Descriptive Statistics

Histogram Maker

Paste your data and turn it into a histogram and a full frequency table. Change the class width and watch the shape change.

Your data

30 values read. Range: 52 to 96.

Class width

Start at

Vertical axis

Class-width suggestions for n = 30

Sturges: about 6 classes, a width near 7.33

Freedman–Diaconis: width near 8.37

These are starting points. Try several widths.

Histogram

Class	Freq.	Relative	Cumulative	Cum. rel.
50 to under 60	2	0.067	2	0.067
60 to under 70	7	0.233	9	0.3
70 to under 80	12	0.4	21	0.7
80 to under 90	7	0.233	28	0.933
90 to under 100	2	0.067	30	1

Each class includes its lower boundary but not its upper one, so a value equal to a boundary goes in the class that starts there.

How to use this tool

Paste your numbers, separated by commas, spaces, or new lines.
Choose a class width. The suggestions show starting points from the Sturges and Freedman–Diaconis rules.
Switch the vertical axis between frequency, relative frequency, and density.
Read the frequency table under the chart, and try several widths to see how the shape changes.

Formula Reference

Sturges' rule

k ≈ 1 + log₂(n)

Freedman–Diaconis width

2 × IQR × n^(−1/3)

Relative frequency

f ÷ n

Frequency density

f ÷ (n × class width)

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Frequently Asked Questions

How do I choose the class width?+

There is no single correct choice. Rules such as Sturges' and Freedman–Diaconis give starting points, and the best width shows the shape clearly without amplifying noise. Try two or three widths and prefer the one that reveals structure without looking jagged.

What is the difference between a histogram and a bar chart?+

A histogram shows the distribution of a continuous numeric variable, so its bars touch and their order is fixed. A bar chart compares separate categories, so its bars have gaps and can be reordered.

What does density mean on the vertical axis?+

Density is the relative frequency divided by the class width, so that bar area, not height, represents proportion. With equal class widths, density has the same shape as frequency; it matters when classes have different widths.

Which class does a value on a boundary go into?+

This tool uses left-closed classes: a class includes its lower boundary but not its upper one, so a value of exactly 70 goes in the 70 to under 80 class.

Your data

30 values read. Range: 52 to 96.

Class width

Start at

Vertical axis

Class-width suggestions for n = 30

Sturges: about 6 classes, a width near 7.33

Freedman–Diaconis: width near 8.37

These are starting points. Try several widths.

Class

Freq.

Relative

Cumulative

Cum. rel.

50 to under 60

0.067

60 to under 70

0.233

0.3

70 to under 80

0.4

0.7

80 to under 90

0.233

0.933

90 to under 100

0.067

How to use this tool

Paste your numbers, separated by commas, spaces, or new lines.

Choose a class width. The suggestions show starting points from the Sturges and Freedman–Diaconis rules.

Switch the vertical axis between frequency, relative frequency, and density.

Read the frequency table under the chart, and try several widths to see how the shape changes.