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SPM Mathematics Glossary

Measures of Dispersion for Ungrouped Data, terms

RangeThe difference between the largest and smallest values in a data set.VarianceA measure of how spread out data is around the mean; the square of the standard deviation.Standard deviationA measure of spread in the same units as the data; the square root of the variance.Interquartile rangeThe spread of the middle half of the data, from the first to the third quartile.MeanThe sum of all values divided by how many there are; the usual average.MedianThe middle value when the data is put in order.ModeThe value that appears most often in a data set.RangeThe difference between the largest and smallest values in a data set.FrequencyThe number of times a value or category occurs in a data set.

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Frequently asked questions

Which dispersion terms should I learn first?

Mean, median and mode should already feel familiar from earlier years, make sure they are solid, since range, variance and standard deviation all measure how spread out data is around these central values. Interquartile range builds on quartiles, so it's usually easiest to leave for last.

What terms in this chapter get confused most?

Range and interquartile range are commonly mixed up: range uses only the highest and lowest values, while interquartile range uses the middle 50% of the data and is less affected by extreme values. Variance and standard deviation are also confused, though standard deviation is simply the square root of variance.

How do dispersion terms appear in exam questions?

Questions usually give a set of ungrouped data and ask you to calculate the range, variance or standard deviation, often using the formula given on the formula sheet. Some also ask you to compare two sets of data using their measures of dispersion and state which is more consistent.

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