Comparing Two Distributions Side by Side

Saying 'group A is higher' only reports one number, usually a mean or median, and ignores everything else happening in the data. Two groups can share the same center but differ wildly in spread, or have similar spreads but very different shapes. A full comparison always covers four things: shape (symmetric, skewed, unimodal, bimodal), center (mean or median), spread (range, IQR, or standard deviation), and outliers (are there any, and do they change which center/spread measure you trust). You pick the measures that match the shape: median and IQR for skewed data or data with outliers, mean and standard deviation for roughly symmetric data without outliers.

Parallel boxplots or back-to-back stemplots make this easy because they put both groups on the same scale, so you can read off all four features at once and describe the difference in context, with units, using comparative language like 'higher,' 'more spread out,' or 'less skewed' rather than just listing two separate summaries. A comparison is never finished until you've said something about every one of the four features, even if the answer is 'spread is about the same.'

This builds directly on summarizing one distribution, now doing it twice and connecting the two summaries with words like 'than.' It also sets up later work comparing groups statistically, where the question becomes whether an observed difference in centers is bigger than what you'd expect from natural variation alone.