Everything covered in this lesson, in one place - useful for revision or printing.
\( \text{pie} \;\cdot\; \text{bar} \;\cdot\; \text{histogram} \;\cdot\; \text{line} \)
Four graphs carry almost all of the Data Handling marks in Grade 9, and for each
one you must be able to do two things: draw it accurately
from a table, and read it to answer questions.
\( \text{angle} = \dfrac{\text{frequency}}{\text{total}} \times 360^\circ \)
A pie chart divides ONE whole into slices. The whole circle is
360°, so each category gets a share in proportion to its frequency.
Work out every angle first, then check they total 360° before you touch the
protractor.
\( \dfrac{18}{60} \times 360^\circ = 108^\circ \)
60 learners named a favourite sport: Soccer 18, Netball 15, Athletics 12,
Swimming 9, Other 6.
Soccer: 108° · Netball: 90° ·
Athletics: 72° · Swimming: 54° ·
Other: 36°
Check: \(108 + 90 + 72 + 54 + 36 = 360\) ✓
\( \text{frequency} = \dfrac{\text{angle}}{360^\circ} \times \text{total} \)
If you are given the angle and the total, work backwards.
A 72° slice of 200 people:
\( \dfrac{72}{360} \times 200 = 40 \) people.
Careful: a 72° slice is NOT 72%. It is one fifth of the circle, so it is
20%. Always divide by 360 first.
\( \sum \text{angles} = 360^\circ \)
Pie charts, in one card. Total the frequencies, turn each into an
angle with \(\frac{f}{\text{total}} \times 360^\circ\), check the angles sum to 360°,
then draw and label every slice.
To read one: divide the angle by 360 first, then multiply by the total (for a count) or by
100 (for a percentage).
\( \text{separate categories} \Rightarrow \text{gaps between bars} \)
A bar graph compares separate categories.
\( \text{two data sets} \Rightarrow \text{a key is compulsory} \)
A double bar graph compares two groups across the same categories
— boys against girls, this year against last year.
Two bars per category, shaded differently, and a key. Without the key the
reader cannot tell which bar is which, and the graph cannot be marked.
\( \text{gaps} = \text{separate categories} \)
Bar graphs, in one card. Equal widths, equal gaps, scale from zero,
full labels. Add a key the moment a second data set appears.
The gaps are not decoration — they tell the reader the categories are separate things.
\( \text{touching bars} \Rightarrow \text{continuous data} \)
A histogram looks like a bar graph but means something different.
It shows continuous data grouped into class intervals — test marks, heights,
times. Because the scale runs continuously, the bars touch.
Drawing a histogram with gaps, or a bar graph with the bars touching, is the most commonly
dropped mark in this topic.
\( \text{midpoint} = \dfrac{\text{lower} + \text{upper}}{2} \)
From a grouped frequency table:
\( \text{modal class} = \text{the tallest bar} \)
Histograms, in one card. Continuous data, grouped into equal
intervals, bars touching, scale from zero.
Midpoints are not needed to draw it — you need them only when estimating the mean.
\( \text{time} \rightarrow x\text{-axis} \)
A broken-line graph shows how one value changes over time.
Plot each point, then join consecutive points with straight line segments. Time always goes
on the x-axis.
The shape carries the meaning: rising, falling, or level.
\( \text{change} = \text{later} - \text{earlier} \)
Temperatures Mon to Sun: 19, 21, 24, 22, 26, 25, 23 °C.
Monday to Friday: \(26 - 19 = 7\) °C increase.
When asked to describe a trend, give the direction and quote
numbers from the graph — "rising overall, from 19 °C to 26 °C, with a dip on
Thursday".
\( \text{plot} \rightarrow \text{join} \rightarrow \text{describe} \)
Line graphs, in one card. Time on the x-axis, points joined by
straight segments, axes labelled with units.
A line graph may start its y-axis above zero, but only if you say so clearly — otherwise it
misleads.
\( \text{the graph must match the data} \)
Choosing correctly is itself a marked skill.
\( \text{title} + \text{axis labels} + \text{scale from } 0 \)
Four of the five commonest errors are about labelling, not mathematics:
\[ \begin{aligned} \text{pie angle} &= \frac{f}{\text{total}} \times 360^\circ \\[4pt] \text{from a pie} &= \frac{\text{angle}}{360^\circ} \times \text{total} \\[4pt] \text{midpoint} &= \frac{\text{lower}+\text{upper}}{2} \end{aligned} \]
All four graphs, end to end.