Scatter graphs and correlation
Do taller people have bigger feet? Does revision time affect test scores? A scatter graph puts two measurements side by side and lets the pattern, if there is one, show itself.
Lesson overview
What you'll learn in this lesson
Describe simple mathematical relationships between two variables in observational and experimental contexts and illustrate using scatter graphs
Key learning points
- • Building the graph
- • Describing what you see
- • Line of best fit and prediction
- • Correlation is not cause
This lesson at a glance
- 30 minutes
- 24 parts to scroll through
- 4 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 24
Visual introductionPicture this
Scatter graphs and correlation
Do taller people have bigger feet? Does revision time affect test scores? A scatter graph puts two measurements side by side and lets the pattern, if there is one, show itself.
In a nutshell
Describe simple mathematical relationships between two variables in observational and experimental contexts and illustrate using scatter graphs
What you already know
Part 2 of 24
Before we start
What you already know
You should already be able to plot coordinates and read the gradient of a straight line.
Key words
Part 3 of 24
Key words
Words you'll need today
- Correlation
- A pattern in how two variables change together.
- Line of best fit
- A straight line drawn through the middle of the pattern.
- Outlier
- A point that sits far away from the pattern.
- Bivariate data
- Data with two measurements for each item.
Reset break
Part 4 of 24
Pause
That's sitting 1 of 6 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Learning cycle
Part 5 of 24
Learning cycle 1 of 2
Plotting and describing
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 6 of 24
Learn
Building the graph
Each item gives one point: the two measurements are its coordinates. Choose scales that spread the points across the grid, and label both axes with units. A scatter graph is never joined up dot-to-dot, because the points are separate observations rather than stages in one process. The shape of the cloud is the information.
Explore the idea
Part 7 of 24
Learn
Describing what you see
Correlation is described by direction and strength. Positive correlation means both rise together; negative means one rises as the other falls; no correlation means the points look scattered. Strength is about how tightly the points cluster around a line. Always describe correlation in the words of the context: 'as revision time increases, test score tends to increase'.
Reset break
Part 8 of 24
Pause
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Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Quick check
Part 9 of 24
Quick check
Part 10 of 24
Learning cycle
Part 11 of 24
Learning cycle 2 of 2
Best fit, prediction and caution
A short piece of teaching, then a check to make sure it has landed.
Reset break
Part 12 of 24
Pause
That's sitting 3 of 6 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Explore the idea
Part 13 of 24
Learn
Line of best fit and prediction
A line of best fit follows the trend with roughly as many points above as below. It lets you estimate a missing value: read up from the x value and across to the y axis. Predicting inside the range of the data is called interpolation and is usually reasonable. Predicting well beyond the data is extrapolation, and it can be badly wrong because the pattern may not continue.
Explore the idea
Part 14 of 24
Learn
Correlation is not cause
Ice cream sales and swimming accidents rise together, but neither causes the other; hot weather drives both. A correlation shows an association, and a cause can only be argued from a controlled experiment or a clear mechanism. Outliers deserve attention too: an unusual point may be a recording error, or it may be the most interesting item in the data set.
Quick check
Part 15 of 24
Reset break
Part 16 of 24
Pause
That's sitting 4 of 6 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Quick check
Part 17 of 24
Common mix-ups
Part 18 of 24
Common mix-ups
Things people often get wrong
- People often join scatter points with straight segments. Points stay separate; only a single line of best fit is drawn.
- People often say a correlation proves a cause. It shows a link, and a third factor is often responsible.
Challenge round
Part 19 of 24
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Reset break
Part 20 of 24
Pause
That's sitting 5 of 6 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Challenge round
Part 21 of 24
Game · Recall cards
As one variable increases the other decreases. This is...
Card 1 of 4
Exit quiz
Part 22 of 24
Exit quiz
Show what you've learned
6 questions, marked together at the end. Nothing is timed.
1. Each point on a scatter graph represents...
2. Height and shoe size rising together shows...
3. A tight cluster around the line means the correlation is...
4. Ice cream sales and sunburn cases correlate because...
5. Reading a value inside the plotted range is...
6. Scatter graph axes should always...
Mastery quiz
Part 23 of 24
Marked quiz
End of lesson quiz: Scatter graphs and correlation
4 questions, marked with the reasoning shown. No timer.
1. As one variable increases the other decreases. This is...
2. A line of best fit should...
3. Predicting far outside the data range is called...
4. A point far from the pattern is called...
Lesson round-up
Part 24 of 24
Lesson round-up
Ready when you are
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Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?
Ask LunaPart 1 of 24 · Watch & discover