, 25, 30. Since there are an even number of values, the median is the average of the two middle numbers (10 and 15). So, the median is (10 + 15) / 2 = 12.5.
• Mode: The numbers 5 and 10 both appear twice, which is more than any other number. So, the modes are 5 and 10 (bimodal).
• Range: 30 - 5 = 25

Problem 10:

Calculate the mean, median, mode, and range for the following: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Solution:

• Mean: (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) / 10 = 55 / 10 = 5.5
• Median: Order the data: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Since there are an even number of values, the median is the average of the two middle numbers (5 and 6). So, the median is (5 + 6) / 2 = 5.5.
• Mode: No number appears more than once. So, there is no mode.
• Range: 10 - 1 = 9

Practice Problems: Level 3 - Advanced Applications and Word Problems

These problems require applying your knowledge of mean, median, mode, and range in more complex scenarios and word problems.

Problem 11:

The following are the scores of 7 students on a math test: 75, 80, 85, 90, 90, 95, 100. Find the mean, median, mode, and range of the scores.

Solution:

• Mean: (75 + 80 + 85 + 90 + 90 + 95 + 100) / 7 = 615 / 7 = 87.86 (approximately)
• Median: The data is already ordered. The middle number is 90. So, the median is 90.
• Mode: The number 90 appears twice, which is more than any other number. So, the mode is 90.
• Range: 100 - 75 = 25

Problem 12:

A basketball team scored the following points in their last 6 games: 68, 72, 70, 65, 75, 70. Calculate the mean, median, mode, and range of the points scored.

Solution:

• Mean: (68 + 72 + 70 + 65 + 75 + 70) / 6 = 420 / 6 = 70
• Median: Order the data: 65, 68, 70, 70, 72, 75. Since there are an even number of values, the median is the average of the two middle numbers (70 and 70). So, the median is (70 + 70) / 2 = 70.
• Mode: The number 70 appears twice, which is more than any other number. So, the mode is 70.
• Range: 75 - 65 = 10

Problem 13:

The ages of 5 employees at a company are: 25, 30, 35, 40, and 45. What are the mean, median, mode, and range of their ages?

Solution:

• Mean: (25 + 30 + 35 + 40 + 45) / 5 = 175 / 5 = 35
• Median: The data is already ordered. The middle number is 35. So, the median is 35.
• Mode: No age appears more than once. So, there is no mode.
• Range: 45 - 25 = 20

Problem 14:

A store sold the following number of items each day for a week: 15, 20, 15, 25, 30, 20, 15. Determine the mean, median, mode, and range of the number of items sold.

Solution:

• Mean: (15 + 20 + 15 + 25 + 30 + 20 + 15) / 7 = 140 / 7 = 20
• Median: Order the data: 15, 15, 15, 20, 20, 25, 30. The middle number is 20. So, the median is 20.
• Mode: The number 15 appears three times, which is more than any other number. So, the mode is 15.
• Range: 30 - 15 = 15

Problem 15:

The prices of 8 different books are: $10, $12, $15, $10, $18, $20, $12, $14. Find the mean, median, mode, and range of the book prices.

Solution:

• Mean: (10 + 12 + 15 + 10 + 18 + 20 + 12 + 14) / 8 = 111 / 8 = 13.88 (approximately)
• Median: Order the data: 10, 10, 12, 12, 14, 15, 18, 20. Since there are an even number of values, the median is the average of the two middle numbers (12 and 14). So, the median is (12 + 14) / 2 = 13.
• Mode: The numbers 10 and 12 both appear twice, which is more than any other number. So, the modes are 10 and 12 (bimodal).
• Range: 20 - 10 = 10

Problem 16:

A group of students recorded the time they spent studying for a test (in minutes): 30, 45, 60, 30, 75, 90. Find the mean, median, mode, and range of the study times.

