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Statistics · Data presentation

Chapter 1 · 3

The idea

Measures of location — mean, median, mode and quartiles

The three averages (mean, median, mode) and the other measures of location (quartiles and percentiles); how to find them from a list and from a frequency table; and how to estimate the median and quartiles of grouped continuous data by linear interpolation.

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Statistics · Data presentation

Measures of location — mean, median, mode and quartiles

The three averages (mean, median, mode) and the other measures of location (quartiles and percentiles); how to find them from a list and from a frequency table; and how to estimate the median and quartiles of grouped continuous data by linear interpolation.

Why it works

Three averages, three questions

A measure of location is a single value that stands in for "where the data sits".

The mean adds everything up and shares it out equally: xˉ=∑xn,or from a frequency tablexˉ=∑fx∑f.\bar{x} = \frac{\sum x}{n}, \qquad \text{or from a frequency table} \quad \bar{x} = \frac{\sum f x}{\sum f}. It uses every value, so it's the most informative — but it's pulled towards outliers and skew.

The median is the middle value once the data is in order. Half the data is below it, half above, so it's barely affected by a few extreme values — the average to trust for skewed data.

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