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Mathematics

Statistics from grouped frequencies

Estimate the mean, standard deviation and median from class lower bounds, upper bounds and frequencies.

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01

Your inputs

The starting values are an example.

One class per line. Non-overlapping intervals and non-negative integer frequencies; up to 100 classes.

Decimals: 12.5 · Thousands: 1,234.56. Follow the field instructions for lists.

02

Your result

Enter your values and select Calculate.

Your calculation will appear here.

Your result will include the relevant values and units.

Understand the calculation

Formula and example

How it is calculated

For class midpoint mᵢ and frequency fᵢ: mean=Σ(fᵢmᵢ)/Σfᵢ. The variance uses the same class midpoints.

Worked example

Classes 0–10, 10–20 and 20–30 with frequencies 2, 4 and 2 have an estimated mean of 15. The interpolated median is also 15.

Things to check

  • Individual values within each class are unknown. Midpoints give approximations, not exact raw-data statistics.
  • The median assumes a uniform distribution within its class. The displayed standard deviation uses divisor N.

Frequently asked questions

Can the classes have different widths?

Yes. Each class uses its own midpoint and width. A histogram would additionally require frequency density rather than frequency alone.