Quartiles & Interquartile Range (Cambridge (CIE) IGCSE International Maths)
Revision Note
Written by: Roger B
Reviewed by: Dan Finlay
Quartiles & Interquartile Range
What are quartiles?
The median splits the data set into two parts
Half the data is less than the median
Half the data is greater than the median
Quartiles split the data set into four parts
The lower quartile (LQ) lies a quarter of the way along the data (when in order)
One quarter (25%) of the data is less than the LQ
Three quarters (75%) of the data is greater than the LQ
The upper quartile (UQ) lies three quarters of the way along the data (when in order)
Three quarters (75%) of the data is less than the UQ
One quarter (25%) of the data is greater than the UQ
You may come across the median being referred to as the second quartile
How do I find the quartiles?
Make sure the data is written in numerical order
Use the median to divide the data set into lower and upper halves
If there are an even number of data values, then
the first half of those values are the lower half,
and the second half are the upper half
All of the data values are included in one or other of the two halves
If there are an odd number of data values, then
all the values below the median are the lower half
and all the values above the median are the upper half
The median itself is not included as a part of either half
The lower quartile is the median of the lower half of the data set
and the upper quartile is the median of the upper half of the data set
Find the quartiles in the same way you would usually find the median
just restrict your attention to the relevant half of the data
What is the interquartile range (IQR)?
The interquartile range (IQR) is the difference between the upper quartile (UQ) and the lower quartile (LQ)
Interquartile range (IQR) = upper quartile (UQ) - lower quartile (LQ)
The IQR measures how spread out the middle 50% of the data is
The IQR is not affected by extreme values in the data
Worked Example
A naturalist studying crocodiles has recorded the numbers of eggs found in a random selection of 20 crocodile nests
31 32 35 35 36 37 39 40 42 45
46 48 49 50 51 51 53 54 57 60
Find the lower and upper quartiles for this data set.
There are 20 data values (an even number)
So the lower half will be the first 10 values
The lower quartile is the median of that lower half of the data
31 32 35 35 36 37 39 40 42 45
So the lower quartile is midway between 36 and 37 (i.e. 36.5)
Do the same thing with the upper half of the data to find the upper quartile
The upper quartile is the median of the upper half of the data
46 48 49 50 51 51 53 54 57 60
So the upper quartile is midway between 51 and 51 (i.e. 51)
Lower quartile = 36.5
Upper quartile = 51
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