This chapter measures how spread out a set of values is, using four tools: range, interquartile range, variance and standard deviation. It belongs to SPM Mathematics and sits in the Form 4 route.
How do the lessons connect?
Each lesson builds on the one before.
- Calculating range and interquartile range: the quickest ways to describe spread.
- Finding variance and standard deviation: spread measured from the mean.
- Comparing data sets using centre and spread: writing a conclusion from two sets.
- Predicting the effect of changing a data set: what happens when values are added, scaled or removed.
A further group, choosing an appropriate summary of a dataset, asks which measure fits which situation.
Five numbers, three measures
Take the data 4, 6, 8, 10, 12. The range is 12 − 4 = 8. The median is 8, the first quartile is 5 and the third quartile is 11, so the interquartile range is 6.
The mean is 8, and the squared deviations are 16, 4, 0, 4, 16, which add to 40. The variance is 40 ÷ 5 = 8, and the standard deviation is √8 ≈ 2.83. One data set, three different measures, each answering a slightly different question.
Who should start where?
A new Form 4 student should work through the four lessons in order and finish with the practice set. A student who can calculate but struggles with wording can go straight to the comparison lesson.
The grouped version of this chapter is dispersion of grouped data. Use the descriptive statistics explorer to check your answers on invented numbers. For a teacher to work through this chapter with you, see online one-to-one Mathematics tuition.