Represent data (Grade 8) — Mathematics Grades 8–11

Drawing a bar graph, histogram, pie chart or broken-line graph for data.

Gr 8 Term 3 — Represent dataTerm 3

Practise Represent data in the app →

What gets asked

Draw a bar graph or double bar graph from a frequency table.
Draw a histogram using given or your own intervals.
Draw a pie chart that shows data proportionally.
Choose and justify the best type of graph for a data set.

You must be able to

Use an even scale on the axis of a bar graph or histogram.
Draw the bars of a histogram touching, with no gaps.
Work out the size of each pie chart sector from its share of the total.
Match the graph type to the kind of data being shown.

Traps that cost marks

Using an uneven scale on the vertical axis, so the bar heights cannot be compared fairly. Each gridline on a graph must stand for the same amount as every other gridline.
Leaving gaps between the bars of a histogram. A histogram's bars must touch, since they show intervals that run into each other.
Using the raw frequency numbers as the sizes of pie chart sectors. Change each frequency to a fraction or a number of degrees of the whole circle first.
Choosing a histogram for categories like favourite sport, which are not number intervals. A histogram is for grouped number data. Categories need a bar graph or pie chart instead.

Worked example

A fundraising table shows: Grade 8 raised R400, Grade 9 raised R600, Grade 10 raised R200. Which graph type fits best?

The data is in separate categories, one amount per grade.
A bar graph or a pie chart both suit categories like this.
A histogram would not fit, because the grades are not number intervals.

Bar graphs and histograms

When the bars of a graph need a gap between them, and when they have to touch.

frequency: How many times a category or a group turns up in the data.
axis: One of the two lines a graph is built on, along the bottom or up the side.
scale: What one step on the axis is worth. It is not always one.
bar graph: A graph with a separate bar for each category, and a gap between the bars.
interval: A group of values with a clear start and end, such as $0$ to $9$ .
histogram: A graph for numbers sorted into intervals. Its bars touch.

Every graph starts from a table: the categories, and the frequency of each. The graph turns those counts into heights.

A graph stands on two lines, each called an axis. Categories go along the bottom. Number the side axis in equal steps. That step size is the scale, and every step is worth the same.

A bar graph gives each category its own bar, as tall as its frequency, with a gap between the bars. A double bar graph puts two bars above each label, one per group, and needs a key.

A histogram is for numbers sorted into intervals. Label the bottom axis with the intervals, like $0$ to $9$ . The bars touch, because the intervals run straight on.

Examples

A table shows soccer

12

, netball

8

, athletics

6

. The side axis goes up in twos. How many steps tall is each bar?

Worked answer

One step on this axis is worth $2$ .
Soccer: $12 \div 2 = 6$ steps.
Netball: $8 \div 2 = 4$ steps.
Athletics: $6 \div 2 = 3$ steps. Leave a gap between the three bars.

Answer: $6$ , $4$ and $3$ steps

Reading the scale first is what turns a frequency into a height.

Grade 8 raised R350 then R500 over two terms. Grade 9 raised R400 then R450. Describe the double bar graph.

Worked answer

Put the two terms along the bottom axis.
Above Term 1 draw two bars side by side, at $350$ and $400$ .
Above Term 2 draw two more, at $500$ and $450$ .
Add a key: which bar is Grade 8, which is Grade 9.

Answer: four bars in two pairs, plus a key

Without a key nobody can tell which bar belongs to which grade.

Airtime bought in a month by

25

learners ran from R5 to R48. Set up a histogram.

Worked answer

Sort them into intervals of $10$ : $0$ to $9$ , $10$ to $19$ , up to $40$ to $49$ .
Label the bottom axis with those $5$ intervals, not with single amounts.
Draw each bar as tall as the frequency of its interval.
Let the bars touch, because the intervals run straight on.

Answer: five touching bars, one for each interval

Every amount from R5 to R48 lands in exactly one interval.

Traps

Using an uneven scale on the vertical axis, so the bar heights cannot be compared fairly. Each gridline on a graph must stand for the same amount as every other gridline.
Leaving gaps between the bars of a histogram. A histogram's bars must touch, since they show intervals that run into each other.
Drawing the bars of a bar graph so that they touch. Separate categories need gaps. Touching bars turn the picture into a histogram.
Labelling the bottom axis of a histogram with single values. Each bar covers a whole interval, so label it $10$ to $19$ , not $10$ .

Learn and practise “Bar graphs and histograms” in the app →

Pie charts and line graphs

Slices of a whole, lines that follow time, and how to pick the right picture for your data.

pie chart: A whole circle cut into slices, one slice for each group in the data.
sector: One slice of the circle, cut from the centre like a slice of cake.
proportional: As big a share of the picture as it is of the data. Twice the count, twice the slice.
broken-line graph: Points joined one to the next by straight lines, showing change over time.

A pie chart is one whole circle. The circle stands for all the data together. Each group gets one sector, and every sector must be proportional. A group with twice the count gets twice the slice.

To size a sector, write its count as a fraction of the total. Then multiply that fraction by $360$ , because a full turn is $36 0^{\circ}$ . Never use the frequency itself as the angle.

A broken-line graph shows change over time. Put the times along the bottom axis, evenly spaced. Plot one point for each time. Then join each point to the next one with its own straight line.

Now choose. Separate groups take a bar graph, or a pie chart when they add up to one whole. Numbers sorted into intervals take a histogram. Anything that changes over time takes a broken-line graph.

Rules to remember

sector angle $= \frac{count}{total} \times 36 0^{\circ}$

Examples

In a class of

40

learners,

10

walk to school. Find the angle of the walking sector.

Worked answer

Write the walkers as a fraction of the class: $\frac{10}{40} = \frac{1}{4}$ .
A full turn is $36 0^{\circ}$ , so multiply by $360$ .
$\frac{1}{4} \times 360 = 90$ .
So that slice is a quarter of the circle.

Answer: $9 0^{\circ}$

Multiplying by $100$ instead would give $25$ , and the slices would not fill the circle.

A spaza shop sold bread as follows: Mon

30

, Tue

34

, Wed

28

, Thu

40

loaves. Describe the broken-line graph.

Worked answer

Put the four days along the bottom axis, the same distance apart.
Put the number of loaves up the side axis.
Plot one point per day, at $30$ , $34$ , $28$ and $40$ .
Join Monday to Tuesday, Tuesday to Wednesday, and Wednesday to Thursday.

Answer: four points joined by three straight lines

The line drops by $34 - 28 = 6$ loaves midweek, and one straight line would hide that.

Money raised: Grade 8 R400, Grade 9 R600, Grade 10 R200. Which graph fits, and which does not?

Worked answer

The three grades are separate groups, with one amount each.
A bar graph shows the three amounts side by side.
They also add up to one whole: $400 + 600 + 200 = 1200$ .
So a pie chart works too, but a histogram does not.

Answer: a bar graph, or a pie chart of the R1 200 raised

Grades are groups, not number intervals, so nothing here can be a histogram.

Traps

Using the raw frequency numbers as the sizes of pie chart sectors. Change each frequency to a fraction or a number of degrees of the whole circle first.
Choosing a histogram for categories like favourite sport, which are not number intervals. A histogram is for grouped number data. Categories need a bar graph or pie chart instead.
Cutting the circle into equal slices whatever the counts are. Every sector must be proportional. Work out each angle before you draw.
Drawing one straight line through all the points of a broken-line graph. Join each point to the next one with its own line, and stop at the last point.

Learn and practise “Pie charts and line graphs” in the app →

Grade 8 Represent data

What gets asked

You must be able to

Traps that cost marks

Worked example

Bar graphs and histograms

Examples

Traps

Pie charts and line graphs

Rules to remember

Examples

Traps

About this material