Year 6 Maths: Averages

Introduction to Averages

Hello, Year 6! Today, we are going to learn about averages. An average helps us understand a set of numbers by finding a single number that represents them all. It’s like finding the middle point of a group of numbers. There are three main types of averages: mean, median, and mode.

1. Mean

What is Mean?

The mean is what most people call the average. To find the mean, you add up all the numbers, and then you divide that total by how many numbers there are.

Example:

Let’s say you have the following numbers: 4, 8, 10.

1. Add them up: $$4 + 8 + 10 = 22$$
2. Count how many numbers: There are 3 numbers.
3. Divide the total by how many numbers: $$\frac{22}{3} \approx 7.33$$

So, the mean is approximately 7.33.

Key Rule for Mean:

• Add all numbers and divide by the total count.

2. Median

What is Median?

The median is the middle number in a sorted list. If there are two middle numbers, you find the mean of those two.

Example:

Consider the numbers: 3, 1, 4, 2.

1. Sort the numbers: 1, 2, 3, 4
2. Find the middle: There are 4 numbers, so the two middle numbers are 2 and 3.
3. Find the mean of the two middle numbers: $$\frac{2 + 3}{2} = 2.5$$

So, the median is 2.5.

Key Rule for Median:

• Sort the numbers and find the middle.

3. Mode

What is Mode?

The mode is the number that appears most often in a list.

Example:

Look at these numbers: 5, 3, 5, 2, 8.

• The number 5 appears twice, while all the others appear once.
• So, the mode is 5.

Key Rule for Mode:

• Find the number that appears most frequently.

Tips and Tricks

• For mean: Always remember to add first, then divide.
• For median: Sorting is key! Always sort before finding the middle.
• For mode: Check for frequency; sometimes there can be more than one mode or no mode at all.

Practice Questions

Easy Level Questions (1-20)

1. What is the mean of 2, 4, 6?
2. Find the median: 7, 3, 9.
3. What is the mode of: 1, 2, 3, 2?
4. Calculate the mean of: 5, 5, 7.
5. What is the median of: 8, 1, 6?
6. Identify the mode in: 4, 4, 4, 5, 6.
7. Find the mean of: 10, 20, 30.
8. What is the median of: 2, 5, 3, 8?
9. The numbers are: 1, 2, 1. What is the mode?
10. Calculate the mean: 15, 10, 5.
11. Find the median of: 12, 15, 10, 18.
12. What is the mode of: 9, 10, 9, 12?
13. Mean of 3, 5, 7?
14. Median of 4, 6, 2?
15. Mode in 1, 1, 2, 3?
16. Mean of 14, 16, 19?
17. Median of 20, 30, 25?
18. What is the mode of: 6, 7, 6, 8?
19. Find the mean: 18, 22, 30.
20. Median of 4, 4, 4, 5, 6?

Medium Level Questions (21-40)

21. Calculate the mean of: 5, 10, 15, 20.
22. What is the median of: 3, 1, 4, 2?
23. Find the mode in the set: 8, 7, 8, 6, 9, 8.
24. Mean of: 2, 4, 6, 8, 10?
25. What is the median of: 11, 13, 15, 17, 19?
26. Identify the mode of: 4, 4, 5, 6, 6, 7.
27. Calculate the mean of: 20, 25, 30.
28. Find the median of: 5, 9, 3, 6.
29. What is the mode of: 1, 1, 2, 3, 2, 3?
30. Calculate the mean: 12, 14, 16, 18.
31. What is the median of: 25, 20, 30, 40?
32. Identify the mode in: 2, 2, 3, 4, 4, 4.
33. Mean of 5, 10, 15, 20, 25?
34. Median of 8, 7, 9, 10?
35. Mode of 3, 3, 3, 4, 5, 5?
36. Mean of 30, 40, 50?
37. What is the median of: 12, 15, 10, 18, 20?
38. Identify the mode in: 5, 5, 6, 7, 7, 7?
39. Calculate the mean of: 1, 2, 3, 4, 5.
40. What is the median of: 8, 9, 10, 12, 11?

