GCSE · Maths · AQA · Spec 8300

Tables, charts and diagrams for categorical and discrete data

One survey, two questions: 'which is most popular?' and 'what fraction walk?' Each needs a different chart. The question picks the picture.

Maths · Statistics

Which picture answers the question?

Pick a scenario, then pick where it belongs. Then switch the rule and sort the same scenarios again.

What kind of data is being collected?

Still to sort

Categorical (0)

The answers are names or labels: a colour, a sport, a way of travelling.

Where the line is: You can count how many gave each answer, but the answers themselves are not numbers.

Ungrouped discrete numbers (0)

The answers are numbers that come in separate steps — often counts like 0, 1, 2, 3, but not always whole numbers — and each value is kept on its own, not grouped.

Where the line is: Unlike categorical data, the values are numbers in order — 3 goals really is one more than 2 goals.

Time series (0)

The same thing recorded again and again over time: each month, each year.

Where the line is: What matters is the order in time — the question is usually 'how is it changing?'

7 of 7 still to sort.

Sort each scenario twice: first by the kind of data, then by the diagram that answers its question best.

Watch out: The same kind of data can need different diagrams. 'Which is most popular?' and 'What share of the whole?' are different questions, even about the same survey.

Predict, then check

Frequency table: cakes sold at a bake sale — Form 9A: 12 · Form 9B: 20 · Form 9C: 14. In the pictogram, one ■ stands for 4 cakes.

How many ■ symbols does Form 9C's row need to show 14 cakes?

Reading the chart

Bar chart or vertical line chart?

Showing 2 layers: Bar chart, Vertical line chart

Explore

Same idea, different data

Top: a bar chart of categorical data. Bottom: a vertical line chart of ungrouped discrete numbers. Tap a label to compare how they are read.

Tap a label to see how each chart is read.

Pie charts

30 pupils share 360°

pupils in this category: 12/30. Sector angle 144 °

Fraction12/30Sector angle144 °

Drag to set how many of the 30 pupils are in one category and watch its sector angle.

Exam line: Forwards: angle = frequency × (360 ÷ total). Backwards: frequency = angle ÷ (360 ÷ total). A 108° sector here is 108 ÷ 12 = 9 pupils.

Watch out: Always check your finished angles add up to 360°. Here: walk 12 → 144°, bus 9 → 108°, car 6 → 72°, cycle 3 → 36°, and 144 + 108 + 72 + 36 = 360.

Pie charts

Bigger slice, more people?

Two pie charts show votes for a class trip. Pie chart A is for Form 8R, 24 pupils: the Zoo sector is 90°. Pie chart B is for the whole of Year 8, 180 pupils: the Zoo sector is 60°.

Which group had more pupils voting for the zoo? Pick the idea closest to what you think.

Form 8R — its Zoo slice is bigger, so more pupils chose the zoo.Form 8R — its Zoo angle is 90°, so 90 pupils chose the zoo.You can't compare them at all — pie charts never tell you numbers.Year 8 — 60° of 180 pupils is 30, but 90° of 24 is only 6.

How sure are you?

I'm sureI think soI'm guessing

Form 8R — its Zoo slice is bigger, so more pupils chose the zoo.

This is a common misconception

The slice is bigger, but it is a bigger share of a much smaller group. 90° is a quarter of 360°, and a quarter of 24 pupils is only 6. The size of a sector tells you the fraction of that pie's own total, never the number of people on its own.

Form 8R — its Zoo angle is 90°, so 90 pupils chose the zoo.

This is a common misconception

Angles are not people. Form 8R only has 24 pupils, so 90 of them can't have voted for anything. Turn the angle into a fraction first: 90 out of 360 is a quarter, and a quarter of 24 is 6 pupils.

You can't compare them at all — pie charts never tell you numbers.

This is a common misconception

A pie chart on its own only shows shares. But here you are told each total, and that is all you need: 90/360 × 24 = 6 pupils in Form 8R, and 60/360 × 180 = 30 pupils in Year 8.

Year 8 — 60° of 180 pupils is 30, but 90° of 24 is only 6.

This matches the evidence

Exactly. You turned each angle into a fraction of its own total: 60/360 = 1/6 of 180 is 30, and 90/360 = 1/4 of 24 is 6. The smaller slice holds five times as many people.

A pie chart shows each category's share of its own total. To compare two pies, turn each share into a number using that pie's total.

