Descriptive statistics: measures of central tendency – mean, median, mode;…

The idea

Central tendency asks where scores cluster, dispersion asks how far they spread. The mean uses every score, making it sensitive but easily distorted by anomalies. The median, the middle score of ordered data, shrugs off anomalies. The mode is the most frequent score. Range is the highest score minus the lowest. Standard deviation is the average distance of scores from the mean; a large one means the group is varied. A percentage is the part over the whole, multiplied by 100. Correlations show relationships between co-variables: positive means as one increases, the other increases; negative means as one increases, the other decreases; zero means no relationship exists.

What earns the marks

• Mean: add every score and divide by how many there are, so it uses all the data and is the most representative measure when there are no anomalies.
• Median: put the scores in order and take the middle one, or the midpoint of the middle two when the number of scores is even.
• Mode: the most frequently occurring score, and the only measure of central tendency available for data in named categories.
• Range: subtract the lowest score from the highest, a quick measure of dispersion that uses only two of the values.
• Standard deviation: the average amount by which scores deviate from the mean, a larger figure meaning greater spread and a less representative mean.
• Percentage: the part divided by the total and multiplied by 100, with the working shown.
• Correlation direction: positive (both variables increase together), negative (one increases as the other decreases), or zero (no relationship).

Common mistakes and how to put them right

• Giving a mean to more decimal places than the raw scores justify, or ignoring the rounding instruction printed in the question.

• Choosing a median without first placing the scores in order, which returns the middle score of an unordered list.

• Reading a large standard deviation as meaning the scores are higher, when it means they are more spread out.

• Describing a zero correlation as 'no result' rather than as a genuine finding of no relationship between the co-variables.

Exam tips

• Calculation marks are awarded for method as well as answer, so set the working out; a wrong final figure with visible correct method can still score.
• If the data contains an obvious outlier, justify the median and say why: it is unaffected by the extreme score.
• Standard deviation items nearly always ask what the figure tells you about the participants, so finish with a sentence on how consistent or varied the group was.
• When interpreting a scattergram, explicitly state whether the correlation is positive, negative, or zero based on the direction of the data points.