Variance for Grouped Data Calculator

Turn class intervals into clear variance insights. Compare population and sample results with midpoint accuracy. Download polished outputs and visualize distributions for better decisions.

Enter grouped data

Use one value per line, or separate values with commas.

Example: 0, 10, 20, 30, 40
Each upper bound must exceed its lower bound.
Counts must align with the interval lists.

Example data table

This sample uses test-score intervals and their frequencies.

Class interval Frequency Midpoint
0 - 10 4 5
10 - 20 7 15
20 - 30 10 25
30 - 40 6 35
40 - 50 3 45

Formula used

Midpoint = (Lower Bound + Upper Bound) / 2

Mean = Σ(f × Midpoint) / Σf

Population Variance = Σ[f × (Midpoint − Mean)²] / Σf

Sample Variance = Σ[f × (Midpoint − Mean)²] / (Σf − 1)

Standard Deviation = √Variance

Grouped calculations use class midpoints as representatives. This makes the answer an estimate, but it is widely accepted for grouped statistical summaries.

How to use this calculator

  1. Enter each class lower bound in order.
  2. Enter matching upper bounds for every class interval.
  3. Add frequencies in the same interval order.
  4. Choose population or sample variance mode.
  5. Set decimal precision for displayed results.
  6. Press calculate to view the summary and table.
  7. Review the graph, then export CSV or PDF.

Frequently asked questions

1. What does this grouped data calculator measure?

It estimates mean, variance, standard deviation, cumulative frequency, and related summary values using class intervals and their frequencies.

2. Why are class midpoints used?

Grouped datasets hide exact raw values. Midpoints act as representative values for each interval, making summary calculations practical and consistent.

3. When should I choose sample variance?

Choose sample variance when your grouped table represents a sample from a larger population. Use population variance when the table contains the full population.

4. Can I paste comma-separated values?

Yes. You can enter values on separate lines or separate them with commas, spaces, or semicolons in each input area.

5. What happens if interval counts do not match?

The calculator stops and shows an error. Lower bounds, upper bounds, and frequencies must all contain the same number of entries.

6. Does the tool support open-ended classes?

No. This version requires clear lower and upper bounds because midpoint calculation depends on complete interval limits.

7. Why is the grouped variance an estimate?

Exact observations inside each class are unknown. The method assumes values cluster around each class midpoint, so the result is approximate.

8. What does the coefficient of variation show?

It shows spread relative to the mean, expressed as a percentage. This helps compare variability across datasets with different scales.

Related Calculators

frequency table generatordecile calculatorrelative dispersiongrouped data calculatorgrouped moderelative errorsummary statistics toolungrouped data calculatorpopulation std deviationunique values count

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.