Grouped Data Input
Enter class limits and frequencies below. Blank rows are ignored.
Example Data Table
| Lower Limit | Upper Limit | Frequency |
|---|---|---|
| 0 | 10 | 4 |
| 10 | 20 | 7 |
| 20 | 30 | 10 |
| 30 | 40 | 6 |
| 40 | 50 | 3 |
Formula Used
Class midpoint: x = (Lower Limit + Upper Limit) / 2
Grouped mean: Mean = Σ(f × x) / Σf
Grouped median: Median = L + [(N / 2 - c.f.) / f] × h
Mean deviation about mean: MD about Mean = Σ[f|x - Mean|] / Σf
Mean deviation about median: MD about Median = Σ[f|x - Median|] / Σf
Coefficient: Coefficient = Mean Deviation / Central Value
Here, L is the lower limit of the median class, c.f. is the cumulative frequency before the median class, f is the median class frequency, h is class width, and N is total frequency.
How to Use This Calculator
- Enter each class interval with a lower limit and upper limit.
- Enter the matching frequency for every class.
- Choose whether the main reported result should use the mean or median.
- Select the number of decimal places you want to display.
- Click Calculate to show the result above the form.
- Review the summary table and the full working table.
- Use the CSV button to save spreadsheet-ready output.
- Use the PDF button to save a clean report.
- For inclusive classes, enter real class boundaries when needed.
About This Mean Deviation Grouped Data Calculator
Mean deviation for grouped data shows how far observations spread from a central value. It is useful in statistics classes, survey summaries, production checks, and business reporting. This calculator helps you work with class intervals and frequencies in one place. You can enter grouped observations, review the computed table, and export the results for records.
Grouped data does not list every original value. Instead, it combines values into ranges. Because of that, the calculator uses class midpoints to represent each interval. It multiplies every midpoint by its frequency, finds the total frequency, and then calculates the arithmetic mean. The same working table also supports the grouped median estimate and cumulative frequencies.
Mean deviation about the mean is based on average absolute distance. First, the calculator finds the mean. Next, it computes the absolute difference between each midpoint and the mean. Then it multiplies that distance by the class frequency. After summing all weighted deviations, it divides by the total frequency. This produces a clear dispersion measure that is easy to interpret.
Mean deviation about the median follows a similar process. The calculator estimates the median from the median class by using cumulative frequency, class width, class frequency, and the lower class limit. It then measures each midpoint’s absolute distance from that median and averages the weighted distances. This second measure is helpful when you want a center that is less affected by skew.
This grouped data tool is built for fast classroom and practical use. It supports dynamic rows, automatic working steps, downloadable tables, and printable reports. You can compare mean deviation about the mean and median without rewriting your data. The example section also shows how grouped intervals should be entered. Use the calculator when you need a simple, structured, and reliable summary of dispersion from frequency distributions.
In exams, always check that upper limits exceed lower limits and frequencies are nonnegative. Equal class widths are common, but the calculator can still process unequal widths for midpoint-based work. Clean interval entry improves accuracy and saves time during interpretation. Once calculated, review totals, cumulative frequencies, and coefficients before exporting your final table or printed summary for future reference and revision.
FAQs
1. What data should I enter for grouped mean deviation?
Use class intervals and their frequencies. Enter each lower limit, upper limit, and frequency in separate rows. Then submit the form to generate the working table and dispersion measures.
2. Does the calculator use class midpoints?
For grouped data, the calculator uses class midpoints. Each interval midpoint represents all values inside that class for mean and mean deviation calculations.
3. Can it calculate mean deviation about the median too?
Yes. The tool estimates the grouped median from cumulative frequency, median class frequency, class width, and lower class limit, then computes mean deviation about that median.
4. Are zero frequencies allowed?
Yes. Zero frequencies are allowed, but the total frequency must be greater than zero. Rows left fully blank are ignored during calculation.
5. Should I enter class boundaries or class limits?
For inclusive integer classes, enter true class boundaries when you need maximum accuracy. That improves grouped median estimation and midpoint representation.
6. What does the coefficient show?
The coefficient expresses mean deviation relative to the chosen central value. It helps compare dispersion across grouped datasets with different scales.
7. What do the export buttons save?
The CSV file saves the summary and working table. The PDF option creates a clean report of the same calculated results for printing or sharing.
8. What should I check before calculating?
Check that every upper limit is greater than the lower limit, frequencies are valid, and class intervals are entered in the correct order.