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 inter–quartile 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
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.