Dotplots and Stemplots

A list of 30 quiz scores tells you nothing until your eye can compare them. Dotplots and stemplots fix that by putting every value where its size places it, so clusters, gaps, and outliers jump out immediately. A dotplot does this with a number line: draw it, scale it to cover the data's range, then for each observation place one dot above its value. If a value repeats, its dots stack. Twenty-four quiz scores become a skyline where tall stacks mean common scores and empty space means nobody scored there.

A stemplot does the same job but keeps more precision. Split each number into a stem (all digits but the last) and a leaf (the last digit). List the stems once, in order, down the page. Then for each data value, write its leaf next to its stem, in increasing order along each row. Turn the plot sideways and you see the same shape a dotplot would show, but now you can read back every original value exactly, down to the last digit.

Both plots belong to the same first step in working with one-variable data: before computing any number like a mean or a standard deviation, look at the shape. Is it roughly symmetric, skewed, or does it have gaps and clusters worth asking about? Dotplots and stemplots work best for small to moderate data sets; once you have hundreds of values, a histogram takes over because individual dots or leaves get too crowded to read.