# 9.2.4 IQR & Range

#### What are IQR and the range?

• The three averages (mean, median and mode) measure what is called central tendency – all give an indication of what is typical about the data, what lies roughly in the middle, etc.
• The range and interquartile range (IQR) measure how spread out the data is
• They only apply to numerical data, and both are easy to work out!

#### What do I need to know?

1. Range (Hi-Lo)

• This is the difference between the highest value in the data and the lowest value

Range = Hi – Lo

• It is usually meant by “average” – it’s like an ideal world where everybody has the same, everything is shared out equally
• It is the TOTAL of all the values DIVIDED by the NUMBER OF VALUES
• For example, find the range of 14, 16, 18, 22

Hi = 22

Lo = 14

Range = 22 – 14 = 8

2. Inter-Quartile Range (IQR)

• This is the difference between the upper quartile and the lower quartile
• You know the median splits data into two
• Well as their name suggests, quartiles split the data into four

IQR = UQ – LQ

For example, find the inter-quartile range of the follow data …

20, 23, 32, 35, 37, 38, 43, 45, 47, 49, 52, 56, 58, 58, 59

#### Exam Tip

Remember with the range that you have to do a calculation (even if it is an easy subtraction).  It is not good enough to write something like the range is 14 to 22.

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