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Maths Quiz - Level 5-6 Data Handling - Averages 01 (Questions)

Learn how to calculate averages and understand how different types of data can affect them. Discover the mean, median and mode in this KS3 Maths topic.

Explore the Topic →

(quiz starts below)

Fascinating Fact:

One very large value can pull the mean up. Monthly pocket money of £5, £6, £6, £7 and £30 has a mean of £10.8 but the median is £6.

In KS3 Maths, pupils explore different types of averages and learn how each one represents data. The mean, median and mode each show something different about a data set and are used in real-world situations like surveys and statistics.

Key Terms

Mean: The total of all values divided by the number of values.
Median: The middle value when data is arranged in order.
Mode: The number that appears most often in a data set.

Frequently Asked Questions (Click to see answers)

What are the three types of averages in KS3 Maths?

The three types of averages are the mean, median and mode. Each one gives different information about how the data is spread or grouped.

Why can the mean be misleading?

The mean can be affected by extreme values, such as one number being much larger or smaller than the rest, which can make the result less representative.

When should I use the median instead of the mean?

The median is more useful when data includes extreme values or outliers, as it is not affected by unusually high or low numbers.

Try These Related Quizzes

1.

What do you do first to find the median of a set of data?

[ ]	Add all the values together
[ ]	Cross off the highest and lowest values
[ ]	Group the frequencies
[ ]	Put data values in order of size

2.

If there is an even number of values in the ordered set, the median is .......

[ ]	halfway between the two middle values
[ ]	halfway between the first and last values
[ ]	the difference between the two middle values
[ ]	the sum of the two middle values

3.

In a set of 20 data values in ascending order, the 10^th is 22 and the 11^th is 24. What is the median?

[ ]	21
[ ]	22
[ ]	23
[ ]	24

4.

The top five boys' names in order of popularity are Oliver, Jack, Ben, Matthew and James. What is the median of this set?

[ ]	James
[ ]	Oliver
[ ]	Ben
[ ]	None of these

5.

Six children recorded their times (in minutes) to do a jigsaw: 12, 10, 15, 19, 11, 17. What is the range of these times?

[ ]	9 minutes
[ ]	12 minutes
[ ]	15 minutes
[ ]	19 minutes

6.

What is the median time for completing the jigsaw?

[ ]	12.5 minutes
[ ]	13 minutes
[ ]	13.5 minutes
[ ]	14 minutes

7.

Three more children completed the jigsaw. Their times were 8, 10 and 24 mins. What is the median now?

[ ]	10 minutes
[ ]	12 minutes
[ ]	14 minutes
[ ]	16 minutes

8.

What is the range of the jigsaw times now?

[ ]	10 minutes
[ ]	12 minutes
[ ]	14 minutes
[ ]	16 minutes

9.

The one extra large value in the set is called an .......

[ ]	outcrop
[ ]	outlier
[ ]	outline
[ ]	outrage

10.

A small range of values indicates a .......

[ ]	greater consistency of the data
[ ]	smaller median
[ ]	smaller number of data values
[ ]	higher average

You can find more about this topic by visiting BBC Bitesize - Averages

Maths Quiz - Level 5-6 Data Handling - Averages 01 (Answers)

1.

What do you do first to find the median of a set of data?

[ ]	Add all the values together
[ ]	Cross off the highest and lowest values
[ ]	Group the frequencies
[x]	Put data values in order of size

Put the lowest at one end and the highest at the other. Then arrange all the others in between, in ascending order

2.

If there is an even number of values in the ordered set, the median is .......

[x]	halfway between the two middle values
[ ]	halfway between the first and last values
[ ]	the difference between the two middle values
[ ]	the sum of the two middle values

Find this by adding the two middle values together then divide by 2. If both middle values are the same, that IS the median

3.

In a set of 20 data values in ascending order, the 10^th is 22 and the 11^th is 24. What is the median?

[ ]	21
[ ]	22
[x]	23
[ ]	24

(22 + 24) ÷ 2 = 23

4.

The top five boys' names in order of popularity are Oliver, Jack, Ben, Matthew and James. What is the median of this set?

[ ]	James
[ ]	Oliver
[ ]	Ben
[x]	None of these

This is qualitative data which cannot be arranged in size order, so there is no median

5.

Six children recorded their times (in minutes) to do a jigsaw: 12, 10, 15, 19, 11, 17. What is the range of these times?

[x]	9 minutes
[ ]	12 minutes
[ ]	15 minutes
[ ]	19 minutes

Largest = 19, smallest = 10, 19 - 10 = 9

6.

What is the median time for completing the jigsaw?

[ ]	12.5 minutes
[ ]	13 minutes
[x]	13.5 minutes
[ ]	14 minutes

In order: 10, 11, 12, 15, 17, 19. The median is halfway between 12 and 15. (12 + 15) ÷ 2 = 13.5

7.

Three more children completed the jigsaw. Their times were 8, 10 and 24 mins. What is the median now?

[ ]	10 minutes
[x]	12 minutes
[ ]	14 minutes
[ ]	16 minutes

The median is lower because two smaller values have been added below the old median

8.

What is the range of the jigsaw times now?

[ ]	10 minutes
[ ]	12 minutes
[ ]	14 minutes
[x]	16 minutes

The range is bigger because the largest and smallest values have both changed

9.

The one extra large value in the set is called an .......

[ ]	outcrop
[x]	outlier
[ ]	outline
[ ]	outrage

Because it lies outside the region of most other values

10.

A small range of values indicates a .......

[x]	greater consistency of the data
[ ]	smaller median
[ ]	smaller number of data values
[ ]	higher average

A larger range shows the values are more spread out and more varied