Revision notes · Maths
There are three types of average, and each has its own purpose:
Mean = total of all valuesnumber of values. This uses every piece of data, but can be skewed by outliers (extreme values).
Median = the middle value when data is arranged in order. For an even number of values, take the mean of the two middle values. The median is not affected by outliers, making it useful for skewed data.
Mode = the most common value (there can be more than one, or none).
Range = highest value − lowest value. This measures spread but is affected by outliers.
The interquartile range (IQR) = Q3 − Q1. Think of Q1 as the value one quarter of the way through your data and Q3 as three quarters of the way. The IQR only looks at the middle 50% of the data, so it ignores extreme values and gives a more reliable picture of the spread.
For grouped data in a frequency table:
You can't find the exact mean — you estimate it using midpoints
Estimated mean = total of (midpoint × frequency)total frequency
The modal class is the group with the highest frequency
The median class is found by working out which class the middle value falls in