Pictograms, bar charts, pie charts and line graphs – Statistics with Ungrouped Data (Senior 1 Mathematics) | Ganzaa

Statistics with Ungrouped Data

Lessons

Senior 1 · Mathematics

Statistics with Ungrouped Data

5 lessons

Lesson 3 of 5

Pictograms, bar charts, pie charts and line graphs

25 min

A table is exact; a graph shows the pattern

A frequency table gives exact numbers, but a reader has to study it to see which value is largest or how things change. A well-drawn graph shows the pattern at a glance. Each type of graph suits a different kind of question, so the skill is to choose the right one, draw it accurately, and read other people's graphs back into numbers.

Definition

Pictogram: a graph that uses a small picture (symbol) to stand for a fixed number of items. It must have a key that says what one symbol stands for; part of a symbol stands for part of that number.

Trees planted by four S1 classes at Umuganda. Half a symbol stands for 5 trees.

Reading it: S1 C has 5 symbols, so $5 \times 10 = 50$ trees; S1 D has $2\tfrac{1}{2}$ symbols, so $2.5 \times 10 = 25$ trees. Altogether the four classes planted $40 + 35 + 50 + 25 = 150$ trees.

Definition

Bar chart: a graph in which each category or value has a bar, and the height of the bar shows its frequency. The bars have equal widths and equal gaps, and the frequency axis starts at 0.

Favourite sport of 40 S1 learners. The bars have equal widths and equal gaps, and the scale starts at 0.

Definition

Pie chart: a circle divided into sectors, one for each category, so that each sector shows that category's share of the whole. The angle of each sector is proportional to its frequency:

\text{sector angle} = \frac{f}{\sum f} \times 360^\circ.

Worked example 1: drawing a pie chart

Draw a pie chart of the favourite sports of the 40 learners in the bar chart above.

Solution The whole circle, $360^\circ$ , stands for all 40 learners, so each learner gets $\frac{360^\circ}{40} = 9^\circ$ .

Sport	Frequency	Sector angle
Football	16	$\frac{16}{40} \times 360^\circ = 144^\circ$
Basketball	10	$\frac{10}{40} \times 360^\circ = 90^\circ$
Volleyball	8	$\frac{8}{40} \times 360^\circ = 72^\circ$
Athletics	6	$\frac{6}{40} \times 360^\circ = 54^\circ$
Total	40	$360^\circ$

Draw a circle and one radius. With a protractor centred on the centre, measure $144^\circ$ from the radius and draw the second radius; measure the next angle from that one, and so on. Label each sector, or add a key.

The same data as a pie chart. The sector angles add up to 360°.

Worked example 2: reading a pie chart

How 72 learners travel to school.

The pie chart shows how 72 S1 learners travel to school. How many learners use each kind of transport?

Solution Each learner's share of the circle is $\frac{360^\circ}{72} = 5^\circ$ , so the number in a sector is its angle divided by $5^\circ$ , or equally

f = \frac{\text{sector angle}}{360^\circ} \times 72.

Transport	Angle	Number of learners
Walk	$200^\circ$	$\frac{200}{360} \times 72 = 40$
Moto	$60^\circ$	$\frac{60}{360} \times 72 = 12$
Bus	$80^\circ$	$\frac{80}{360} \times 72 = 16$
Bicycle	$20^\circ$	$\frac{20}{360} \times 72 = 4$
Total	$360^\circ$	72 ✓

Worked example 3: from a bar chart to a frequency table

Goals scored per match by a school football team.

(a) Write the frequency table. (b) How many matches did the team play? (c) How many goals did it score altogether?

Solution

Read the top of each bar against the vertical scale:
Goals $(x)$ 0 1 2 3 4
Matches $(f)$ 3 6 5 4 2
$3 + 6 + 5 + 4 + 2 = 20$ matches.
Multiply each number of goals by the number of matches in which it happened: $0 \times 3 + 1 \times 6 + 2 \times 5 + 3 \times 4 + 4 \times 2 = 0 + 6 + 10 + 12 + 8 = 36$ goals. (Adding the heights of the bars, 20, counts matches, not goals.)

Definition

Line graph: a graph of points joined by straight line segments, used to show how a quantity changes over time. Time goes along the horizontal axis.

