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Chapter Overview

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Maths

Box plots - Higher

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Box plots

In a nutshell

Box plots are a diagram used to show the spread of data and are a useful way of summarising.

Features of a box plot

A box plot shows minimums, maximums and quartiles but does not show exact values. See the example below for drawing each of these features on your own box plot.

Definitions

Box plot feature	Definition	Formula (where n is total frequency)
Lower quartile (Q₁ or LQ)	Value $25\%$ of the way through the data	$\frac{n+1}{4}$
Median (Q₂)	Value $50\%$ of the way through the data	$\frac{n+1}{2}$
Upper quartile (Q₃or UQ)	Value $75\%$ of the way through the data	$\frac{3(n+1)}{4}$
Interquartile range (IQR)	Contains middle $50\%$ of the data	Upper quartile minus lower quartile: $Q_3-Q_1$

Example 1

Olivia is collecting data about the ages of her friends' siblings. The answers she collects are $1,1,2,2,3,4,5,5,5,5,7,7,7,7,8$ . The median of these numbers is $5$ .

Work out the upper and lower quartiles and the interquartile range.

Lower quartile	Work out the position of Q₁: $\frac{n+1}{2} = \frac{15+1}{4}=4$ The $4$ th value is the lower quartile: $\underline2$
Upper quartile	Work out the position of Q₃: $\frac{3(n+1)}{2} = \frac{3(15+1)}{4}=12$ The $12$ th value is the upper quartile: $\underline7$
Interquartile range	$\text{IQR} = 7-2=\underline5$
Median	$\underline5$

Drawing a box plot

Drawing a box plot involves using all the quantities worked out in the example above.

procedure

1.	Draw a scale.
2.	Mark on the LQ, UQ and median and draw a box with a line where the median is.
3.	Mark on the maximum and minimum and connect to the box with a line.

Example 2

Using the values calculated in example $1$ , draw a box plot to represent the data.

Box plots

In a nutshell

Box plots are a diagram used to show the spread of data and are a useful way of summarising.

Features of a box plot

A box plot shows minimums, maximums and quartiles but does not show exact values. See the example below for drawing each of these features on your own box plot.

Definitions

Box plot feature	Definition	Formula (where n is total frequency)
Lower quartile (Q₁ or LQ)	Value $25\%$ of the way through the data	$\frac{n+1}{4}$
Median (Q₂)	Value $50\%$ of the way through the data	$\frac{n+1}{2}$
Upper quartile (Q₃or UQ)	Value $75\%$ of the way through the data	$\frac{3(n+1)}{4}$
Interquartile range (IQR)	Contains middle $50\%$ of the data	Upper quartile minus lower quartile: $Q_3-Q_1$

Example 1

Olivia is collecting data about the ages of her friends' siblings. The answers she collects are $1,1,2,2,3,4,5,5,5,5,7,7,7,7,8$ . The median of these numbers is $5$ .

Work out the upper and lower quartiles and the interquartile range.

Lower quartile	Work out the position of Q₁: $\frac{n+1}{2} = \frac{15+1}{4}=4$ The $4$ th value is the lower quartile: $\underline2$
Upper quartile	Work out the position of Q₃: $\frac{3(n+1)}{2} = \frac{3(15+1)}{4}=12$ The $12$ th value is the upper quartile: $\underline7$
Interquartile range	$\text{IQR} = 7-2=\underline5$
Median	$\underline5$

Drawing a box plot

Drawing a box plot involves using all the quantities worked out in the example above.

procedure

1.	Draw a scale.
2.	Mark on the LQ, UQ and median and draw a box with a line where the median is.
3.	Mark on the maximum and minimum and connect to the box with a line.

Example 2

Using the values calculated in example $1$ , draw a box plot to represent the data.

Frequently Asked Questions (FAQ)

FAQs

Question: How to draw a box plot?

Answer: To draw a box plot: 1. Draw a scale. 2. Mark on the LQ, UQ and median and draw a box with a line where the median is. 3. Mark on the maximum and minimum and connect to the box with a line.
Question: What is the interquartile range?

Answer: The interquartile range contains middle 50% of the data. It is the lower quartile minus upper quartile.
Question: What is a box plot?

Answer: Box plots are a diagram used to show the spread of data and are a useful way of summarising.

Theory

Exercises

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Box plots - Higher

Box plots

​​In a nutshell

Features of a box plot

​​Definitions

Example 1

Drawing a box plot

procedure

Example 2

Box plots

​​In a nutshell

Features of a box plot

​​Definitions

Example 1

Drawing a box plot

procedure

Example 2

Theory understood?

In a nutshell

Definitions

In a nutshell

Definitions