# Range, averages and two sources of data · Years 8–9

> Range, averages and two sources of data, Years 8–9: The range and more. Explanation, worked examples and free practice for the national curriculum in England.

In Range, averages and two sources of data (Years 8–9) you practise 5 skills: The range · The mean · The median and the mode · Comparing two sources of data · Reading between the values in a table and a graph.

The range shows how spread out the data is: subtract the smallest value from the largest value.

The mean is the sum of the values divided by the number of values. The median is the value in the middle, once the values are in order from smallest to largest. The mode is the value that appears most often.

When you compare two groups, start with the means. If the means are equal, the group with the smaller range is more consistent.

When something changes at a steady rate, you can work out a value that is not in the table: find how much it changes in one unit, and carry on from there.

**Tip:** Before you work out a median, put all the values in order from smallest to largest.

## What you learn

### The range

- Example: These are the points scored by the players in a team in one game: 48, 7, 24, 45, 37. What is the range?
- Answer: 41
- Solution: The largest value is 48, and the smallest value is 7. 48 − 7 = 41 The range is 41.

### The mean

- Example: These are the scores of the students in a group in a test: 40, 91, 62, 52, 43, 90. What is the mean?
- Answer: 63
- Solution: The sum of the scores: 40 + 91 + 62 + 52 + 43 + 90 = 378 There are 6 scores: 378 ÷ 6 = 63 The mean is 63.

### The median and the mode

- Example: What is the mode of the numbers? 27, 6, 15, 4, 6, 5, 4, 22, 4.
- Answer: 4
- Solution: The number 4 appears 3 times, more than any other number. So the mode is 4.

### Comparing two sources of data

- Example: The bar chart shows how many points two basketball teams, the Lions and the Tigers, scored in five games. (A double bar chart: first game: the Lions 25, the Tigers 55; second game: the Lions 70, the Tigers 30; third game: the Lions 25, the Tigers 25; fourth game: the Lions 45, the Tigers 20; fifth game: the Lions 65, the Tigers 60) Which team has the higher mean?
- Options: The Tigers · The Lions
- Answer: The Lions
- Solution: The Lions' points: 25 + 70 + 25 + 45 + 65 = 230 230 ÷ 5 = 46 The Tigers' points: 55 + 30 + 25 + 20 + 60 = 190 190 ÷ 5 = 38 The Lions have the higher mean.

### Reading between the values in a table and a graph

- Example: The table shows the height of a tree every two years. It grows at a steady rate. (A table: year 2, 60 cm; year 4, 66 cm; year 6, 72 cm; year 8, 78 cm) What was the height in year 5?
- Answer: 69 cm
- Solution: Every two years the tree grows 6 cm, so it grows 3 cm each year. In year 4 the height was 66 cm. One year later: 66 + 3 = 69 In year 5 the height was 69 cm.

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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