Introduction

Hello, everyone! Today, we’re going to learn about four important ways to describe a set of numbers: mean, median, mode, and range. These are all useful tools in maths that help us understand data better. Let’s break each one down step by step!

What is the Mean?

The mean is what most people call the average. To find the mean, you need to follow these steps:

  1. Add up all the numbers in your set.
  2. Divide the total by how many numbers there are.

Example:

If we have the numbers 4, 8, and 10:

  • First, add them together: 4 + 8 + 10 = 22
  • Then, divide by the number of numbers (which is 3): 22 ÷ 3 = 7.33

So, the mean is 7.33.

What is the Median?

The median is the middle number in a list of numbers when they are arranged in order. If there are two middle numbers (in an even set), you find the mean of those two numbers.

Example:

For the numbers 3, 1, 4, and 2:

  • First, arrange them: 1, 2, 3, 4
  • There are four numbers, so the middle ones are 2 and 3. Find the mean: (2 + 3) ÷ 2 = 2.5

So, the median is 2.5.

What is the Mode?

The mode is the number that appears most often in a set. There can be one mode, more than one mode, or no mode at all.

Example:

In the set 1, 2, 2, 3, and 4:

  • The number 2 appears twice, while all the others appear once.

So, the mode is 2.

What is the Range?

The range tells you how spread out the numbers are. To find the range, subtract the smallest number from the largest number.

Example:

For the numbers 2, 5, and 10:

  • The smallest number is 2, and the largest is 10.
  • So, the range is 10 – 2 = 8.

The range is 8.

Summary of Key Points

  • Mean: Add all the numbers and divide by how many there are.
  • Median: The middle number in an ordered list.
  • Mode: The number that appears the most.
  • Range: The difference between the largest and smallest numbers.

Questions for Practice

Easy Level (20 Questions)

  1. Find the mean of 2, 4, 6.
  2. What is the median of 5, 3, and 9?
  3. Identify the mode of 1, 2, 2, 3.
  4. Calculate the range of 7, 8, and 10.
  5. Find the mean of 10, 20, 30.
  6. What is the median of 1, 2, 3, 4, 5?
  7. Identify the mode of 5, 5, 6, 7.
  8. Calculate the range of 3, 6, 9.
  9. Find the mean of 100, 200, 300.
  10. What is the median of 8, 6, 7?
  11. Identify the mode of 10, 20, 20, 30.
  12. Calculate the range of 12, 15, 19.
  13. Find the mean of 1, 1, 2, 2.
  14. What is the median of 11, 12, 13, 14, 15?
  15. Identify the mode of 3, 4, 4, 5, 5.
  16. Calculate the range of 5, 10, 15.
  17. Find the mean of 5, 7, 9.
  18. What is the median of 2, 4, 6, 8?
  19. Identify the mode of 6, 7, 6, 8, 9.
  20. Calculate the range of 1, 2, 3, 4, 5.

Medium Level (20 Questions)

  1. Find the mean of 4, 8, 6, 10.
  2. What is the median of 3, 7, 8, 9, 10?
  3. Identify the mode of 1, 2, 2, 3, 3, 4.
  4. Calculate the range of 10, 20, 30, 40.
  5. Find the mean of 15, 25, 35, 45.
  6. What is the median of 5, 12, 15, 20?
  7. Identify the mode of 3, 3, 3, 4, 5.
  8. Calculate the range of 50, 60, 70, 80.
  9. Find the mean of 2, 5, 8, 10, 15.
  10. What is the median of 1, 2, 3, 4, 5, 6?
  11. Identify the mode of 9, 10, 10, 11, 12.
  12. Calculate the range of 100, 150, 200, 250.
  13. Find the mean of 23, 27, 30.
  14. What is the median of 5, 10, 15, 20, 25?
  15. Identify the mode of 8, 8, 8, 9, 10.
  16. Calculate the range of 14, 18, 22.
  17. Find the mean of 10, 20, 30, 40, 50.
  18. What is the median of 9, 7, 12, 6?
  19. Identify the mode of 2, 3, 3, 4, 5.
  20. Calculate the range of 5, 15, 25, 35.

Hard Level (20 Questions)

  1. Find the mean of 45, 55, 65, 75.
  2. What is the median of 12, 15, 20, 25, 30, 35?
  3. Identify the mode of 5, 6, 6, 7, 8, 8, 9.
  4. Calculate the range of 3, 12, 24, 36.
  5. Find the mean of 10, 20, 30, 40, 50, 60, 70.
  6. What is the median of 16, 22, 24, 28, 30, 32?
  7. Identify the mode of 11, 12, 12, 13, 14, 14, 14.
  8. Calculate the range of 100, 200, 300, 400, 500.
  9. Find the mean of 7, 14, 21, 28, 35.
  10. What is the median of 5, 10, 15, 20, 25, 30?
  11. Identify the mode of 9, 10, 10, 11, 11, 12.
  12. Calculate the range of 1, 4, 6, 8, 10.
  13. Find the mean of 23, 25, 27, 29.
  14. What is the median of 18, 20, 22, 24, 26, 28?
  15. Identify the mode of 5, 6, 7, 7, 8, 9.
  16. Calculate the range of 2, 5, 9, 13, 17.
  17. Find the mean of 36, 48, 60, 72.
  18. What is the median of 2, 4, 6, 8, 10, 12, 14?
  19. Identify the mode of 1, 2, 2, 3, 3, 3, 4.
  20. Calculate the range of 1, 3, 7, 8, 10.

Answers and Explanations

Easy Level Answers:

  1. Mean: 4
  2. Median: 5
  3. Mode: 2
  4. Range: 3
  5. Mean: 20
  6. Median: 3
  7. Mode: 5
  8. Range: 6
  9. Mean: 200
  10. Median: 7
  11. Mode: 20
  12. Range: 7
  13. Mean: 1.5
  14. Median: 13
  15. Mode: 4 and 5
  16. Range: 10
  17. Mean: 7
  18. Median: 6
  19. Mode: 6
  20. Range: 4

Medium Level Answers:

  1. Mean: 7
  2. Median: 8
  3. Mode: 2 and 3
  4. Range: 30
  5. Mean: 25
  6. Median: 12.5
  7. Mode: 3
  8. Range: 30
  9. Mean: 10
  10. Median: 3
  11. Mode: 10
  12. Range: 150
  13. Mean: 25
  14. Median: 15
  15. Mode: 8
  16. Range: 8
  17. Mean: 30
  18. Median: 8
  19. Mode: 3
  20. Range: 30

Hard Level Answers:

  1. Mean: 60
  2. Median: 23
  3. Mode: 6 and 8
  4. Range: 33
  5. Mean: 40
  6. Median: 24
  7. Mode: 14
  8. Range: 400
  9. Mean: 21
  10. Median: 17.5
  11. Mode: 10 and 11
  12. Range: 9
  13. Mean: 26.25
  14. Median: 24
  15. Mode: 7
  16. Range: 9
  17. Mean: 54
  18. Median: 8
  19. Mode: 2 and 3
  20. Range: 9

Conclusion

I hope you now have a clearer understanding of mean, median, mode, and range! Practice these concepts with the questions provided, and you’ll become experts in no time. If you have any questions, feel free to ask!