Charts and graphs of data · Code with Martin

Data in a picture

A table of numbers is honest, but boring and hard to read. A chart shows the same data in one look. Today you will meet the three most common — and learn when to use which and how not to fall for a graph that lies.

A bar chart compares categories: how many votes each snack got in a survey. The taller the bar, the more.

A pie chart shows parts of a whole: how 100 % is split. The whole circle = the whole, sectors = shares. Great for “how much of the whole”, bad for exact comparing of close values.

A line chart follows change over time: temperature during the day, channel followers by months. Points joined by a line, it is read left to right — that is really a function graph from lesson 10.

And then the second skill, maybe more valuable: reading critically. A chopped axis, a weird scale or missing labels can make a small difference into drama. Graphs in ads and on social media do this all the time. After today you will see through them.

Sofie is doing a class project survey on snacks: a roll 12 votes, an apple 8, a bar 6, nothing 2. “A bar chart, an obvious choice,” she draws. Adam next to her shows a graph from an ad: “Look, their yoghurt has a bar twice as high as the competition!” Sofie looks at the axis: it starts at 90 and ends at 100. “A chopped axis. The difference is 98 against 94 — four percent, and it looks like a double.” Adam blinks: “So the graph did not lie with numbers, but with the picture.” Exactly. That is why you read the axis before the bars.

💡

Before reading every chart, three checks: What is on the axes? Does the vertical axis start at zero? Are there numbers by the sectors or bars? Without that, do not trust the picture.

Which chart for what — and how to build it

Bar (comparing categories): 1) categories on the horizontal axis, 2) counts on the vertical, start at zero, 3) equally wide bars, 4) label the values. Use for: votes in a survey, numbers of pupils, shop prices.

Pie (parts of a whole): 1) calculate the whole (the sum of all values), 2) convert each value to percents: share = value/whole · 100, 3) convert percents to degrees of a sector: 1 % = 3.6° (because 360°/100), 4) draw with a compass and a protractor. Use for: makeup of a class, a budget, time in a day.

Line (change over time): 1) time on the horizontal axis, 2) values on the vertical, 3) plot points and join. Use for: temperature, height, view counts, saved by months.

A detector of lying graphs: — the vertical axis does not start at zero → differences look bigger than they are; — numbers and labels are missing → you cannot check; — 3D effects and pictures instead of bars → the front piece looks bigger; — a pie chart where the sum is not 100 % → someone counted wrong, or on purpose.

If a graph passes the checks, trust it. If not, find the original numbers.

Example 1: a pie chart from a survey

Question: A survey on snacks in a class with 25 votes: a roll 10, an apple 8, a bar 5, nothing 2. Convert the votes to percents and sector degrees for a pie chart.

Method: Whole: 10 + 8 + 5 + 2 = 25 votes.

Roll: 10/25 = 40 % → 40 · 3.6 = 144°. Apple: 8/25 = 32 % → 115.2°. Bar: 5/25 = 20 % → 72°. Nothing: 2/25 = 8 % → 28.8°.

Check: 40 + 32 + 20 + 8 = 100 % and 144 + 115.2 + 72 + 28.8 = 360°. Both match.

Example 2: reading a line graph

Question: A graph of the saved amount by months: January 200, February 350, March 350, April 600, May 500 Kč. When did saving grow fastest, when did it stall and when did it fall?

Method: I read differences between neighbouring points:

January → February: +150. February → March: 0 (a horizontal stretch — stall). March → April: +250 (the steepest stretch — fastest growth). April → May: −100 (it falls — something was bought).

Answer: Fastest between March and April, a stall in March, a fall in May. The steepness of the line = the speed of change. That is the whole of reading line graphs.

Example 3: spot manipulation

Question: An ad shows a bar chart of satisfaction: brand A 96 %, brand B 91 %. The vertical axis goes from 90 to 100. Bar A is six times higher than bar B. Is the graph honest?

Method: I check the axis: it starts at 90, not at zero. Bar A measures from 90 to 96 (height 6 ticks), bar B from 90 to 91 (height 1 tick). That is why A looks six times better.

The real difference: 96 against 91, so 5 percentage points — both brands are almost the same.

Answer: The numbers are true, the picture cheats with a chopped axis. An honest graph would start at zero and the bars would be almost the same height.

⚠️

A pie chart must add up to 100 %. When you add the sectors and 87 % or 112 % comes out, there is a mistake somewhere — in calculating shares, or in the data (someone voted twice, something is counted in more categories). A sum check is the first thing after drawing and when reading someone else’s chart.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. Start with ten. When it goes well, add more.

Practise the mean — with every data problem someone will ask for it. Write a whole number.

Practise the questions

On paper

One survey of your own, two charts and one detective task.

Do a mini survey (family, friends, made-up data is fine): a favourite day of the week, at least 10 votes. Draw a bar chart with a labelled axis from zero.
Convert the same data to a pie chart: percents, degrees (1 % = 3.6°), a check of the sum 100 % and 360°.
Draw a line graph of your made-up saving over 6 months — let there be growth, a stall and a fall. Label where what is.
Find (in a paper, on the web, in an ad) one graph and run it through the detector: axes, zero, labels. Write a verdict: honest, or it cheats?

Now you 💪

For each type of data you pick the right chart (comparing/parts of a whole/change).
You can convert votes to percents and sector degrees.
You recognise a chopped axis and you know what it does to how a graph is seen.

✅

Done when: You have three charts drawn by hand with checks and one other graph run through the manipulation detector.

What to take from this lesson

Bar = comparing, pie = parts of a whole, line = change over time.
Pie chart: percents times 3.6 = degrees. The sum must give 100 % and 360°.
The steepness of a line in a line graph shows the speed of change.
A chopped axis exaggerates differences. Read the axes before the bars.
A graph without labels and numbers is a picture, not proof.