Worked example 4: from a line graph to a table

Average monthly rainfall at Kigali Airport, 1991–2020, rounded to the nearest millimetre.

(a) Write the rainfall for each month in a table. (b) Which are the wettest and the driest months, and what is the difference between them? (c) Describe the pattern.

Solution

Read each point against the vertical scale:
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
84 84 129 136 89 20 10 30 65 109 121 76
The wettest month is April ( $136\,\text{mm}$ ) and the driest is July ( $10\,\text{mm}$ ); the difference is $136 - 10 = 126\,\text{mm}$ .
The graph has two peaks: a long rainy season from March to May and a short one from October to December. They are separated by a long dry season (June to August) and a shorter, less dry one (January to February). The line segments only join the monthly readings to show the trend; a point halfway between two months has no meaning.

Which graph should you use?

Graph	Best for	Example
pictogram	simple counts that must catch the eye	trees planted by each class
bar chart	comparing the sizes of categories or values	favourite sports; goals per match
pie chart	showing each category as a share of one whole	how the class travels to school
line graph	showing change over time	rainfall month by month

Warning

Graphs that mislead

A bar chart whose scale does not start at 0 makes small differences look huge. Always start the frequency axis at 0 and keep the steps equal.
A pie chart whose angles do not add up to $360^\circ$ has an error. Check the total of your angles before you draw.
A line graph for categories (such as sports) is wrong: the line between "football" and "basketball" means nothing. Use a bar chart.
A pictogram without a key cannot be read.

Tip

For a pie chart, first find the angle for one item: $360^\circ \div \sum f$ . Every sector angle is then a frequency times that number ( $9^\circ$ per learner in Worked example 1, $5^\circ$ in Worked example 2).

Math Antics: Data And Graphs (13 min). Watch how the same data can be shown as a bar graph, a line graph and a pie chart, and why each one suits a different kind of question.

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Practice

Draw graphs on squared paper with a ruler and a protractor. Questions 5 and 6 are harder.

In the pictogram of trees, how many more trees did S1 C plant than S1 B?
Draw a bar chart of this data about 30 learners' favourite fruit: banana 11, mango 8, avocado 6, pineapple 5.
Calculate the sector angles for a pie chart of the fruit data in question 2, and draw the pie chart.
From the rainfall graph, find the total rainfall in the three months March, April and May.
In a pie chart of the 150 trees planted at Umuganda, what is the sector angle for S1 A (40 trees)?
A pie chart shows how a family of 5 spends its monthly income of 180,000 Frw. The sector for food has an angle of $150^\circ$ . How much does the family spend on food?
Mutesi drew a line graph of the number of learners who chose each subject as their favourite. Explain what is wrong, and say which graph she should use.

Show answersHide answers

$50 - 35 = 15$ trees.
Four bars of heights 11, 8, 6 and 5, with equal widths and gaps, on a scale from 0.
Each learner gets $360^\circ \div 30 = 12^\circ$ : banana $132^\circ$ , mango $96^\circ$ , avocado $72^\circ$ , pineapple $60^\circ$ (total $360^\circ$ ).
$129 + 136 + 89 = 354\,\text{mm}$ .
$\frac{40}{150} \times 360^\circ = 96^\circ$ .
$\frac{150}{360} \times 180\,000 = 75\,000$ Frw.
Subjects are categories with no order in time, so the lines joining the points mean nothing. She should draw a bar chart (or a pie chart).

Sources and credits

8.2: Visualizing Data, from Contemporary Mathematics by Donna Kirk and contributors, OpenStax, provided by LibreTexts, licensed under CC BY 4.0 (licence read on the page, 26 September 2026). Adapted by Ganzaa.
Rainfall data: 1991–2020 climate normals for Kigali Airport from the US National Oceanic and Atmospheric Administration (NOAA), as tabulated in the Wikipedia article Kigali; rounded by Ganzaa.
Video: Math Antics - Data And Graphs, mathantics, embedded from YouTube.

The other data sets, the graphs, the worked examples, the practice items and the quiz questions were written by Ganzaa.

1A table is exact; a graph shows the pattern

2Which graph should you use?

A table is exact; a graph shows the pattern

Which graph should you use?