Charts & Graphs

Spec reference: Statistics
Key idea: Draw and interpret statistical charts including bar charts, pie charts, histograms, scatter graphs and cumulative frequency.

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Bar charts

Used for discrete or categorical data. Bars should have equal width and gaps between them.

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Pie charts

Each sector represents a category. The angle for each sector:

$$\text{Angle}=\frac{\text{frequency}}{\text{total}}\times 360°$$

Example

30 students were asked their favourite subject. 12 chose Maths.

$$\text{Angle}=\frac{12}{30}\times 360°=\boxed{{\displaystyle 144°}}$$

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Scatter graphs & correlation

Used to show the relationship between two variables.

Correlation	Meaning
Positive	As $x$ increases, $y$ increases
Negative	As $x$ increases, $y$ decreases
No correlation	No relationship

The line of best fit passes through the mean point and has roughly equal points on each side.

WARNING

Correlation does NOT mean causation.

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Cumulative frequency

Plot cumulative frequency against the upper class boundary.

From a cumulative frequency graph:

• Median = value at $\frac{n}{2}$
• LQ = value at $\frac{n}{4}$
• UQ = value at $\frac{3n}{4}$
• IQR = UQ − LQ

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Box plots

Shows: minimum, lower quartile (LQ), median, upper quartile (UQ), maximum.

$$\text{IQR}=\text{UQ}-\text{LQ}$$

Box plots are useful for comparing distributions.

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Histograms

Used for continuous grouped data. The area of each bar represents frequency.

$$\text{Frequency density}=\frac{\text{Frequency}}{\text{Class width}}$$

WARNING

In a histogram, it is the area (not height) that represents frequency.

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Frequency polygons

Connect the midpoints of each bar in a frequency chart. Used to compare distributions.

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Exam tips

Watch out for

• Pie chart angles must add up to exactly 360°
• For cumulative frequency, plot at the UPPER end of each class interval
• In histograms with unequal class widths, use frequency density (not frequency) on the y-axis

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Test Yourself

Question 1 of 5

30 students, 10 prefer sport. Pie chart angle?