Measure relative dispersion from grouped frequency distributions. Enter intervals, frequencies, and boundaries for precise results. Download tables, review formulas, and compare variability with confidence.
| Class Interval | Frequency |
|---|---|
| 10 - 20 | 4 |
| 20 - 30 | 7 |
| 30 - 40 | 10 |
| 40 - 50 | 6 |
| 50 - 60 | 3 |
Class Midpoint: x = (Lower Limit + Upper Limit) / 2
Mean for Grouped Data: Mean = Σ(f × x) / Σf
Population Variance: Σ[f(x - Mean)²] / N
Sample Variance: Σ[f(x - Mean)²] / (N - 1)
Standard Deviation: √Variance
Coefficient of Variation: (Standard Deviation / |Mean|) × 100
This method uses class midpoints to estimate dispersion from a grouped frequency distribution.
The coefficient of variation for grouped data measures relative spread. It compares the standard deviation with the mean. This makes variation easier to compare across different grouped distributions. It is widely used in statistics, quality review, market studies, and classroom analysis.
Grouped data often appears in intervals. Raw values are not always available. A grouped frequency table solves that problem. The midpoint of each class stands in for the values inside that class. This creates an efficient estimate of the mean and standard deviation. The coefficient of variation then converts that spread into a percentage.
This calculator accepts lower limits, upper limits, and frequencies. It finds class midpoints first. Then it calculates f × x, the grouped mean, variance, standard deviation, and the coefficient of variation. It also shows cumulative frequency and the weighted squared deviations. This working table helps verify every step.
A lower coefficient of variation means the grouped distribution is more stable around the mean. A higher value means the data is more dispersed. This helps when you compare exam results, production batches, survey ranges, or grouped income bands. Because the answer is relative, it is more useful than standard deviation alone in many comparison tasks.
Use class limits in matching order. Make sure each frequency belongs to the correct interval. Avoid zero total frequency. Choose the sample option only when the grouped data represents a sample. Choose the population option when the grouped table covers the entire population. The result is most meaningful when the mean is not zero.
The CSV export is useful for reporting and audit trails. The PDF option helps with printing and sharing. The example table helps users test the layout before entering live grouped data. This makes the tool practical for students, analysts, and anyone working with interval frequency distributions.
It shows relative dispersion. The value compares standard deviation with the mean. A smaller percentage suggests more consistency. A larger percentage suggests more variability in the grouped distribution.
Grouped data hides individual values inside intervals. Midpoints provide a standard estimate for each class. That estimate supports grouped mean, variance, and standard deviation calculations.
Use population when the grouped table represents the full data set. Use sample when the grouped table is only part of a larger population and you want a sample estimate.
Yes. CV is especially useful for comparisons because it is a relative measure. It helps compare distributions that have different means or different measurement scales.
The value becomes undefined when the mean is zero. Since CV divides standard deviation by the mean, a zero mean prevents a valid percentage result.
No. Blank lines are ignored. The important rule is that lower limits, upper limits, and frequencies must still contain the same number of valid numeric entries.
Yes. The calculator accepts line breaks, commas, or semicolons. You can paste values from a sheet quickly, as long as each series stays aligned.
Not always. Lower variation means greater consistency, but the desired level depends on context. Some studies value stability, while others expect natural variation across grouped observations.
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.