Analyze grouped frequency tables with fast variability summaries. See range, variance, quartiles, and standard deviation. Export results instantly for reports, revision, and classroom practice.
| Class Interval | Frequency |
|---|---|
| 10 - 20 | 4 |
| 20 - 30 | 7 |
| 30 - 40 | 10 |
| 40 - 50 | 6 |
| 50 - 60 | 3 |
Use the sample above to test grouped range, variance, standard deviation, quartiles, and relative dispersion outputs.
Grouped data uses class midpoints and frequencies. Each midpoint is x = (lower + upper) / 2.
Grouped mean: Mean = Σ(f×x) / Σf
Range: Highest class upper limit - Lowest class lower limit
Mean deviation about mean: Σ[f|x-Mean|] / Σf
Population variance: Σ[f(x-Mean)2] / Σf
Sample variance: Σ[f(x-Mean)2] / (Σf - 1)
Standard deviation: √Variance
Quartiles for grouped data: Q = L + ((Position - Cumulative before class) / f) × h
Interquartile range: Q3 - Q1
Quartile deviation: (Q3 - Q1) / 2
Coefficient of range: (H - L) / (H + L)
Coefficient of quartile deviation: (Q3 - Q1) / (Q3 + Q1)
Coefficient of variation: (Standard deviation / Mean) × 100
Measures of variability explain how widely values spread around the center. Grouped data appears in reports, surveys, exams, factories, and field studies. Raw values are often unavailable. Frequency classes make storage easier, but they also require estimated calculations. This calculator handles that task clearly. It turns class intervals into usable measures of dispersion.
The tool computes range, coefficient of range, mean deviation, variance, standard deviation, quartiles, interquartile range, quartile deviation, and coefficient of variation. These measures support different decisions. Range shows total spread. Standard deviation shows average dispersion around the grouped mean. Quartile measures focus on the middle half of the distribution. Coefficient of variation helps compare relative spread between different datasets.
Grouped formulas use class midpoints instead of individual values. Each midpoint represents the observations inside that class. Frequencies weight each midpoint. The grouped mean comes first. Then the calculator evaluates absolute deviation and squared deviation. Quartiles are estimated by interpolation inside the quartile class. This method is standard in statistics courses and practical data summaries.
Use range for a fast overview. Use variance and standard deviation for detailed analytical work. Use interquartile range when extreme values may distort results. Use coefficient of variation when comparing datasets measured in different scales or with different means. For classroom problems, grouped calculations give reliable estimates when classes are reasonably formed.
This page keeps the process simple. You enter intervals and frequencies. The result appears quickly. The computation table shows each step. That supports learning, checking, and reporting. You can also export the output for revision notes, assignments, and documentation tasks.
Grouped data is data arranged into class intervals with matching frequencies. It is common when datasets are large or summarized in a frequency distribution table.
Midpoints approximate the values inside each class interval. They allow grouped mean, variance, and standard deviation to be estimated when original raw observations are unavailable.
Choose population when the table covers the entire dataset. Choose sample when the grouped table represents only a sample drawn from a larger population.
It shows relative spread as a percentage of the mean. This is useful for comparing variability across datasets with different units or different average sizes.
They are estimated by grouped quartile interpolation. The calculator locates the quartile class using cumulative frequency, then applies the standard interpolation formula within that class.
Auto sort only reorders the class intervals during calculation. It helps when rows are entered out of order and improves grouped frequency processing.
Yes. The calculator accepts decimal inputs for class limits and frequencies. This helps with continuous grouped data and weighted grouped summaries.
Range uses the full spread from minimum class boundary to maximum class boundary. IQR uses only the middle fifty percent of the grouped distribution.
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.