Histogram vs bar graph: the difference that matters

Histogram vs bar graph: the short answer

A histogram and a bar graph both use rectangular bars whose height is a count, which is why they are so easy to mix up. They answer different questions because they display different kinds of data. A histogram summarizes one quantitative variable, a variable measured as a number, such as height in centimeters or minutes spent on homework. A bar graph summarizes one categorical variable, a variable that sorts each observation into a group, such as eye color or favorite sport.

That one difference in data type drives every visible feature of the two graphs. Because a histogram sits on a number line, its bars touch and their left-to-right order is fixed. Because a bar graph sits on a list of separate categories, its bars have gaps and you can arrange them in any order. Getting the data type right, which you can check with the quantitative versus categorical distinction, tells you which graph to draw and which rules apply.

What each graph shows

A bar graph, also called a bar chart, displays the frequency (count) or relative frequency (proportion) for each category of a categorical variable. Each bar stands for one category, and its height is how many observations fell in that category, or the fraction that did. You may order the bars however helps your reader: alphabetically, from tallest to shortest, or in a natural sequence like days of the week. The order carries no statistical meaning, so rearranging the bars never changes what the graph says.

A histogram displays the distribution of a quantitative variable by grouping the values into equal-width intervals called bins. Each bar covers one bin along the number line, and its height is the count, or proportion, of values that land inside that interval. Because the axis is numeric, the bins run in order from smallest to largest and cannot be rearranged. Changing the bin width changes how the histogram looks, so the same data can appear smooth with wide bins or spiky with narrow ones.

A histogram can also be drawn horizontally, with the bins running up the vertical axis; the touching bars and the fixed numeric order stay the same either way.

Differences you can see at a glance

Here are the differences you can spot without doing any arithmetic, straight from a picture of each graph.

The touching-bars-versus-gaps difference is the quickest to see, because it comes straight from whether the horizontal axis is a number line or a list of labels.

Reading shape from a histogram

A histogram has a shape, and that shape carries information, because its bars sit in a fixed numeric order. Read three things off it. First, where the tall bars cluster, which marks the peak; that peak locates the center only when the shape is roughly symmetric, since for a skewed distribution the mean and median sit toward the longer tail, away from the tallest bars. Second, how far the bars spread along the axis, which gives the range.

Third, check whether one side has a longer tail. If the longer tail points toward the larger values on the right, the distribution is right-skewed; if it points toward the smaller values on the left, it is left-skewed, a difference covered in skewed left versus skewed right. A roughly even shape with a single central peak is called symmetric.

A bar graph has no shape in this sense. Because you can reorder its categories at will, any skew you think you see would disappear if you sorted the bars differently. That is why questions about shape, center, and spread apply only to graphs that keep quantitative values in order, such as a histogram, a dotplot, or a stem-and-leaf plot. For a compact summary of the same quantitative data, a boxplot shows center and spread through the five-number summary.

When each graph is the wrong choice

The classic trap is a variable whose values are digits but not measurements. Jersey numbers, zip codes, and area codes are written as numbers, yet the 34 on a jersey is only a label, not a quantity larger than 12. Treat those as categorical and use a bar graph, because ordering them by size or averaging them would be meaningless. The test is simple: if adding or averaging the values makes no sense, the variable is categorical.

Going the other way is also wrong. Do not draw a histogram of favorite sport or blood type, because there is no number line to place the categories on and no natural smallest-to-largest order. And do not close the gaps on a bar graph to make it resemble a histogram, since those gaps signal on purpose that the categories are separate groups rather than points on a scale.

Deciding which graph your data needs

When you are handed a variable and asked to graph it, start with one question: is each value a number you could meaningfully add or average, or a label that names a group? If it is a number, such as test scores, reaction times, or heights, draw a histogram, or a dotplot or stem-and-leaf plot for a small data set. If it is a label, such as color, brand, or yes-or-no responses, draw a bar graph or a pie chart. When the values are counts of something, like the number of siblings a student has, they are still numeric, so a histogram or dotplot fits.

Practice makes this automatic. You can drag data points and watch a histogram change shape in the descriptive statistics sandbox, which builds the intuition faster than memorizing a rule.

Mistakes to avoid

A few errors show up again and again.

• Do not read shape or skew from a bar graph, because its category order is arbitrary and the outline carries no meaning.
• Do not treat ID-style numbers such as zip codes or jersey numbers as quantitative; they are labels, so a bar graph is correct.
• Do not let the bars touch on a bar graph or leave gaps on a histogram, because the spacing itself tells the reader which kind of data you have.
• A histogram groups values into bins, so you cannot recover the exact original values from it, only the count in each interval.
• Keep the count style consistent within one graph: use frequency (counts) or relative frequency (proportions) throughout, not a mix of both.