This guide covers the statistics histograms from math class, not the brightness histogram on a camera screen. Each shape below comes with a short made-up dataset you can paste into the histogram maker to rebuild the graph and change the bins yourself. We built every histogram on this page in Chartjuice from those same datasets, and where the tool's bin settings changed the picture, we say so. If you're still deciding whether you need a histogram at all, histogram vs bar graph covers that first.

Start with the axes and the bins

Look at the horizontal axis first. It shows what's being measured, such as test scores, with the values grouped into bins. Each bin is a range of values, and each bar sits on one bin.

Then look at the vertical axis, which shows how many values fall in each bin. On a frequency histogram, a bar that reaches 6 means 6 values landed in that range.

The point students miss most often is that a bar is a range, not a single value. If one bin of test scores runs from 70 to 80, the bar over it counts every score in that range, but it doesn't tell you what any one student scored.

That's also why the bars touch. The bins run along a number line, so one bar ends exactly where the next begins, and a visible gap means an empty bin rather than a spacer.

A value that sits exactly on an edge can only be counted once, so every histogram follows a rule about which bin owns the edge. In Chartjuice's histogram maker, each bin includes its lower edge and excludes its upper edge, so a score of 80 counts in the 80 to 90 bar, and the last bin includes both edges. If your counts are off by one from a textbook's answer, check which edge rule the book uses.

Three quick checks come before any reading:

  1. The axis labels and units.
  2. The bin width, which is the distance from one bin edge to the next.
  3. Whether the vertical axis shows counts or proportions.

Read the counts, peak, center and spread

Take a made-up test where 20 students took the test and the bins are 10 points wide. The 50s bin has 1 score, the 60s have 3, the 70s have 7, the 80s have 5 and the 90s have 4. The 70s bar is the tallest, at 7, and the counts add up to 20.

Read one bar's count

Find the bar and follow its top edge across to the vertical axis. The number where it meets the axis is how many students scored in that bin, so on a frequency histogram the height is a count and the bar is a range.

Add the counts for a total

Add the heights of every bar to get the number of values in the dataset. You'll need that total before you can find the middle value or turn a count into a proportion.

Find the peak

The tallest bar marks the bin with the most values. Say it as a range, such as "more scores fall in the 70s than in any other bin," because a bar doesn't give you the exact mode.

Locate the center

With 20 values, the median sits between the 10th and 11th values in order. Count up from the left with a running total of bar heights: 1 after the 50s, 4 after the 60s, then 11 after the 70s. The running total passes 10 and 11 inside the 70s bar, so the median is somewhere in the 70s. A histogram can tell you which bin holds the median, but not its exact value.

Judge the spread

Look at where the bars begin and end. Subtract the left edge of the first bar from the right edge of the last bar for a rough range, here 50 to 100, or about 50 points. Bars bunched close together mean a small spread, and bars stretched across the axis mean a large one.

Frequency or relative frequency?

Check the vertical axis label. A frequency histogram counts values, and a relative frequency histogram shows each bin's share of the total, so all the bars add up to 1 (or 100%). The shape stays the same, and only the scale on the vertical axis changes. If a question asks "how many," read the count, and if it asks "what fraction," read the proportion or divide the count by the total.

Symmetric and uniform shapes

In these two shapes the bars balance, so the mean and median land close together.

Symmetric histogram

Say a class measures heights in inches and gets these 13 values: 61, 63, 63, 63, 65, 65, 65, 65, 65, 67, 67, 67, 69. With bins 2 inches wide, Chartjuice draws five bars from 60 to 70 that read 1, 3, 5, 3, 1. The tallest bar sits in the middle and the left half mirrors the right.

Symmetric histogram of 13 class heights in 2-inch bins from 60 to 70 inches, with bars of 1, 3, 5, 3 and 1 Students Height (inches) 0 1 2 3 4 5 60–61 62–63 64–65 66–67 68–69 chartjuice.com
Symmetric: class heights in 2-inch bins.

