Calculated Results
Results appear here after submission. The summary stays above the form, as requested.
Plotly Histogram
Grouped Data Table
| # | Lower | Upper | Width | