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Maths

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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%25\% of the way through the data

n+14\frac{n+1}{4}​​

Median (Q2)

Value 50%50\% of the way through the data

n+12\frac{n+1}{2}​​

Upper quartile (Q3 or UQ)

Value 75%75\% of the way through the data

3(n+1)4\frac{3(n+1)}{4}​​

Interquartile range (IQR)

Contains middle 50%50\% of the data

Upper quartile minus lower quartile: Q3Q1Q_3-Q_1​​


Example 1

Olivia is collecting data about the ages of her friends' siblings. The answers she collects are 1,1,2,2,3,4,5,5,5,5,7,7,7,7,81,1,2,2,3,4,5,5,5,5,7,7,7,7,8. The median of these numbers is 55.​


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


Lower quartile

Work out the position of Q1n+12=15+14=4\frac{n+1}{2} = \frac{15+1}{4}=4

The 44​​th value is the lower quartile: 2\underline2

Upper quartile

Work out the position of Q33(n+1)2=3(15+1)4=12\frac{3(n+1)}{2} = \frac{3(15+1)}{4}=12

The 1212​th value is the upper quartile: 7\underline7​​

Interquartile range

IQR=72=5\text{IQR} = 7-2=\underline5​​

Median

5\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 11, draw a box plot to represent the data.


Maths; Statistics; KS4 Year 10; Box plots - Higher




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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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