Averages and Range

Mode, median and mean

• An average is a single value standing for a whole set of data, and three of them are used here
• The mode is the value occurring most often
  • A set can have more than one mode, or none if every value appears equally often
  • It is the only average usable with categorical data such as colours
• Put the data in order and the value sitting in the centre is the median
  • With an even number of values there is no single middle, so take the midpoint of the two central ones
  • Forgetting to order the data first is the commonest error in the whole topic
• Add every value together and divide by how many there were, and the result is the mean
  • It need not come out whole, and rounding it to an integer for the sake of tidiness is wrong
• The range is not an average at all: it measures spread, and equals the largest value minus the smallest

Which one to use

• The mean uses every value, which makes it the most representative, but also the most distorted by an extreme value
• The median ignores how far away the extremes are, so it stands up better when the data contains one
• The mode is the only choice for non-numerical data, and is useful where the most common value is what matters
• Where a question asks which average is most appropriate, look for an extreme value and say so