Solution:

• Mean: (30 + 45 + 60 + 30 + 75 + 90) / 6 = 330 / 6 = 55
• Median: Order the data: 30, 30, 45, 60, 75, 90. Since there are an even number of values, the median is the average of the two middle numbers (45 and 60). So, the median is (45 + 60) / 2 = 52.5.
• Mode: The number 30 appears twice, which is more than any other number. So, the mode is 30.
• Range: 90 - 30 = 60

Problem 17:

The number of customers visiting a cafe each day for a week was: 25, 30, 28, 32, 25, 35, 40. What are the mean, median, mode, and range of the daily customer count?

Solution:

• Mean: (25 + 30 + 28 + 32 + 25 + 35 + 40) / 7 = 215 / 7 = 30.71 (approximately)
• Median: Order the data: 25, 25, 28, 30, 32, 35, 40. The middle number is 30. So, the median is 30.
• Mode: The number 25 appears twice, which is more than any other number. So, the mode is 25.
• Range: 40 - 25 = 15

Problem 18:

The heights (in inches) of 6 basketball players are: 72, 75, 78, 72, 80, 82. Calculate the mean, median, mode, and range of their heights.

Solution:

• Mean: (72 + 75 + 78 + 72 + 80 + 82) / 6 = 459 / 6 = 76.5
• Median: Order the data: 72, 72, 75, 78, 80, 82. Since there are an even number of values, the median is the average of the two middle numbers (75 and 78). So, the median is (75 + 78) / 2 = 76.5.
• Mode: The number 72 appears twice, which is more than any other number. So, the mode is 72.
• Range: 82 - 72 = 10

Problem 19:

A weather station recorded the following high temperatures (in degrees Fahrenheit) over 10 days: 65, 68, 70, 72, 75, 75, 78, 80, 82, 85. Find the mean, median, mode, and range of the high temperatures.

Solution:

• Mean: (65 + 68 + 70 + 72 + 75 + 75 + 78 + 80 + 82 + 85) / 10 = 750 / 10 = 75
• Median: Order the data: 65, 68, 70, 72, 75, 75, 78, 80, 82, 85. Since there are an even number of values, the median is the average of the two middle numbers (75 and 75). So, the median is (75 + 75) / 2 = 75.
• Mode: The number 75 appears twice, which is more than any other number. So, the mode is 75.
• Range: 85 - 65 = 20

Problem 20:

The number of books read by 9 students in a summer program were: 5, 8, 5, 10, 12, 5, 7, 9, 11. Calculate the mean, median, mode, and range of the number of books read.

Solution:

• Mean: (5 + 8 + 5 + 10 + 12 + 5 + 7 + 9 + 11) / 9 = 72 / 9 = 8
• Median: Order the data: 5, 5, 5, 7, 8, 9, 10, 11, 12. The middle number is 8. So, the median is 8.
• Mode: The number 5 appears three times, which is more than any other number. So, the mode is 5.
• Range: 12 - 5 = 7

Why Practice is Key

Working through these mean, median, mode and range practice problems not only reinforces your understanding of the definitions but also hones your calculation skills. These statistical measures are essential building blocks for more advanced statistical analysis and are used in various fields, from data science to finance. The more you practice, the more comfortable and confident you'll become in applying these concepts.

Real-World Applications

Understanding mean, median, mode, and range isn't just about acing tests; it's about interpreting the world around you. Consider these examples:

• Finance: Calculating the average return on investment (mean), identifying the most common expense (mode), or determining the spread of stock prices (range).
• Healthcare: Finding the average blood pressure of patients (mean), understanding the most frequent age of diagnosis for a disease (mode), or analyzing the variability in patient recovery times (range).
• Education: Determining the average test score (mean), understanding the middle performance level of students (median), or identifying the most common grade (mode).
• Marketing: Analyzing average customer spending (mean), identifying the price point that customers most frequently purchase (mode), or assessing the variation in purchase amounts (range).

By understanding these measures, you can make more informed decisions, identify trends, and gain deeper insights from data.

Conclusion

Mastering mean, median, mode, and range is a crucial step in understanding statistics. By working through these practice problems, you’ve strengthened your ability to calculate these measures and apply them in various contexts. Remember to review the definitions, practice regularly, and consider how these concepts can be applied in the real world to enhance your analytical skills.