Problem with averages


Averages (mean, median, mode) give us a way of determining where the center of a set of data is, but they don’t tell us how the data varies.

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Range


Range tells us over how many numbers the data extends, i.e. how spread out the data is. The smallest value is called the lower bound, and the largest value is the upper bound.

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$$ Range = Upper \; Bound - Lower \; Bound $$

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Range only describes the width of the data, not how the data is distributed between the bounds. We could have different datasets with the same range, but one dataset may have outliers and the range could be misleading. Range is sensitive to outliers.

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Because the range is calculated using the most extreme values of the data, it’s impossible to tell what that data actually looks like, and whether it contains outliers.

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A better way would be to ignore the outliers and calculate the mini-range. Quartiles are a consistent way of ignoring outliers.

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Quartiles


  1. Sort data in ascending order.