CIE IGCSE Maths

Revision Notes

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 Demo, IGCSE & GCSE Maths revision notes

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

 

Quartiles Demo, IGCSE & GCSE Maths revision notes

IQR = UQ – LQ

IQR and Range RN 1

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

IQR and Range RN 2

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.

Worked Example

IQR and Range Worked Example 1, downloadable IGCSE & GCSE Maths revision notes IQR and Range Worked Example 2, downloadable IGCSE & GCSE Maths revision notes

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