Grouped Data Mean Variance and Standard Deviation Calculator

Solve grouped data measures using interval midpoints. Compare totals, spread, and weighted averages with confidence. Visualize frequency behavior, export results, and verify calculations easily.

Grouped Data Calculator Input

Enter lower limits, upper limits, and frequencies. The page calculates class midpoints automatically for every valid row.

Lower Limit Upper Limit Frequency Action

Example Data Table

Use this sample grouped distribution to test the calculator quickly.

Class Interval Frequency
0 - 104
10 - 207
20 - 3011
30 - 406
40 - 502

Formula Used

1) Midpoint of each class

Midpoint = (Lower Limit + Upper Limit) / 2

2) Mean for grouped data

Mean = Σ(f × midpoint) / Σf

3) Population variance

Variance = Σ[f × (midpoint − mean)2] / Σf

4) Sample variance

Variance = Σ[f × (midpoint − mean)2] / (Σf − 1)

5) Standard deviation

Standard Deviation = √Variance

These formulas use class midpoints as grouped representatives. That gives strong estimates when intervals are reasonable and frequencies are recorded correctly.

How to Use This Calculator

  1. Enter each class lower limit in the first column.
  2. Enter each class upper limit in the second column.
  3. Enter the corresponding frequency for every class.
  4. Choose population variance or sample variance.
  5. Set the number of decimal places you want.
  6. Click Calculate Statistics to generate results.
  7. Review the table, summary cards, and Plotly chart.
  8. Download the result as CSV or PDF when needed.

Frequently Asked Questions

1) What does this grouped data calculator measure?

It calculates the grouped mean, variance, standard deviation, total frequency, cumulative frequency, and coefficient of variation using class intervals and their frequencies.

2) Why does the calculator use class midpoints?

Grouped data does not list every original value. Midpoints act as class representatives, making it possible to estimate the center and spread efficiently.

3) When should I choose population variance?

Use population variance when your grouped table represents the entire dataset you want to analyze, not just a sample from a larger population.

4) When should I choose sample variance?

Choose sample variance when your grouped table summarizes a sample and you want an estimate of the wider population variance.

5) Can I enter decimal class limits?

Yes. The calculator accepts decimal lower limits, upper limits, and frequencies, making it useful for continuous grouped data and weighted grouped tables.

6) What happens if frequencies are zero or negative?

Negative frequencies are rejected. Zero frequencies are mathematically possible, but total frequency must still be greater than zero for valid results.

7) What does the coefficient of variation show?

It compares the standard deviation with the mean as a percentage. This helps compare relative spread across grouped datasets with different scales.

8) What does the chart help me understand?

The Plotly chart shows class frequencies alongside cumulative frequency. It helps reveal where data clusters and how totals build across intervals.

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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.