Statistics · Averages & range
Chapter 1 · 3
The idea
Estimating averages from grouped data
Why a mean from a grouped frequency table can only ever be an estimate, how to use midpoints in , and why the mode and median come out as a class rather than a number.
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Statistics · Averages & range
Estimating averages from grouped data
Why a mean from a grouped frequency table can only ever be an estimate, how to use midpoints in $\frac{\sum fx}{\sum f}$, and why the mode and median come out as a class rather than a number.
Why it works
Grouping destroys information
A grouped frequency table is a summary, and summarising costs you something. Once 40 waiting times have been recorded as "13 of them were between 10 and 20 minutes", those 13 individual times are gone. Nobody — not you, not the examiner — can get them back out of the table. That one fact is the whole of this topic: grouping destroys information, so any average you calculate afterwards is a reconstruction rather than a measurement. This is why the exam always says "work out an estimate for the mean". The word is not padding, and an answer that never admits it is an estimate has missed the point of the question.Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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