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Statistics

Statistics

Charts and scatter diagrams

Scatter Plot Core + Extended 7 min read

On this page
  1. In this note
  2. Formula bank
  3. Pie charts, pictograms and bar charts
  4. Scatter diagrams and correlation
  5. Ways they test it
  6. Mistakes to avoid
  7. Summary
  8. Practice
  9. Can I do this?
  10. Quiz

In this note

Syllabus 9.4 and 9.5: charts and scatter diagrams
  • 9.4Draw and read pie charts, pictograms and bar charts (including dual and composite).
  • 9.5Plot a scatter diagram and describe the correlation.
  • 9.5Draw a line of best fit by eye and use it to estimate.

Before you start: angles in a full turn (360°). Next: Cumulative frequency.

Formula bank

Pie angleLearn it\(\text{angle}=\dfrac{\text{frequency}}{\text{total}}\times360^\circ\)Use it when drawing a pie chart.
Back from an angleLearn it\(\text{frequency}=\dfrac{\text{angle}}{360}\times\text{total}\)Use it when reading a pie chart.
PictogramLearn itcount = number of symbols × what one symbol stands forUse it when a key like '☺ = 4 people'.
CorrelationLearn itpositive: up together; negative: one up, other down; none: no patternUse it when 'describe the correlation'.

Pie charts, pictograms and bar charts

Pie chart of drinks chosen by 120 peopleTea90°Coffee135°Juice75°Water60°
120 people: each person gets 360 ÷ 120 = 3°.

A pie chart shares 360° in proportion. 30 out of 120 chose tea: \(\tfrac{30}{120}\times360=90^\circ\). Reading back, a 72° slice is \(\tfrac{72}{360}\times120=24\) people. A pie chart shows PROPORTIONS: you need the total to get numbers.

General methodHow to answer any pie chart question

  1. Find the total frequency.
  2. Degrees per item = 360 ÷ total.
  3. Each angle = frequency × degrees per item (check they add to 360°).
  4. Reading: frequency = angle ÷ degrees per item.

In a pictogram each symbol stands for a number given in the key: if one symbol = 4 people, three and a half symbols = 14 people. A dual bar chart puts bars side by side to compare groups; a composite (stacked) bar chart stacks the parts of a whole in one bar.

Try it yourself

1
A pie chart shows 120 people. Angle for 45 coffee drinkers (degrees)?
Show answer

Answer 135

2
A pie chart of 50 people has a 72° slice. How many people?
Show answer

Answer 10

Scatter diagrams and correlation

Scatter diagram: hours revised against test mark, with a line of best fit1234567891020304050607080hmark
More revision goes with higher marks: positive correlation.

A scatter diagram plots pairs of values as points (draw them as small crosses in the exam). If the points rise from left to right the correlation is positive; if they fall it is negative; if there is no pattern there is no correlation. Correlation does not prove one thing causes the other.

General methodHow to draw and use a line of best fit

  1. Draw ONE straight ruled line by eye, following the trend.
  2. It should go across the whole data set, with about the same number of points on each side.
  3. To estimate: go up from the x value to the line, then across to the y axis.
  4. Only estimate inside the range of the data; outside it (extrapolation) is unreliable.

Example Use the line of best fit to estimate the mark of a student who revised for 4.5 hours.

Up from 4.5 to the line, across to the mark axis.

  1. the line passes about (4.5, 53)

Answer about 53 (anything from 51 to 55 is fine)

Try it yourself

1
From the line of best fit, estimate the mark for 6.5 hours.
Show answer

Answer about 65

Ways they test it

Type 1 Pie angle

"Complete the pie chart." (2 marks)

Spot it a frequency table and a part-drawn pie.

  1. 360 ÷ total.
  2. × each frequency.

For example 30 of 120

  1. \(30\times3\)

Answer 90°

Type 2 Read a pie chart

"The pie chart shows 360 students. How many…?" (2 marks)

Spot it a measured angle.

  1. Measure the angle.
  2. ÷ 360 × total.

Type 3 Correlation

"What type of correlation is shown?" (1 mark)

Spot it a scatter diagram.

  1. Positive / negative / none.

Type 4 Line of best fit + estimate

"Draw a line of best fit. Use it to estimate…" (2 marks)

Spot it 'line of best fit'.

  1. Ruled, through the middle of the points.
  2. Read across.

Mistakes to avoid

  • ✗ A curved or dot-to-dot line of best fit✓ one straight ruled line
  • ✗ Line of best fit forced through (0, 0)✓ follow the points
  • ✗ 'Positive' with no word 'correlation' when asked to describe✓ 'positive correlation'
  • ✗ Pie angles that don't add to 360°✓ check the total

Summary

  • Pie: angle = frequency ÷ total × 360°.
  • Pictogram: symbols × key value.
  • Scatter: positive, negative or no correlation; one straight line of best fit by eye.

If you see …

  • a pie chart360 ÷ total first.
  • 'estimate' with a scatter diagramuse the line of best fit.

Practice

Practice: easy, medium, hard

Easy

1
A pie chart of 120 people. Angle for 30 tea drinkers?
Show answer

Answer 90

2
One symbol = 4 people. How many people do 3½ symbols show?
Show answer

Answer 14

3
Taller people tend to weigh more. Correlation? (positive, negative or none)
Show answer

Answer positive

Medium

1
A pie chart of 120 people has a 72° slice. How many people?
Guide me

What is it asking? a number

What do we know? 3° per person

Plan \(72\div3\)

Show working
  1. 24

Answer 24

2
A pie chart of 120 people: 20 chose water. Angle?
Guide me

What is it asking? an angle

What do we know? 3° per person

Plan \(20\times3\)

Show working
  1. 60°

Answer 60

3
As a car gets older its value falls. Correlation?
Guide me

What is it asking? a type

What do we know? one goes up

Plan the other goes down

Show working
  1. negative

Answer negative

Hard

1
Line of best fit (scatter above): estimated mark for 4.5 hours?
Guide me

What is it asking? an estimate

What do we know? up from 4.5

Plan across to the mark axis

Show working
  1. ≈ 53

Answer about 53

PartAnswer / workingMarksGuidance
ruled line of best fitB1
51 to 55B1
Total: 2 marks
2
A pie chart of 50 people has a 72° slice. How many people?
Guide me

What is it asking? a number

What do we know? \(\tfrac{72}{360}\)

Plan \(\times50\)

Show working
  1. 10

Answer 10

PartAnswer / workingMarksGuidance
\(\tfrac{72}{360}\times50\)M1
10A1
Total: 2 marks
3
A pie chart of 120 people: the coffee angle is 135°. How many chose coffee?
Guide me

What is it asking? a number

What do we know? 3° per person

Plan \(135\div3\)

Show working
  1. 45

Answer 45

PartAnswer / workingMarksGuidance
45B1
Total: 1 mark

Can I do this?

Anything unticked: revise that section first. All ticked: take the quiz.

Quiz

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