Understand the terms mean, median and mode (to include: explaining the…

The idea

The three measures of central tendency summarise data differently, dictating their appropriate use at A-level. The mean (total divided by n) uses every value, making it the most sensitive measure, ideal for interval data without outliers. However, extreme scores distort the mean. The median is the middle value of an ordered set (or midpoint of the two central values). It resists outliers, making it suitable for ordinal data or skewed interval data. The mode is the most frequent score, essential for nominal data, though it may be unrepresentative or absent. For reaction times of 210, 220, 230, 240 and 980 ms, the mean of 376 is skewed by the 980 ms outlier. The median of 230 ms better represents the typical performance. In a positive skew, the mean is higher than the median and mode; in a normal distribution, all three are equal.

What earns the marks

• Definitions: the mean is the arithmetic average of all scores, the median is the central value of an ordered set, and the mode is the most frequently occurring score.
• Levels of measurement: nominal data require the mode, ordinal data are best summarised by the median, and interval/ratio data allow the mean unless anomalies distort it.
• Skewed distributions: in a positive skew, the mean is pulled higher than the median and mode by extreme high scores; in a negative skew, the mean is pulled lower.
• Justifying selection: always justify the choice of measure using specific features of the data in the stem, such as identifying a specific outlier (e.g., 980 ms) that distorts the mean.
• Strengths and limitations: the mean is highly sensitive but vulnerable to outliers; the median is robust against extreme scores but ignores exact values; the mode works with categories but may not exist.

Common mistakes and how to put them right

• Failing to put the scores in numerical order before identifying the median, resulting in selecting the centre of the unordered list.

• Reporting 'no mode' as a mode of zero, when zero is a valid score.

  Put it right: The absence of any repeated value should be explicitly stated as having no mode.

• Choosing the mean for ordinal data (e.g., subjective rating scales from 1 to 10), where the intervals between points are not guaranteed to be equal.

Exam tips

• When asked which measure is most appropriate, name the measure and provide a justification explicitly linked to the data set provided, such as the presence of an outlier or the level of measurement.
• If a data set is skewed, explicitly state which direction the mean is pulled and by which specific score to demonstrate understanding of distortion.