Statistics · Data presentation
Chapter 1 · 4
The idea
Cumulative frequency, box plots and outliers
Building a cumulative frequency diagram and reading the median, quartiles and percentiles off it by plotting against the UPPER class boundary; testing for outliers with the 1.5×IQR rule or the mean ± 2 standard deviations rule; drawing a box plot whose whiskers stop at the most extreme value that is NOT an outlier; and comparing two distributions with a measure of location and a measure of spread.
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Statistics · Data presentation
Cumulative frequency, box plots and outliers
Building a cumulative frequency diagram and reading the median, quartiles and percentiles off it by plotting against the UPPER class boundary; testing for outliers with the 1.5×IQR rule or the mean ± 2 standard deviations rule; drawing a box plot whose whiskers stop at the most extreme value that is NOT an outlier; and comparing two distributions with a measure of location and a measure of spread.
Why it works
The running total
A grouped frequency table hides where individual values sit, so we can't read the median straight off it. A cumulative frequency diagram fixes that by recording, at each class, the running total of "how many values so far".Plot against the UPPER class boundary
The cumulative frequency for a class is the total of that class and all earlier ones — and you only know you have reached that total once you pass the top of the class. So each point is , starting from the lower end of the first class with cumulative frequency . Join the points (a smooth curve or straight segments) to get a graph you can read both ways.Keep reading — free
The rest of the explanation, plus 4 worked examples you step through move by move.
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