Cycling club members, 2011–2019

Year: 2015. Members: 58

Table: 2011 40 · 2012 46 · 2013 44 · 2014 52 · 2015 58 · 2016 57 · 2017 64 · 2018 70 · 2019 68. Slide the point along the line to read each year.

Exam line: Describe a trend in words, with numbers: 'Overall, membership rose from 40 in 2011 to 68 in 2019, with small falls in 2013, 2016 and 2019.'

Watch out: Only the corners of the line, at whole years, are real readings. Slide the point to halfway between two years and it shows a value nobody recorded — the joining line only shows the direction of change.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Pick the picture that answers the question — then build it and read it.

What you need to know

A frequency table lists each category or value with how many times it occurs.
Bar charts and pictograms compare the frequencies of categories; a pictogram needs a key.
A pie chart shows each category's share of a total: angle = frequency × (360 ÷ total).
A vertical line chart shows ungrouped discrete numerical data on a number scale.
Time-series data are shown in a table or a line graph with time on the horizontal axis.
Choose the diagram from the kind of data AND the question you want answered.

The big picture

Frequency tables organise data; bar charts and pictograms compare frequencies of categories; pie charts show each category's share of a total; vertical line charts show how often each separate numerical value occurs; and time-series tables and line graphs show change over time. The kind of data and the question decide which to use.

Key points

1Categorical data are labels; ungrouped discrete numerical data can only take separate values (often whole-number counts, but not always), each kept on its own; time-series data are readings taken over time.

2On a bar chart the height of each bar is its frequency; bars are equal width with equal gaps between them.

3In a pictogram, divide a frequency by the key to find the symbols, and multiply by the key to read them back — part symbols stand for part of the key.

4Pie chart angles: work out 360 ÷ total, multiply by each frequency, and check the angles add up to 360°.

5A pie chart shows shares, not numbers: to compare two pie charts you need each one's total.

6On a vertical line chart the horizontal axis is a number scale, and each line stands on one value.

7On a time-series graph the joining lines show the trend; only the plotted times are real readings.

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Worked example

Problem

The goals scored in 16 football matches were: 1, 0, 2, 1, 3, 0, 1, 2, 1, 4, 0, 1, 2, 1, 0, 2. Make a frequency table and describe how to draw the vertical line chart.

⚠ Watch out

Treating a pie chart's angle as the number of people. A 90° sector does not mean 90 people — it means a quarter of the total. Turn angles into fractions of 360°, then multiply by the total.

🧠

Memory hook

Name it, count it, or time it? Names → bar chart, pictogram or pie. Separate number values, like counts → vertical line chart. Time → line graph. Then ask: 'how many?' (bars) or 'what share?' (pie).

✓

Check yourself

A pie chart shows how 40 people travel to work. The train sector is 63°. How many people take the train? (360 ÷ 40 = 9° per person, so 63 ÷ 9 = 7 people.)

Flashcards

(13)

What does a frequency table show?

Each category or value, with the number of times it occurs (its frequency). Build it by tallying through the data once.

On a bar chart, what does the height of a bar tell you?

The frequency of that category. The bars are all the same width, so only height carries information.

Why are there gaps between the bars of a bar chart for categorical data?

The categories are separate labels, not points on a number scale — nothing lies between them.

Why must a pictogram have a key?

The key says how many each symbol stands for. Without it the symbols can't be turned into frequencies.

Key: one symbol = 8 cars. What is a quarter of a symbol worth?

2 cars (a quarter of 8).

What kind of data is a vertical line chart used for?

Ungrouped discrete numerical data — values that come in separate steps, each kept on its own. They are often whole-number counts, such as number of pets or goals, but not always.

How is the horizontal axis of a vertical line chart different from a bar chart's?

It is a number scale in order with equal steps, not a list of category labels.

Pie chart: how do you get from a frequency to an angle, and back again?

Work out 360 ÷ total (degrees per item). Multiply a frequency by it to get the angle; divide an angle by it to get the frequency.

You've tallied a frequency table. How do you check it?

Add the frequencies — the total must equal the number of data values you started with.

Pie A has a bigger 'red' sector than pie B. Does A have more red?

Not necessarily — each pie shows shares of its own total. You need the totals to compare numbers.

What is time-series data?

The same thing recorded at different times, where the order in time matters — like sales each month.

What do the joining lines on a time-series line graph show?

The direction of change (the trend) between readings. Points between the plotted times are not real readings.

Which diagram answers 'what share of the whole?'

A pie chart.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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Which picture answers the question?

Bigger slice, more people?

Cycling club members, 2011–2019

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