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# Box plots - Higher 0%

Summary

# 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 (Q3 or 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.

​​

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