The median is 65 and the mean is also 65, because every height below the middle has a partner the same distance above it, and their pulls on the mean cancel out.

Uniform histogram

Now roll a die 24 times, with each face from 1 to 6 coming up exactly four times. With one bar per face, every bar reaches 4, so the histogram is a flat block with no peak and no tail. Real rolls would wobble a little, with some bars slightly taller or shorter, and the shape would still read as roughly uniform. The mean and median both sit at 3.5, in the middle of the faces.

Uniform histogram of 24 die rolls with six bars of 4, one for each face Rolls Die face 0 1 2 3 4 1–1.833 1.833–2.667 2.667–3.5 3.5–4.333 4.333–5.167 5.167–6 chartjuice.com
Uniform: 24 die rolls, with Bins set to Count and 6 so each face gets its own bar.

Getting one bar per face took a second try when we built it. With Bins set to Width and a width of 1, the 5s and 6s landed in the same last bar, which reached 8, because the last bin includes both of its edges. Setting Bins to Count and 6 instead gave six bars of 4. Whole-number data like dice rolls or ratings can trip over that edge rule, so if the top bar looks twice as tall as it should, try Count.

On a test, "symmetric" and "uniform" are different answers. A symmetric histogram has a peak with mirrored sides, while a uniform one has bars of about the same height. In both, you can say the mean is approximately equal to the median.

Skewed right and skewed left shapes

A skewed histogram has one long tail and its peak off to one side. The tail names the direction, so a tail stretching right is skewed right and a tail stretching left is skewed left. Going by where the tall bars sit is the most common way to get the direction backward.

Skewed right histogram

Students report their commute to school in minutes: 5, 5, 8, 10, 10, 12, 12, 15, 15, 18, 20, 25, 35, 45, 55. With bins 10 minutes wide, the bars from left to right read 3, 7, 2, 1, 1, 1. Most students live close by, so the tall bars are on the left, and a few long commutes stretch a thin tail to the right.

Right-skewed histogram of 15 commute times in 10-minute bins, tall on the left with a thin tail to the right Students Commute (minutes) 0 1 2 3 4 5 6 7 0–9 10–19 20–29 30–39 40–49 50–59 chartjuice.com
Skewed right: commutes to school in 10-minute bins.

The median is 15 minutes and the mean is about 19.3. The long commutes pull the mean toward the tail, while the median only depends on position in the ordered list, so in a right-skewed histogram the mean sits above the median.

Skewed left histogram

Here are 15 scores on an easy quiz: 50, 65, 75, 85, 88, 90, 92, 92, 94, 95, 95, 96, 97, 98, 99. With bins 10 points wide, the bars read 1, 1, 1, 2, 10. Most students did well, so the tall bar is on the right and a few low scores form a tail on the left. The median is 92 and the mean is 87.4, pulled down toward the tail.

Left-skewed histogram of 15 quiz scores in 10-point bins, with a tall bar from 90 to 100 and a thin tail to the left Students Quiz score 0 2 4 6 8 10 50–59 60–69 70–79 80–89 90–99 chartjuice.com
Skewed left: scores on an easy quiz in 10-point bins.

For a test answer, find the long tail, name the skew by the side it's on, and place the mean on the tail side of the median. Right skew means the mean is greater than the median, and left skew means the mean is less than the median.

Bimodal histograms, gaps and outliers

A bimodal histogram has two separate peaks. Two peaks usually mean two groups are mixed into one dataset, and that changes how you describe the center.

Say you record the hour of day for 24 visits to a website: 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 12, 15, 17, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 22. The histogram shows a morning peak and an evening peak with a dip between them, because morning visitors and evening visitors are two different groups.

The mean of these hours is about 14.8 and the median is 16, so both land in the quiet afternoon stretch where hardly anyone visited. Neither one describes a typical visit, which is why the honest summary of a bimodal histogram is the two peaks themselves.

