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Information
may be collected by people for their work. For example, journalists
need information to write articles and teachers need classwork and
homework marks in order to write reports for parents.
Data
Items of information are called data. If you are asked about your
favourite colour, your answer is an item of data. If many people
are asked, the data will be collected in a tally table and
charts may be drawn to show the information about their favourite
colours.
From this simple bar chart it can be seen that 2 people chose red,
3 blue and 1 yellow. Bar charts are very useful for showing data
that is individual (e.g. pets, favourite lesson).
Pie Charts
Data can be charted as segments of a circle. This type of chart
is called a pie chart.
If there are 6 people and each one has an equal share of the circle,
each segment would be 60º as 360º ÷ 6 = 60º.
 |
| Yellow |
60º |
| Red |
120º |
| Blue |
180º |
|
Pie charts are popular because they are useful for comparing data
quickly.
Pie Charts for Grouped Data
Information can be confusing when there are many ways to answer
a question.
If you were asked about your pocket money, your item of data could
be one of many possible answers.
Data is often grouped to avoid the confusion caused by many answers.
For pocket money, the data could be placed in groups such as:
- 'less than £2'
- '£2 and less than £4'
- '£4 and less than £6'
- '£6 or more'
The
whole circle is then divided by the number of people asked, the
total frequency. Each group frequency is multiplied by this number
to find the correct share of the circle.
The total frequency is 10 people. Each person is represented in
the pie chart by (360º ÷ 10) = 36º
| Pocket
Money |
Frequency |
Angle
in the circle |
| Less
than £2 |
1 |
36º |
| £2
and less than £4 |
4 |
4
x 36 = 144º |
| £4
and less than £6 |
3 |
3
x 36 = 108º |
| £6
or more |
2 |
2
x 36 = 72º |
| Total |
10 |
360º |
Histograms for Grouped Data
A histogram is commonly used to represent grouped data. It looks
like a bar chart, but there are several differences. The sections
of the chart join and the axes have scales. In this example all
the groups have the same width.
| Pocket
Money |
Frequency |
| Less
than £2 |
1 |
| £2
and less than £4 |
4 |
| £4
and less than £6 |
3 |
| £6
or more |
2 |
| Total
|
10 |
Estimates of the number of people receiving a particular amount
can be made from the chart.
Line graphs
These are used instead of bar charts when one item of data is connected
with the next item. This happens with data about a hospital patient's
temperature. A line graph is used to show how the temperature changes
through the day.
| Time |
Temperature
(º C) |
| 0900 |
33 |
| 1200 |
34 |
| 1500 |
35 |
| 1800 |
34 |
| 2100 |
35 |

When the data is grouped the points are shown at the centre of the
group to show that it represents the whole range of values.
| Shoe
size |
Shoe
size |
| Less
than 2 |
3 |
| 2
but less than 4 |
2 |
| 4
but less than 6 |
4 |
| 6
but less than 8 |
1 |
| Total |
10 |
Scatter Diagrams
These show two items of data for each person. The shape of the scatter
diagrams indicates whether there is a relationship between the two
categories of information.
|
Student
|
Maths
mark(10)
|
English
mark (10)
|
|
A
|
1
|
8
|
|
B
|
1
|
6
|
|
C
|
3
|
5
|
|
D
|
4
|
3
|
|
E
|
6
|
3
|
|
F
|
6
|
5
|
|
G
|
7
|
1
|
Each point is plotted using the Maths and English marks as co-ordinates.
The general direction of the points shows that, for this group of
students, those that do well in English do poorly in Maths. This
is called negative correlation between English and Maths
marks.
The other possibilities are: positive correlation, if those
that did well in English also did well in Maths; and no correlation,
if the mark in English had no connection with the Maths mark.
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