Dotplot vs histogram vs stemplot: how to choose

Dotplot vs histogram vs stemplot: the short answer

All three graph the same thing: the distribution of one quantitative variable, a variable measured as a number. Each keeps the values in their natural order from smallest to largest, so all three let you read shape, center, and spread. What changes is how much of the raw data each keeps and how many values it handles well.

A dotplot shows every value as its own dot and is best for small data sets. A stemplot (stem-and-leaf plot) also keeps every value, storing its digits, and suits small-to-medium data sets. A histogram groups values into intervals and shows only the count in each, trading the individual values for the ability to handle large data sets. Match the graph to the size of the data and you will almost always pick the right one.

What a dotplot shows

A dotplot places one dot for each observation above its value on a number line, stacking dots when values are equal or nearly equal. Nothing is grouped, so you can count every observation and see each value directly.

That makes a dotplot ideal for small data sets and for spotting clusters, gaps, and outliers at a glance. Its limits appear as the data grow: with hundreds of values, or values spread across a wide range with few repeats, the stacks get tall or thin and the picture becomes hard to read. For small counts of a discrete quantity, such as the number of siblings each student has, a dotplot is often the clearest graph there is.

What a stemplot shows

A stemplot, or stem-and-leaf plot, splits each value into a stem (the leading digit or digits) and a leaf (usually the final digit). The stems run down the left in order, and each leaf is written beside its stem, also in order. A value of 82 with stems by tens becomes a stem of 8 and a leaf of 2.

The payoff is that a stemplot keeps every original value while also showing the shape, since the rows act like sideways bars. You can read the exact data back off it, find the median by counting leaves, and compare two groups with a back-to-back stemplot that shares one column of stems. It works well for small-to-medium data sets; with a very large data set the rows of leaves grow unwieldy, and a histogram becomes the better summary.

What a histogram shows

A histogram groups the values into equal-width intervals called bins along a number line and draws a bar over each bin whose height is the count, or proportion, of values in that interval. Because the axis is numeric, the bars touch and their order is fixed from smallest to largest.

The trade is deliberate: a histogram gives up the individual values and shows only how many fall in each bin, which is exactly what lets it summarize hundreds or thousands of observations cleanly. Changing the bin width changes the appearance, so the same data can look smooth with wide bins or spiky with narrow ones. A histogram is the standard graph for large quantitative data sets, and it is the one whose shape you read for skew, covered in skewed left versus skewed right.

The three side by side

The deciding row is whether the graph keeps exact values. Dotplots and stemplots do, so they shine on small data; the histogram gives them up to handle large data.

When to use which

Let the size and nature of the data decide. For a small data set, especially a discrete count with repeats, use a dotplot, because every value shows and clusters and gaps stand out. For a small-to-medium data set where you want to keep the exact numbers, use a stemplot, which doubles as a table you can read values back from.

For a medium-to-large data set, use a histogram, because binning is what makes many values readable, even though you lose the individual numbers. To compare two groups, a back-to-back stemplot or two dotplots or histograms drawn on the same scale all work. You can drag values and watch a histogram reshape in the descriptive statistics sandbox to build a feel for how binning changes the picture.

The classic mix-up and how to avoid it

The frequent error is confusing a histogram with a bar graph, and reading exact values off a histogram that no longer holds them. A histogram's touching bars sit on a number line and show quantitative data, whereas a bar graph's separated bars show categories, a distinction drawn out in histogram versus bar graph. And once values are binned, a histogram can tell you that the median falls in the 80-to-90 interval but not that it is exactly 82.

Avoid both with two habits. First, check the horizontal axis: a number line means quantitative data and a histogram, dotplot, or stemplot; a list of category labels means a bar graph. Second, when a question needs an exact value such as the median or a specific data point, use a dotplot or stemplot, which keep the numbers, rather than a histogram, which keeps only bin counts.