Analyze grouped observations with fast statistical summaries. Input intervals, frequencies, limits, and assumptions with ease. Get precise mean, deviation, variance, plots, and downloads instantly.
| Class Interval | Lower Limit | Upper Limit | Midpoint | Frequency | f × x | x − Mean | f × (x − Mean)² |
|---|
Enter grouped class intervals and corresponding frequencies. Use decimal values if needed.
| Class Interval | Frequency | Midpoint |
|---|---|---|
| 0 - 10 | 4 | 5 |
| 10 - 20 | 7 | 15 |
| 20 - 30 | 10 | 25 |
| 30 - 40 | 6 | 35 |
| 40 - 50 | 3 | 45 |
Midpoint: x = (Lower Limit + Upper Limit) / 2
Total Frequency: N = Σf
Grouped Mean: Mean = Σ(f × x) / Σf
Population Variance: σ² = Σ[f × (x − Mean)²] / N
Population Standard Deviation: σ = √σ²
Sample Variance: s² = Σ[f × (x − Mean)²] / (N − 1)
Sample Standard Deviation: s = √s²
Coefficient of Variation: CV = (Standard Deviation / Mean) × 100
This calculator uses class midpoints because grouped data stores values in intervals instead of exact raw observations.
Grouped data appears when values are summarized into class intervals. This format helps when datasets are large, continuous, or reported in frequency tables. Instead of using every raw observation, grouped statistics estimate the center and spread by using class midpoints and frequencies.
The mean of grouped data represents the weighted average of all class midpoints. Each midpoint is multiplied by its class frequency, and the total is divided by the total number of observations. This gives a practical estimate of the dataset’s average value.
Standard deviation measures how far the grouped values spread around the mean. A smaller deviation suggests the class frequencies cluster near the center. A larger deviation suggests wider variability across intervals. This is useful in business analysis, education reports, quality control, survey summaries, and performance tracking.
This calculator also shows population variance, sample variance, and coefficient of variation. These measures help compare dispersion levels, evaluate consistency, and understand how stable a grouped distribution appears. The computation table reveals every midpoint, weighted product, and squared deviation term, which improves transparency and checking.
The included graph makes patterns easier to inspect. Frequency bars display where observations concentrate. Export tools help save results for reports, assignments, and audits. Because grouped data uses intervals, the output is an estimate based on midpoint assumptions, but it remains a standard and reliable statistical method for summarized frequency distributions.
The grouped mean estimates the average value of a frequency distribution by using class midpoints and frequencies instead of every raw observation.
Grouped tables do not show exact individual values. Midpoints provide a practical representative value for each class interval during estimation.
Population deviation divides by total frequency. Sample deviation divides by total frequency minus one when the grouped table represents a sample.
Yes. The calculator uses each interval’s own midpoint, so unequal widths can still be processed correctly for grouped mean and deviation.
Yes. Zero-frequency classes do not change the totals, but they can remain in the table if they help preserve interval structure.
Yes. Negative lower or upper limits work properly as long as each upper limit is greater than its lower limit.
The result is an estimate because grouped data replaces raw values with class midpoints. It is standard for summarized frequency distributions.
No. The graph is only a visual summary. All results come from the numerical formulas applied to your interval and frequency entries.
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.