# 5: The Distribution of Data

$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

When we measure something, such as the percentage of yellow M&Ms in a bag of M&Ms, we expect two things:

• that there is an underlying “true” value that our measurements should approximate, and
• that the results of individual measurements will show some variation about that "true" value

Visualizations of data—such as dot plots, stripcharts, boxplot-and-whisker plots, bar plots, histograms, and scatterplots—often suggest there is an underlying structure to our data. For example, we saw in Chapter 3 that the distribution of yellow M&Ms in bags of M&Ms is more or less symmetrical around its median, while the distribution of orange M&Ms was skewed toward higher values. This underlying structure, or distribution, of our data as it effects how we choose to analyze our data. In this chapter we will take a closer look at several ways in which data are distributed.

This page titled 5: The Distribution of Data is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey.