Represent data (Grade 9) — Mathematics Grades 8–11

Drawing a bar graph, histogram, pie chart or scatter plot to display data.

Gr 9 Term 4 — Represent dataTerm 4

Practise Represent data in the app →

What gets asked

Draw a bar graph or a double bar graph from a frequency table.
Group data into intervals and draw a histogram.
Calculate the size of a sector and draw a pie chart.
Draw a scatter plot to compare two sets of data.

You must be able to

Choose histogram intervals that do not overlap and leave no gaps.
Convert a percentage or fraction of the data into a sector angle out of 360 degrees.
Use a consistent scale on the axis of a bar graph.
Plot one point per item on a scatter plot, for its two values.

Traps that cost marks

Using 100 instead of 360 degrees when turning a percentage into a sector angle. A pie chart is a full circle, so multiply the fraction of the data by 360 degrees, not 100.
Choosing histogram intervals that overlap, so a value could fall in two of them. Each interval needs a clear start and end so every value fits in exactly one.
Using an inconsistent scale on the vertical axis of a bar graph. Keep equal gaps between the numbers on the axis, so the bar heights are fair.

Worked example

In a survey of 40 learners, 15 named soccer as their favourite sport. Calculate the size of the soccer sector on a pie chart.

Write the data as a fraction of the total: $\frac{15}{40}$ .
Multiply by 360°: $\frac{15}{40} \times 360°$ .
The soccer sector is $135°$ .

Draw graphs and charts

Turning a table of counts into a picture, and picking the picture that tells the truth.

frequency: How many times a value or category turns up in the data.
interval: A group of values with a clear start and end, such as $0 \leq x < 20$ .
histogram: A graph for grouped numbers. Its bars touch, because the intervals run on.
sector: A slice of a circle, cut from the centre like a slice of cake.
broken-line graph: Points joined one to the next by straight lines, showing change over time.
scatter plot: A graph with one dot per item, showing two things about it at once.

Every graph starts from a frequency table: categories down one side, counts beside them. Keep the steps on the number axis equal, or the bars will lie about the data.

A bar graph shows separate categories, so leave gaps between its bars. A histogram shows grouped numbers, so its bars touch. The gap is the whole difference.

Choose intervals that cannot overlap. With $0 \leq x < 20$ and $20 \leq x < 40$ , a mark of $20$ has exactly one home to go to.

A pie chart is a full circle, so the whole data set is $36 0^{\circ}$ . Work out each category's fraction of the total. Multiply that fraction by $360$ for the angle of its sector.

A broken-line graph shows change over time. Plot the points and join each to the next with a straight line. A scatter plot puts one dot per item, and those dots are never joined.

Rules to remember

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

Examples

In a survey of

60

learners,

25

walk to school. Find the angle of the walking sector on a pie chart.

Worked answer

Write the walkers as a fraction of the total: $\frac{25}{60}$ .
A full circle is $36 0^{\circ}$ , so multiply by $360$ .
$\frac{25}{60} \times 360 = 150$ .
The walking sector is $15 0^{\circ}$ .

Answer: $15 0^{\circ}$

Multiplying by $100$ instead gives about $42$ , and the slices would not fill the circle.

Twenty test marks run from

3

19

. Group them into intervals of

5

for a histogram.

Worked answer

Start at $0$ and go up in fives.
Use $0 \leq x < 5$ , $5 \leq x < 10$ , $10 \leq x < 15$ and $15 \leq x < 20$ .
A mark of $10$ now falls in the third interval only.
Draw the bars touching, because the intervals run on.

Answer: $0 \leq x < 5$ ; $5 \leq x < 10$ ; $10 \leq x < 15$ ; $15 \leq x < 20$

Every mark from $3$ to $19$ has exactly one interval to go in.

A teacher records the height and shoe size of each of

25

learners. Which graph shows both at once?

Worked answer

Each learner has two measurements: height and shoe size.
One goes along the bottom axis and the other up the side.
Put ONE dot for each learner, where the two meet.
That gives $25$ dots on a scatter plot, and none are joined.

Answer: a scatter plot with $25$ dots

One dot per ITEM, not one per measurement, or the count comes out double.

Traps

Using 100 instead of 360 degrees when turning a percentage into a sector angle. A pie chart is a full circle, so multiply the fraction of the data by 360 degrees, not 100.
Choosing histogram intervals that overlap, so a value could fall in two of them. Each interval needs a clear start and end so every value fits in exactly one.
Drawing the bars of a bar graph touching one another. Separate categories get gaps between them. Touching bars make it a histogram.
Joining the points of a broken-line graph with one smooth curve. Join each point to the NEXT one with a straight line, and stop there.

Learn and practise “Draw graphs and charts” in the app →

Grade 9 Represent data

What gets asked

You must be able to

Traps that cost marks

Worked example

Draw graphs and charts

Rules to remember

Examples

Traps

About this material