# Data, frequency and relative frequency · Years 8–9

> Data, frequency and relative frequency, Years 8–9: Frequency tables and more. Explanation, worked examples and free practice for the national curriculum in England.

In Data, frequency and relative frequency (Years 8–9) you practise 5 skills: Reading data from a table and a chart · Frequency tables · Frequency of grouped data · Relative frequency · Comparing groups of different sizes.

The frequency of an answer is the number of times it appears. When there are many different values, such as test scores, you put them into groups: 60–69, 70–79 and so on, and count how many values are in each group.

The relative frequency is the frequency divided by the number of people who answered. If 10 out of 40 pupils chose blue, the relative frequency of blue is 10/40, which is a quarter, or 25%. All the relative frequencies add up to 100%.

When you compare two groups of different sizes, compare the relative frequencies, not the numbers themselves. 12 out of 50 is more pupils than 8 out of 25, but 24% is less than 32%.

**Tip:** Before you compare groups, check: are they the same size? If not, convert to percentages.

## What you learn

### Reading data from a table and a chart

- Example: The pupils in the class chose their favourite colour. (Bar chart: blue 12, red 18, green 16) How many pupils answered altogether?
- Answer: 46
- Solution: The lines on the axis go up in steps of 2. 12 + 18 + 16 = 46 Altogether 46 pupils answered.

### Frequency tables

- Example: The children in the neighbourhood chose a sports club. These are the answers: Swimming, basketball, basketball, swimming, basketball, swimming, basketball, football, swimming, football, swimming, swimming. How many children chose basketball?
- Answer: 4
- Solution: Basketball appears 4 times in the list, so its frequency is 4.

### Frequency of grouped data

- Example: These are the scores of the pupils in a class test: 77, 84, 73, 54, 76, 74, 80, 58, 69, 82, 89, 50, 79, 80, 79, 77, 95, 65, 97, 68. How many pupils got a score in the group 60–69?
- Answer: 3
- Solution: The scores in the group: 69, 65, 68. Altogether 3 pupils.

### Relative frequency

- Example: The children in the neighbourhood chose a sports club. (Frequency table: club and the number of children) What is the relative frequency of running? Write it as a fraction.
- Answer: 1/5
- Solution: There are 10 children altogether, and 2 of them chose running. The relative frequency is 2/10, which is 1/5.

### Comparing groups of different sizes

- Example: Oak School and Pine School asked their pupils which fruit they like best. (Double bar chart: apples 18 and 5, bananas 14 and 2, grapes 5 and 5) At which school did more pupils choose apples?
- Options: Pine School · Oak School
- Answer: Oak School
- Solution: Oak School: 18, Pine School: 5. So more pupils chose apples at Oak School.

The exercises are made by rules and the answers are worked out in code. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).

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