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Maths

Inter-quartile range, cumulative frequency, box and whisker plots - Higher

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# Grouping data

It is often better to display data in a table. This section will look at different ways to organise data, and revise the following terms:

1. Classes are the groups the data is organised into.
2. Class boundaries are the boundaries between one class and the next.
3. Each class has an upper class boundary and lower class boundary. This is a practical application of lower and upper bounds that you met in Number.
4. The class width is the difference between the upper class boundary and lower class boundary.
5. The midpoint of the class is the middle of the upper and lower class boundaries (i.e, the median).

## Grouping discrete data

The table shows the number of people on 12 different buses. Discrete data is normally grouped in the following way:

Number of people on a bus4-67-910-1213-15
Frequency2721

From the table we can see that there were 7 buses with 7-9 people on them. But we have no way of telling exactly how many people were on each bus.

Now look at the class widths: they are all 3.

The midpoints of the classes are 5, 8, 11 and 14, as shown in red.

## Grouping continuous data

There are many ways to represent continuous data in a table.

### Example 1

This table shows the heights (h) of 25 people. The class widths are all 10.

• Height
• (cm)

120 h <130

130 h <140

140 h <150

150 h <160

Frequency46105

The class boundaries are 120, 130, 140, 150 and 160.

The midpoints of the classes are 125, 135, 145 and 155, shown in red.

### Example 2

Length (cm)110-129130-149150-169170-189
Frequency5311

• The class boundaries are 109.5, 129.5, 149.5, 169.5 and 189.5.
• The class widths are all 20.
• The midpoints of the classes are 119.5, 139.5, 159.5 and 179.5.

### Example 3

Height (cm)2-45-78-1011-14
Frequency7625

• The class boundaries are 1.5, 4.5, 7.5, 10.5 and 14.5.
• The class widths are all 3, except the last one which is 4.
• The midpoints of the classes are 3, 6, 9 and 12.5.

### Example 4

Age (years)21-3031-4041-5051-60
Frequency81034

This table looks very similar to the table in example 2, and you might assume that the class boundaries are 20.5, 30.5 etc - but they are not! Remember that if you are 16 now, you will be 16 right up until your 17th birthday.

• Therefore, the class boundaries are 21, 31, 41, 51 and 61.
• The class widths are all 10.
• The midpoints of the classes are 25.5, 35.5, 45.5 and 55.5.

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