Mean Median Mode Range Worksheets With Answers

Mean, Median, Mode, and Range Worksheets with Answers: A Comprehensive Guide

Understanding mean, median, mode, and range is fundamental to grasping descriptive statistics. These measures help us summarize and interpret data sets, providing valuable insights into the central tendency and spread of data. This comprehensive guide provides a detailed explanation of each concept, along with numerous practice worksheets and their corresponding answers to solidify your understanding.

What are Mean, Median, Mode, and Range?

Before diving into worksheets, let's clearly define each term:

1. Mean: The mean, often called the average, is the sum of all values in a data set divided by the number of values. It represents the central tendency of the data.

Example: For the data set {2, 4, 6, 8, 10}, the mean is (2+4+6+8+10)/5 = 6.

2. Median: The median is the middle value in a data set when it's ordered from least to greatest. If the data set has an even number of values, the median is the average of the two middle values. The median is less sensitive to outliers than the mean.

Example: For the data set {2, 4, 6, 8, 10}, the median is 6. For the data set {2, 4, 6, 8}, the median is (4+6)/2 = 5.

3. Mode: The mode is the value that appears most frequently in a data set. A data set can have one mode (unimodal), more than one mode (bimodal, trimodal, etc.), or no mode if all values appear with equal frequency.

Example: For the data set {2, 4, 4, 6, 8}, the mode is 4. The data set {2, 4, 6, 8} has no mode. The data set {2, 2, 4, 4, 6} is bimodal with modes 2 and 4.

4. Range: The range is the difference between the highest and lowest values in a data set. It indicates the spread or variability of the data.

Example: For the data set {2, 4, 6, 8, 10}, the range is 10 - 2 = 8.

Worksheet 1: Basic Calculations

This worksheet focuses on calculating the mean, median, mode, and range for simple data sets.

Instructions: Calculate the mean, median, mode, and range for each data set.

Data Sets:

1. {5, 10, 15, 20, 25}
2. {3, 6, 9, 12, 15, 18}
3. {1, 1, 2, 2, 3, 3, 3, 4, 4, 5}
4. {10, 12, 14, 16, 18, 20, 22}
5. {7, 7, 7, 7, 7}

Answers:

1. Mean: 15, Median: 15, Mode: None, Range: 20
2. Mean: 10.5, Median: 10.5, Mode: None, Range: 15
3. Mean: 2.7, Median: 2.5, Mode: 3, Range: 4
4. Mean: 16, Median: 16, Mode: None, Range: 12
5. Mean: 7, Median: 7, Mode: 7, Range: 0

Worksheet 2: Data Sets with Outliers

This worksheet introduces data sets containing outliers, which can significantly affect the mean.

Instructions: Calculate the mean, median, mode, and range for each data set. Observe how outliers impact the mean.

Data Sets:

1. {1, 2, 3, 4, 5, 100}
2. {10, 12, 14, 16, 100}
3. {5, 5, 5, 5, 100}
4. {1, 1, 1, 1, 100}
5. {20, 22, 24, 26, 1000}

Answers:

1. Mean: 19.16, Median: 3.5, Mode: None, Range: 99
2. Mean: 28.4, Median: 14, Mode: None, Range: 90
3. Mean: 22, Median: 5, Mode: 5, Range: 95
4. Mean: 20, Median: 1, Mode: 1, Range: 99
5. Mean: 220.4, Median: 24, Mode: None, Range: 980

Worksheet 3: Real-World Applications

This worksheet applies mean, median, mode, and range to real-world scenarios.

Instructions: Read each scenario and determine which measure of central tendency or spread (mean, median, mode, or range) is most appropriate to answer the question. Then, calculate that measure.

Scenarios:

1. A teacher wants to know the average score of her students on a test. The scores are: {70, 80, 85, 90, 95, 100}. Which measure should she use and what is the result?
2. A store owner wants to know the most popular shoe size sold. The sizes sold are: {8, 8.5, 9, 9, 9.5, 10, 10, 10, 10.5, 11}. Which measure should he use and what is the result?
3. A farmer wants to know the spread of his crops' yield in kilograms. The yields are: {100, 105, 110, 115, 120}. Which measure should he use and what is the result?
4. A company wants to know the typical salary of its employees. The salaries are: {$30,000, $35,000, $40,000, $45,000, $50,000, $1,000,000}. Which measure best represents the typical salary and why? What is the result of the chosen measure?
5. A meteorologist tracks the daily high temperatures for a week. The temperatures are: {72, 75, 78, 80, 82, 85, 88}. What is the average high temperature for the week?

Answers:

1. Mean: 88.33
2. Mode: 10
3. Range: 20
4. Median: $42,500. The median is a better representation because the mean is heavily skewed by the outlier ($1,000,000).
5. Mean: 78.43

Worksheet 4: Analyzing Frequency Distributions

This worksheet involves calculating measures from frequency distributions (data presented in a table showing frequencies of each value).

Instructions: Calculate the mean, median, mode, and range for each data set presented in the frequency distribution table.

Data Sets:

Table 1:

Value	Frequency
1	2
2	4
3	6
4	3
5	1

Table 2:

Value	Frequency
10	5
20	10
30	15
40	10
50	5

Answers:

Table 1:

• Mean: 2.7
• Median: 3
• Mode: 3
• Range: 4

Table 2:

• Mean: 25
• Median: 30
• Mode: 30
• Range: 40

Worksheet 5: Challenging Problems

These problems require a deeper understanding of the concepts and their application.

Instructions: Solve the following problems:

1. The mean of five numbers is 12. Four of the numbers are 10, 11, 13, and 14. What is the fifth number?
2. The median of a set of seven numbers is 20. The range is 10. If the smallest number is 15, what is the largest number?
3. A data set has a mean of 15, a median of 12, and a mode of 10. Is it possible to construct such a data set? If so, provide an example. If not, explain why not.
4. Two data sets have the same mean, but different ranges. What does this tell you about the data?

Answers:

1. 14: (10 + 11 + 13 + 14 + x)/5 = 12; x = 14
2. 25: The median is the middle value; if the smallest number is 15 and there are seven numbers, the median is the 4th number. The range is 10, so the largest number is 15 + 10 = 25.
3. Yes. A possible data set: {10, 10, 12, 18, 20}. This data set has a mean of 15, a median of 12, and a mode of 10.
4. The data sets have the same average value but different spread or variability. One data set's values are more clustered around the mean, while the other is more spread out.

These worksheets provide a comprehensive range of exercises, from simple calculations to more complex problem-solving. Remember that consistent practice is key to mastering these fundamental statistical concepts. By working through these examples and understanding the solutions, you'll build a solid foundation for more advanced statistical analysis. This foundational understanding of mean, median, mode, and range will be invaluable in various fields, from data science to everyday problem-solving. Remember to always check your work meticulously and ensure your understanding before moving onto more complex statistical concepts. Good luck!