Statistics · Cumulative frequency & box plots
Chapter 1 · 3
The idea
Quartiles & the interquartile range
Why the quartiles are a quarter and three quarters of the way through the data rather than along the number line, how to find them from an ordered list and from a cumulative frequency curve, and why the interquartile range beats the range as a measure of spread.
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Statistics · Cumulative frequency & box plots
Quartiles & the interquartile range
Why the quartiles are a quarter and three quarters of the way *through the data* rather than along the number line, how to find them from an ordered list and from a cumulative frequency curve, and why the interquartile range beats the range as a measure of spread.
Why it works
The quarter marks
The median splits ordered data in half. The quartiles do the same job at the quarter marks: the lower quartile (LQ) is the value a quarter of the way through the data, and the upper quartile (UQ) is the value three quarters of the way through. With the median between them they cut the data into four groups of equal size — a quarter of the values in each.That phrase — a quarter of the way through the data — is the whole topic, and it is where most of the marks are lost. It does not mean a quarter of the way along the number line.
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The rest of the explanation, plus 3 worked examples you step through move by move.
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