Class Width Calculator

Class width, class limits, midpoints and frequencies for a frequency table.

Class width = (maximum − minimum) ÷ number of classes, rounded up. For data from 12 to 72 in 5 classes, (72 − 12) ÷ 5 = 12, which is bumped to 13 so the maximum fits in the last class.

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How to use it

Paste your data, or enter the minimum and maximum.
Enter the number of classes (Sturges' rule is suggested).
Read the class width and the frequency table.

What you enter

Data, or minimum and maximum
Number of classes

What you get

Class width
Class limits and midpoints
Frequencies
Suggested number of classes

Formula

Class width = ⌈(max − min) ÷ k⌉ | Sturges: k = 1 + log₂(n) | Midpoint = (lower + upper) ÷ 2

Worked example

Input: 15 values from 12 to 72, 5 classes

Result: Class width 13

Classes 12–25, 25–38, 38–51, 51–64, 64–77 cover all values.

Questions

How do you find the class width?

Subtract the smallest value from the largest, divide by the number of classes you want, and round up to a convenient number.

Why round the class width up?

Rounding down would leave the largest values outside the last class. Many textbooks also add 1 when the division is exact for the same reason.

How many classes should I use?

Usually 5 to 20. Sturges' rule gives k = 1 + log₂(n), so 100 values suggest about 8 classes.

How do you find a class midpoint?

Add the lower and upper class limits and divide by 2.

Limitations

Rounding conventions differ between textbooks; check which one your course uses.

References

Sturges HA (1926) Journal of the American Statistical Association 21(153):65-66.

More Statistics

All free tools · By Dr. Zubair Khalid, DVM, MS, PhD.