Analyze grouped frequency distributions with clear steps and instant outputs. Review interval midpoints, dispersion, and totals. Export results and summaries for accurate academic and practical use.
Provide class lower limit, upper limit, and frequency for each class interval.
| Class Lower Limit | Class Upper Limit | Frequency | Midpoint | f × x | Action |
|---|---|---|---|---|---|
| 5 | 25 | ||||
| 15 | 135 | ||||
| 25 | 300 | ||||
| 35 | 280 | ||||
| 45 | 270 |
The chart displays grouped frequencies against class midpoints.
| Class Interval | Frequency (f) | Midpoint (x) | f × x | x - Mean | (x - Mean)² | f(x - Mean)² |
|---|---|---|---|---|---|---|
| Total | - | - | - | - | - | - |
| Class Interval | Frequency | Midpoint |
|---|---|---|
| 0 - 10 | 5 | 5 |
| 10 - 20 | 9 | 15 |
| 20 - 30 | 12 | 25 |
| 30 - 40 | 8 | 35 |
| 40 - 50 | 6 | 45 |
This example is preloaded in the calculator. You can replace values with your own grouped dataset.
For grouped data, the midpoint of each class is used as the representative value.
Midpoint: x = (Lower Limit + Upper Limit) / 2
Grouped Mean: Mean = Σ(fx) / Σf
Population Variance: σ² = Σ[f(x - Mean)²] / Σf
Population Standard Deviation: σ = √σ²
Sample Variance: s² = Σ[f(x - Mean)²] / (Σf - 1)
Sample Standard Deviation: s = √s²
These formulas estimate central tendency and spread when data is summarized into intervals rather than listed individually.
Grouped data appears when values are organized into class intervals with frequencies. This calculator estimates the mean and standard deviation using class midpoints. It helps summarize distribution center and variability without expanding the entire raw dataset.
The tool suits classroom work, exam preparation, research notes, and routine statistical analysis. It calculates total frequency, grouped mean, population variance, sample variance, and both standard deviation forms. The detailed table also makes each intermediate step easier to inspect.
The included frequency graph uses class midpoints on the horizontal axis and frequencies on the vertical axis. This visual summary helps compare how observations are distributed across intervals. Higher bars show where values concentrate more strongly.
Because grouped statistics rely on midpoints, the answer is an estimate of the original raw-data mean and standard deviation. For many practical datasets, this estimate is useful and efficient, especially when only grouped frequency tables are available.
It finds the grouped mean, population variance, population standard deviation, sample variance, sample standard deviation, and supporting frequency totals from interval-based data.
Grouped tables do not list every original value. The midpoint represents each class interval, allowing estimation of the dataset center and spread.
No. Grouped calculations are estimates because each class interval is represented by one midpoint instead of all original observations.
Population deviation divides by total frequency. Sample deviation divides by total frequency minus one, which adjusts for sample-based estimation.
Yes. The calculator accepts decimal lower limits, upper limits, and frequencies, though frequencies are usually whole numbers in most grouped tables.
You can keep a zero frequency row, but it will not affect totals. Rows with empty values should be completed before calculation.
Yes. You can download a CSV file for table data and a PDF file for a report-style snapshot of the calculated results.
Grouped data is used when observations are summarized into intervals, such as exam scores, ages, income bands, heights, or measurement ranges.
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.