KS3 data handling averages - working out the median

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

In KS3 Maths, data means information, and you'll be busy practising how to handle it – analysing, creating graphs, and designing questionnaires. This quiz focuses on averages in data handling, specifically the median value.

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There are three ways to find the average in a set of data: the mean (add totals and divide), the mode (most frequent), and the median. The median is the middle value when data is arranged from lowest to highest.

While mostly about median values, this quiz also explores ranges. Range is the difference between the highest and lowest data. For example, if Tom has 1 pet, Dick has 2, and Harry has 6, the range is 5 (6 - 1). The median is 2, the middle figure.

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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

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

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

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

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

What is the median time for completing the jigsaw?

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

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

What is the range of the jigsaw times now?

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

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)

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

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

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

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

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

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

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

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

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