Averages and Spread

The range tells you how spread out all the data values are. The interquartile range tells you the spread of the middle 50% of values.

Quartiles

Quartiles divide the data into four equal groups. 

If you have a data set with n values and put the data in ascending order then:

Q1 position (the lower quartile) = (n+1)/4
Q2 Position (the median) = 2(n+1)/4
Q3 Position (the upper quartile) = 3(n+1)/4

Example: What is the upper quartile of the values 3,4,6,9,30,54,87

There are 7 values overall so the position of the upper quartile is 3(7+1)/4 = 6

So the upper quartile is the number in position 6.

i.e. the upper quartile is 54.

Interquartile Range

This is just the difference between the upper and lower quartile. It contains the middle 50% of values.

Stem and Leaf Diagrams

You might be asked to put values into a stem and leaf diagram before finding the the median etc. This is easy to do…just make something like the diagram below (just remember to include a key).stem and leaf diagramBox Plots

These give you a summary of the spread of data and look like this:box plotComparing Data

If asked to compare two sets of data do the following:

  • Look at the mean, media or mode – say which data set has the highest value and what this means in the context of the data (e.g. older people are generally heavier).
  • Look at the spread – the smaller this is the smaller the variation in the data.