Data is another word for information. In KS3 Maths you'll get plenty of practise handling data - analysing information, creating graphs or charts, designing questionnaires. This particular quiz is about averages in data handling and, more specifically, the median value.

There are three generally accepted ways to find the average in a set of data - the mean (the figure found by adding the totals together and then dividing by the number of totals used), the mode (the amount which appears most often) and the median. The median is the set of data which appears in the middle when the data is arranged from lowest to highest.

Though concentrating mainly on median values, this quiz also looks at ranges of values. The range is the difference between the highest and the lowest pieces of data. If you were to look at the number of pets Tom, Dick and Harry have. If Tom has 1, Dick has 2 and Harry has 6 the range would be 5 (6 - 1). The median would be 2 because this is the midmost figure.

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

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 .......

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

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

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?

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

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

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

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

outlier

outline

outrage

Because it lies outside the region of most other values

10.

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

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

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