GCSE · Maths · OCR · Spec J560

Outliers

Is the biggest number always the odd one out? Not even close. And some outliers hide inside numbers that look perfectly normal. Let's go and find them.

Maths · Scatter graphs

Which of these students are outliers?

Most of this group sit together in a crowd. Tap a student, then tap the box where they belong. Tip: compare each student with others who revised a similar number of hours.

Still to sort

Outlier: extreme in both variables (0)

Far from the crowd on hours and on score

Where the line is: Both values are significantly greater than the rest, or both significantly lower.

Outlier: normal in one, unusual in the other (0)

One value looks ordinary, but the point is unusual for others with a similar value of it

Where the line is: Compare the point with students who have a similar value in the ordinary variable.

Not an outlier (0)

Sits with the crowd, even if it is the highest or lowest value

Where the line is: Judged by distance from where most points are clustered, not by being at the end of the data.

10 of 10 still to sort.

Made-up data, real skill. Ten students: hours of revision and test score out of 100.

Watch out: The biggest number is not automatically the outlier. Ask how far a point sits from the crowd.

Maths · Scatter graphs

What do you really think an outlier is?

Someone points at a scatter graph and says, 'That point is an outlier.'

Which of these is closest to what you think right now?
How sure are you?

Maths · Scatter graphs

Outlier or error? They are not the same thing

Tick every set that each case belongs to. Some belong in both, and one belongs in neither.

  • A Is an outlier
  • B Was recorded in error
  1. A totals row plotted as if it were one more data point
  2. A point far from the crowd, whose figure was checked and is correct
  3. Two digits swapped when typing a value, so the point still sits inside the crowd
  4. A correctly recorded point in the middle of the crowd

Two ways to present a graph with an outlier

Keep the outlier in viewvsZoom in on the majority

Same data set, different view. Start with the row people get wrong.

Focus

Is the outlier still in the data set?

Keep the outlier in view

Yes

Zoom in on the majority

Yes. Zooming in does not remove it

The insight

Zooming changes what you can see on the graph. It does not change what is in the data.

What it is good for

Keep the outlier in view

Highlighting a difference

Zoom in on the majority

Making the trend clearer

Readings for interpolation

Keep the outlier in view

Less precise than when zoomed in

Zoom in on the majority

More precise readings for the majority of points

Predict, then check

You know the line of best fit. Now add one outlier to it.

The same outlier is added to two scatter graphs: one with only a few points, one with a very large number of points. Where does it pull the line of best fit more?

Maths · Scatter graphs · Exam practice

Now say it in your own words

A scatter graph plots population (x-axis) against greenhouse gas emissions (y-axis) for 20 towns. Nineteen of the points form a band. Town Q has a population of about 50 000 and emissions of 910 kilotonnes. Towns with a similar population emit about 200 to 260 kilotonnes. Town Q's figures were checked against the original records and were recorded correctly.

Explain what the outlier shows, in context, and say whether Town Q should be removed from the data set. [3 marks]

0 words · your answer stays on this page and is not sent anywhere.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Look for the point that stands apart from the crowd

What you need to know

  • An outlier is a data point extremely large or small compared with the rest, lying far from where most results cluster.
  • On a scatter graph you can see outliers: they sit well away from the crowd of points.
  • One kind has values in both variables significantly greater, or significantly lower, than the rest.
  • Another kind is normal for one variable, but unusually high or low in the other compared with points with a similar value.
  • Have a goA student revised a normal 8 hours but scored far below everyone else who revised about 8 hours. Is that outlier extreme in both variables, or the other kind?

    The other kind: normal for hours, but unusual for its score.

    Only one of its two values is out of line, compared with points that have a similar value in the other variable.

  • That second kind is much easier to spot on a scatter graph than in a list or table of numbers.
  • The highest or lowest value is only an outlier if it is significantly far from where most of the data is clustered.
  • Have a goMaya spots the top mark in a table of scores, 96, and shouts 'Outlier!' Most of the other scores sit between 84 and 95. Is she right?

