Levels of organisation: understand the terms mean, mode and median

The idea

Mean, mode and median are three measures of a typical or central value in a data set. The mean is the arithmetic average: add all values and divide by how many there are. The mode is the value that appears most often; a data set can have one mode, several modes, or no mode if every value is different. The median is the middle value once the data are arranged in order; with an even number of values, it is the mean of the two middle values. For example, in 3, 5, 5, 8, 9 the mean is 30 ÷ 5 = 6, the mode is 5 and the median is 5. In 2, 4, 6, 8 the median is (4 + 6) ÷ 2 = 5. Choosing the right measure matters: the mode suits categories such as blood group, while the median resists extreme values.

What earns the marks

• States that the mean is the sum of all values divided by the number of values.
• Defines the mode as the most frequently occurring value and notes that a set may have no mode or more than one mode.
• Defines the median as the middle value after ordering the data, using the mean of the two middle values when the count is even.
• Applies each term correctly to a small data set, for example identifying mean, mode and median of 3, 5, 5, 8, 9.
• Explains that the median is unaffected by extreme values whereas the mean is pulled towards them.

Common mistakes and how to put them right

• Forgetting to order the data before finding the median.

  Put it right by rewriting the values in ascending order first.

• Dividing by the number of different values rather than the total number of values when calculating the mean.

  Put it right by counting every data point, including repeats.

• Assuming every data set has exactly one mode.

  Put it right by checking for ties and accepting no mode or multiple modes.

• Confusing the mode with the highest value.

  Put it right by counting how often each value occurs rather than comparing sizes.

Exam tips

• Underline the words mean, mode and median in the question so you answer the measure actually requested.
• Show the ordered list and the sum when calculating, so method marks are visible even if the final value slips.
• Check whether the question says give a reason: link the choice of measure to the presence of extreme values or to categorical data.