Representing Data

Spec reference: Statistics
Key idea: Draw and interpret a range of statistical diagrams.

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Types of data

• Discrete data: can only take specific values (e.g. number of children)
• Continuous data: can take any value in a range (e.g. height, weight)

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Charts and diagrams

Diagram	Best used for
Bar chart	Discrete or categorical data
Pie chart	Proportions of a whole
Frequency polygon	Comparing distributions
Histogram	Continuous grouped data (unequal class widths)
Scatter graph	Relationship between two variables
Stem-and-leaf	Comparing two data sets
Box plot	Comparing distributions using quartiles
Cumulative frequency	Finding median, quartiles, IQR

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Histograms

In a histogram: Frequency density = ${\displaystyle \frac{\text{Frequency}}{\text{Class width}}}$

The area of each bar represents the frequency.

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Cumulative frequency

• Plot cumulative frequency against the upper class boundary
• Connect points with a smooth curve
• Read off median at ${\displaystyle \frac{n}{2}}$, LQ at ${\displaystyle \frac{n}{4}}$, UQ at ${\displaystyle \frac{3n}{4}}$

$$\text{Interquartile range (IQR)}=\text{UQ}-\text{LQ}$$

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Scatter graphs

Correlation	Description
Positive	Both variables increase together
Negative	One increases as the other decreases
No correlation	No clear relationship

The line of best fit passes through the mean point $(\overline{x},\overline{y})$.

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Test Yourself

Question 1 of 5

In histogram, area of bar represents?