Hard Level Questions (41-60)

41. Mean of: 15, 20, 25, 30, 35?
42. What is the median of: 21, 22, 23, 24, 25, 26?
43. Identify the mode in: 4, 5, 6, 7, 8, 8, 9?
44. Calculate the mean of: 10, 20, 30, 40, 50.
45. What is the median of: 101, 105, 103, 104, 102?
46. Find the mode of: 1, 2, 2, 3, 4, 4, 4, 5?
47. Mean of: 100, 200, 300, 400, 500?
48. What is the median of: 15, 25, 35, 45, 55, 65?
49. Identify the mode in: 7, 7, 8, 9, 10, 10, 10?
50. Calculate the mean of: 2, 4, 8, 16, 32?
51. What is the median of: 1, 3, 5, 7, 9, 11?
52. Find the mode in: 12, 12, 13, 14, 14, 15, 15?
53. Mean of: 45, 55, 65, 75, 85?
54. What is the median of: 5, 8, 8, 8, 10, 10, 12?
55. Identify the mode in: 2, 2, 2, 3, 3, 4, 4, 4?
56. Calculate the mean of: 33, 44, 55, 66, 77?
57. What is the median of: 20, 30, 40, 50, 60, 70?
58. Mode of: 2, 3, 3, 4, 5, 5, 5, 6?
59. Mean of: 10, 20, 30, 40, 50, 60, 70?
60. What is the median of: 2, 3, 4, 5, 6, 7, 8, 9?

Answers and Explanations

Easy Level Answers:

1. $$\frac{2 + 4 + 6}{3} = 4$$
2. Median: 7 (middle number)
3. Mode: 2
4. $$\frac{5 + 5 + 7}{3} = 5$$
5. Median: 6 (middle number)
6. Mode: 4
7. $$\frac{10 + 20 + 30}{3} = 20$$
8. Median: 4 (middle number)
9. Mode: 1
10. $$\frac{15 + 10 + 5}{3} = 10$$
11. Median: 15 (middle number)
12. Mode: 9
13. $$\frac{3 + 5 + 7}{3} = 5$$
14. Median: 4 (middle number)
15. Mode: 1
16. $$\frac{14 + 16 + 19}{3} = 16$$
17. Median: 25 (middle number)
18. Mode: 6
19. $$\frac{18 + 22 + 30}{3} = 23.33$$
20. Median: 4

Medium Level Answers:

21. $$\frac{5 + 10 + 15 + 20}{4} = 12.5$$
22. Median: 2 (middle number)
23. Mode: 8
24. $$\frac{2 + 4 + 6 + 8 + 10}{5} = 6$$
25. Median: 15 (middle number)
26. Mode: 4
27. $$\frac{20 + 25 + 30}{3} = 25$$
28. Median: 5.5 (mean of middle numbers)
29. Mode: 2
30. $$\frac{12 + 14 + 16 + 18}{4} = 15$$
31. Median: 25 (middle number)
32. Mode: 4
33. $$\frac{5 + 10 + 15 + 20 + 25}{5} = 15$$
34. Median: 8.5 (mean of middle numbers)
35. Mode: 3
36. $$\frac{30 + 40 + 50}{3} = 40$$
37. Median: 18 (middle number)
38. Mode: 7
39. $$\frac{1 + 2 + 3 + 4 + 5}{5} = 3$$
40. Median: 9

Hard Level Answers:

41. $$\frac{15 + 20 + 25 + 30 + 35}{5} = 25$$
42. Median: 23 (middle number)
43. Mode: 8
44. $$\frac{10 + 20 + 30 + 40 + 50}{5} = 30$$
45. Median: 103 (middle number)
46. Mode: 4
47. $$\frac{100 + 200 + 300 + 400 + 500}{5} = 300$$
48. Median: 35 (middle number)
49. Mode: 10
50. $$\frac{2 + 4 + 8 + 16 + 32}{5} = 12.4$$
51. Median: 6 (middle number)
52. Mode: 12
53. $$\frac{45 + 55 + 65 + 75 + 85}{5} = 65$$
54. Median: 8 (middle number)
55. Mode: 2
56. $$\frac{33 + 44 + 55 + 66 + 77}{5} = 55$$
57. Median: 45 (middle number)
58. Mode: 5
59. $$\frac{10 + 20 + 30 + 40 + 50 + 60 + 70}{7} = 40$$
60. Median: 5.5 (mean of middle numbers)

I hope you enjoyed learning about averages today! Remember to practice, and soon you will be a pro at finding them!