Lesson 2 of 11 · 7 min
Range
NCERT §13.2, §13.3
The coach agrees the averages hide something. His first idea is simple: look at each opener's best and worst innings and see how far apart they are.
The lesson in notes
In short
Measures of dispersion: range, quartile deviation, mean deviation and standard deviation. The rationalised chapter studies all of them except quartile deviation.
Range = maximum value − minimum value. It is the simplest measure of spread and has the same unit as the data.
NCERT's batsmen: ranges 117 − 0 = 117 and 60 − 46 = 14, so the first batsman's scores are far more scattered.
Trial openers (made up): Arjun's range is 58 − 42 = 16 runs; Kabir's is 110 − 0 = 110 runs.
Range uses only the two extreme values. One unusual innings changes it completely, and it says nothing about how the other observations lie around the centre.
So a better measure must use the deviation of every observation from a central value, x − a. The two such measures in this chapter are mean deviation and standard deviation.