Course 1.2Lesson 3 of 5

Scatter plots, bars and histograms

Different questions need different graphs. A line graph shows how one measurement changes with another, such as time. A scatter plot, plt.scatter, shows two measurements of each person or object as one dot, and colour or size can show a third measurement. np.corrcoef gives the correlation, a number between minus 1 and 1, and a strong correlation is not proof that one thing causes the other. A bar chart, plt.bar or ax.bar, compares amounts in separate groups, and ax.bar_label writes the numbers. A histogram, plt.hist, shows how many measurements fall in each bin, and it shows the centre and the spread of a measurement. np.histogram gives the same counts as numbers.

about 35 min1 simulation2 practice questions

Lesson 3 of 5Show all lessons

Try the code and the simulations beside the lesson.

What you will be able to do

After this lesson you can

choose between a line graph, a scatter plot, a bar chart and a histogram,
draw each one with matplotlib, and
read the correlation, the centre and the spread from them.

Choosing the graph

The kind of graph depends on the question.

The question	The graph
How does a measurement change in time or with another quantity?	line graph (`plt.plot`)
Is there a link between two measurements of the same things?	scatter plot (`plt.scatter`)
How do separate groups compare?	bar chart (`plt.bar`)
How are the repeated measurements of one quantity spread?	histogram (`plt.hist`)

The scatter plot

Predict first. The ten students are taller when they are older. Will the dots go up or down to the right?

A scatter plot titled Height and weight of ten students. Ten dots rise from the lower left to the upper right, from 148 centimetres and 41 kilograms to 178 centimetres and 72 kilograms. The dots are coloured by age with a colour bar from 13, dark purple, to 18, yellow.

Each student is one dot: the height across, the weight up. There is no line, because the students are separate people, and the order of the dots does not matter.
c=age colours each dot by the age, with the colour map "viridis", and s=70 sets the size of the dots. plt.colorbar(label=...) shows what the colours mean. With the colour, the graph shows three measurements at once.
The dots go from the lower left to the upper right. Taller students weigh more. This is a positive correlation.
np.corrcoef(height, weight) gives a table of correlations. The number at [0, 1] is the correlation coefficient between the two. It is always between $-1$ and $1$ . A value near 1, such as the 0.993 here, means that the dots lie almost on a rising line. A value near 0 means no link, and a value near $-1$ means a falling line.

A warning that every scientist keeps in mind: correlation is not cause. Taller students also tend to be older, and older students weigh more. When two things go up together, there may be a third thing behind both, or it may be by chance. The graph shows that two measurements are linked, but it does not say why.

Set the slope to 0: the correlation printed by the code drops close to 0, because there is no trend left, only the scatter.

The bar chart

A bar chart titled Rainfall in five months. The bars for June to October have the heights 180, 320, 290, 210 and 90 millimetres, and each bar has its number written above it. July has the tallest bar.

Do not use a line to join bars, and do not join the dots of a scatter plot. The bars are separate groups, and a line between them would suggest a change between the groups that does not exist.

The histogram

Predict first. The rod is 10 cm long. When it is measured 200 times, will every measurement give 10.00?

A histogram titled 200 measurements of a rod, with eight green bars. The bars are low at the left, grow to a peak of about 64 measurements in the bar around 10.0 centimetres, and become low again at the right. A dashed black line marks the mean, near 10.0.

rng.normal(loc=10.0, scale=0.2, size=200) makes 200 random numbers around 10.0 with a typical spread of 0.2. We use random numbers here to imitate the measurements of an experiment. The next chapters explain how random numbers work.
np.histogram(lengths, bins=8) sorts the measurements into 8 bins (equal ranges) and counts how many fall in each. It gives the counts and the edges of the bins. The counts add up to 200.
plt.hist(lengths, bins=8) draws these counts as bars, and the bars touch, because the bins follow each other without a gap. This is different from a bar chart of separate groups.
The picture is a hill. Most measurements are near the middle (the tallest bar), and fewer are far from it. The centre of the hill is the mean, and the width of the hill is the spread. A narrow hill means precise measurements. A wide hill means large scatter.
plt.axvline(lengths.mean(), ...) draws a vertical dashed line at the mean.

How many bins? Too few, and the shape is lost. Too many, and each bin has only a few measurements and the shape is jagged. For 200 measurements, 8 to 15 bins is a good choice. Try 4, and then 50, to see the difference.

Common mistakes

Joining the dots of a scatter plot with a line. The order of the dots has no meaning.
Saying that a high correlation proves a cause. It does not.
Using a line graph for separate groups. Use bars.
Taking a histogram for a bar chart. A histogram bins one measurement into ranges. The bars touch.
Too few or too many bins.
Forgetting the labels and the units. Every graph needs them.

Practice

Start with two quick questions. Each New numbers gives you a fresh one, so you can practise as long as you like.

Then the labs and the problems:

Warm-up. Open the lab Count the bars. You draw a bar chart, and the checker counts the bars and reads their heights.
Build. Open the lab Histogram numbers and the problem Choose the chart.
Stretch. Open the problem Histogram of marks.

Remember these

Line graph for a change, scatter plot for a link between two measurements, bar chart for separate groups, histogram for the spread of one measurement.
plt.scatter(x, y, c=..., s=...) and plt.colorbar show a third measurement.
np.corrcoef(x, y)[0, 1] is between $-1$ and $1$ . Correlation is not cause.
ax.bar_label writes the values on the bars. np.histogram gives the counts as numbers.