    No. 96 sits with the crowd.

    A highest value is only an outlier if it is significantly far from where most of the data is clustered, and 96 is close to the rest.

  • A scatter graph may have more than one outlier, separate or clustered together, or no outliers at all.
  • Have a goTwo points sit close together, well away from every other point on a scatter graph. How many outliers is that: none, one or two?

    Two outliers, clustered together.

    A scatter graph can show more than one outlier, and outliers can be clustered together.

  • Interpret an outlier in context, like a town with far more greenhouse gas emissions than towns of similar population.
  • An outlier could be an error, like a plotted totals row, but it may just be an unusual result.
  • Outliers must be carefully considered and only removed from a data set if they were recorded in error.

The big picture

An outlier is a point that sits far from where most of the data is clustered, not just the biggest or smallest value. On a scatter graph you can spot two kinds, interpret them in context, and decide what to do with them. A point is only removed if it was recorded in error.

Key points

1An outlier is a point far from where most of the data is clustered. Distance from the crowd decides it, not being the biggest or smallest.
2There are two kinds on a scatter graph: extreme in both variables, or normal in one variable but unusual for points with a similar value of it.
3A scatter graph can have one outlier, several (separate or clustered together), or none.
4Interpret an outlier in context: say what it means for the real situation.
5An outlier is only removed if it was recorded in error. Zooming in on the majority does not remove it from the data set.

Worked example

Problem

Six plants are measured. Each point is (age in days, height in cm): (2, 4), (4, 8), (6, 12), (8, 16), (10, 20) and (6, 5). Which point, if any, is an outlier, and is it the tallest or the oldest plant? Describe it in context and decide whether to remove it.

⚠ Watch out

Calling the highest or lowest value the outlier just because it is at the end of the data. Ask how far it sits from where the crowd is clustered. And do not delete a point just because it is an outlier: remove it only if it was recorded in error.

🧠

Memory hook

Crowd first, loner second. An outlier is the point that stands apart from the crowd, whatever its size.

✓

Check yourself

One point is at the top-right end of the crowd; another sits well below the crowd's middle. Which is the outlier, and why?

Flashcards

(13)
What is an outlier?
A data point extremely large or small compared with the rest of the data set. It lies far from where the majority of the results are clustered.
How do you spot an outlier on a scatter graph?
Look for a point that lies far away from where the majority of the points are clustered.
What is the first kind of outlier on a scatter graph?
A point with values in both variables significantly greater (or significantly lower) than the rest of the data points.
What is the second kind of outlier on a scatter graph?
A point that is normal for one variable but unusually high or low in the other, compared with points that have a similar value in that variable.
Why is the second kind of outlier easier to spot on a scatter graph than in a table?
The graph shows each point next to the points with a similar value, so the odd one stands out. In a list of numbers each value looks ordinary.
Is the highest value in a data set always an outlier?
No. It is only an outlier if it is significantly far from where the majority of the data is clustered.
How many outliers can a scatter graph have?
More than one (separate or clustered together), or none at all.
What does interpreting an outlier in context mean?
Say what it shows about the real situation, for example a town with much more greenhouse gas emissions than other towns with a similar population.
Are all outliers errors? Are all errors outliers?
No to both. An outlier may just be an unusual result, and a typo with transposed digits can still lie within the rest of the data.
When should an outlier be removed from a data set?
Only if it was recorded in error. Outliers must be carefully considered first.
Does zooming in on the majority of the points remove the outlier?
No. The outlier is still in the data set. Zooming in gives more precise readings for interpolation and makes the trend clearer.
When is it useful to keep an outlier visible on the graph?
When you want to highlight a difference. Decisions about an outlier depend on what the scatter graph is used for.
What effect does an outlier have on the line of best fit?
With only a small amount of data it has a bigger effect. With a sufficiently large amount of data it has very little effect.

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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