4.2 Representing data
Charts and graphs
Everything on charts and graphs that can come up in the WJEC GCSE Mathematics and Numeracy, in all three units. Each skill below has the method, the mistake that costs the most marks, a worked example, and free practice marked the way WJEC marks it.
Practise charts and graphs free
A worked example
Interquartile range · [2 marks]
Here are the marks of 11 students in a quiz: 13, 10, 7, 8, 14, 9, 15, 11, 17, 12, 16. Work out the interquartile range.
- M1In order: 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17. Lower quartile = 3rd value = 9, upper quartile = 9th value = 15
- A115 − 9 = 6
The exam skills (5)
Scatter graphs
- Positive: as one goes up, so does the other (points slope up).
- Negative: as one goes up, the other goes down.
- None: no pattern.
Watch out: Saying correlation means one causes the other.
Pie charts
- Find the angle for one person: 360 ÷ total.
- Multiply by each frequency.
- Check the angles add up to 360°.
Watch out: Using 100 instead of 360.
Cumulative frequency
- Median: read across from half the total.
- Lower quartile from a quarter, upper quartile from three quarters.
- Read down to the horizontal axis.
Watch out: Reading across from the middle of the axis value, not half the total frequency.
Box plots
- The line in the box is the median.
- The box goes from the lower quartile to the upper quartile; IQR = UQ − LQ.
- The whiskers go to the smallest and biggest values.
Watch out: Giving the middle of the whole plot as the median.
Interquartile range
- Put the values in order.
- With n values, the lower quartile is value (n + 1) ÷ 4 and the upper quartile is value 3(n + 1) ÷ 4.
- IQR = upper quartile − lower quartile.
Watch out: Giving the range (biggest − smallest).
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