Histogram Maker: Free, With Frequency Table

Q: How do I describe the shape of a histogram?

Look at symmetry, peaks and outliers. A symmetric histogram looks about the same on both sides of its center. A right-skewed histogram has a long tail to the right (common for incomes and waiting times), and a left-skewed one has a tail to the left. One peak is unimodal; two clear peaks are bimodal, which often means two groups are mixed together.

How to use the histogram maker

Paste your numbers into the box: one column from a spreadsheet, or values separated by commas or spaces.
Leave Bins on Automatic, or choose your own number of bins or bin width (and, optionally, where the first bin starts).
Add a title and axis label, and pick counts or percentages for the vertical axis.
Click Make histogram. Tick Overlay a normal curve to compare your data with a bell curve.
Read the description of the shape and the frequency table, then download the chart as a PNG.

How a histogram is built

A histogram splits the number line into equal-width ranges called bins, counts how many values fall in each, and draws a bar for every bin. The automatic setting picks the number of bins with Sturges' rule, then rounds the width to a tidy number like 2, 5 or 10.

Number of bins: k = ⌈log₂ n⌉ + 1

Bin width: w ≈ max − mink

Relative frequency: count in binn × 100%

n: How many values are in the data set
k: The number of bins (bars)
w: The width of each bin, rounded to a convenient number
⌈ ⌉: Round up to the next whole number
max − min: The range of the data: the largest value minus the smallest

Worked example

A clinic records how long 12 patients wait, in minutes: 3, 7, 8, 12, 14, 15, 15, 18, 21, 22, 27 and 35. Build a frequency table for a histogram with bins 10 minutes wide.

Find the range
35 − 3 = 32 minutes
Choose the bins: width 10, starting at 0, so 0–10, 10–20, 20–30 and 30–40
k = 4 bins
Count the values in each bin
0–10: 3, 10–20: 5, 20–30: 3, 30–40: 1
Find the tallest bar's relative frequency
512 × 100% = 41.7%

What it means: the most common wait is 10 to 20 minutes, which covers 41.7% of patients. The bars fall away more slowly on the right, where one patient waited 35 minutes, so the waits are slightly skewed to the right. That's typical for waiting times, which can't go below zero but occasionally run long.

How to read a histogram

Center: where the tallest bars are. For a quick number, the mean and median summarize the center.
Spread: how wide the bars reach. A wide histogram means the values vary a lot; the standard deviation measures this.
Shape: symmetric, skewed right (long tail of large values) or skewed left (long tail of small values). The calculator measures this with the skewness coefficient.
Peaks: one peak is typical. Two separate peaks often mean two different groups are mixed in the data, like the heights of adults and children together.
Gaps and outliers: isolated bars far from the rest are worth checking. They may be data entry errors or genuinely unusual cases.

The shape you see depends partly on the bins you choose. If a feature appears with one bin width but disappears with another, it is probably noise. Real patterns tend to show up across several reasonable settings.

Frequently asked questions

What is the difference between a histogram and a bar graph?

A histogram shows the distribution of one numeric variable: the x-axis is a number line split into ranges (bins), and the bars touch because the ranges are continuous. A bar graph compares separate categories, such as products or countries, and its bars are spaced apart. Use the bar graph maker for categories.

How many bins should a histogram have?

There is no single right answer. A common starting point is Sturges’ rule, k = ⌈log₂ n⌉ + 1, which gives about 7 bins for 50 values and 11 for 1,000. Too few bins hide the shape; too many make it look noisy. Try a few settings and choose the one that shows the pattern most clearly without inventing bumps.

Which bin does a value on the edge go into?

This histogram maker puts a value that falls exactly on a bin edge into the higher bin, so each bin includes its lower edge and excludes its upper edge. The only exception is the last bin, which also includes its upper edge so the largest value is counted. Excel and most textbooks use a similar convention.

What is a relative frequency histogram?

It is the same chart, but each bar shows the percentage of all values in that bin instead of the count. The bars add up to 100%. Relative frequency is useful for comparing data sets of different sizes.

How do I describe the shape of a histogram?

Look at symmetry, peaks and outliers. A symmetric histogram looks about the same on both sides of its center. A right-skewed histogram has a long tail to the right (common for incomes and waiting times), and a left-skewed one has a tail to the left. One peak is unimodal; two clear peaks are bimodal, which often means two groups are mixed together.

What does the normal curve overlay show?

It draws a normal (bell) curve with the same mean and standard deviation as your data, scaled to match the bars. If the bars follow the curve closely, the data are roughly normal, which many statistical tests assume. Large gaps between the bars and the curve point to skew, outliers or more than one peak.