Gaps

An empty bin shows up as a space with no bar, meaning no values fall in that range. With one-hour bins, the visits data has no visits at 13, 14 or 16, and those empty hours mark the boundary between the two groups.

Outliers

A lone bar far from the rest is a possible outlier. Call it "possible," because the histogram only shows that a value is unusual, not that it's a mistake, so check the data before removing it. Add one student with a 120-minute commute to the commute times above and a new bar appears far to the right, separated from the others by empty bins.

That one value moves the mean from about 19.3 to about 25.6, because it adds its full size to the total, while the median stays at 15 because it's just one more entry at the end of the ordered list. When a histogram has an outlier, expect the mean to shift toward it and the median to stay nearly put. A box plot of the same column is a good second check, since it marks values beyond 1.5 times the IQR as separate dots.

How bin width changes the picture

The bin width can make a shape appear or disappear, and the website visits show it clearly. Here's the same column of 24 hours drawn three ways in the histogram maker with Bins set to Width.

  • With a width of 1, there are 14 bars from 8 to 22, reading 2, 4, 3, 1, 1, 0, 0, 1, 0, 1, 1, 3, 4, 3. The last bar holds both the 21s and the 22, since the last bin includes its upper edge. Both groups are visible, but the bars jump around so much that the picture looks noisy.
  • With a width of 3, the bars read 2, 8, 1, 2, 8, 3. Two tall bars sit on either side of a dip, and the bimodal shape is unmistakable.
  • With a width of 8, the bars read 12 and 12. The dip is gone and the histogram looks flat, so a reader who saw only this version would never guess the visits came in two waves.
Histogram of 24 website visits by hour with one-hour bins, showing a morning group and an evening group with jagged bars Visits Hour of day 0 1 2 3 4 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 chartjuice.com
Website visits by hour, bin width 1.
Histogram of the same 24 visits with three-hour bins, showing two clear peaks with a dip between them Visits Hour of day 0 2 4 6 8 6–8 9–11 12–14 15–17 18–20 21–23 chartjuice.com
The same visits, bin width 3: the two peaks stand out.
Histogram of the same 24 visits with eight-hour bins, showing two equal bars of 12 and no dip Visits Hour of day 0 2 4 6 8 10 12 8–15 16–23 chartjuice.com
The same visits, bin width 8: the dip disappears.

All three use identical data, and only the bins changed. A common starting point is the square root of the number of values, which for 24 values suggests about 5 bins, with the bin width rounded to a convenient number. The histogram maker's Auto setting uses the Freedman-Diaconis rule instead, which bases the width on the spread of the middle half of the data. Either way, use fewer bins if the bars look jagged and more if the shape looks like one featureless block.

On a test, check the bin width before you name a shape. If the question gives you the bins, answer from those, and if you're drawing the graph yourself, try more than one width and say which one you used.

Rebuild the examples in the histogram maker

Open the histogram maker, which needs no signup. Click Paste data and paste one dataset from this page as a single column with its name in the first row, then click Use this data. You can also type the values straight into the table under the chart. Check that Value is set to that column under Chart columns.

To see bin width at work, open the Style tab, go to Histogram options and set Bins to Width. Try 1, 3 and 8 on the website visit hours and watch the two peaks appear and then flatten out. Count gives you a set number of equal bins instead, which is handy when a worksheet says "use 6 bins" and, as the dice showed, when your data is whole numbers. The maker's example gallery also has ready-made Right-skewed data and Bimodal distribution presets if you want a second look at those shapes.

Files are read in your browser and never uploaded. When the graph looks right, click Download for a PNG at 1x, 2x or 4x, with an optional transparent background, or an SVG, or use Copy image to paste it into a worksheet or slide. Free downloads carry a small, faint "chartjuice.com" mark in the bottom-right corner, which Pro removes.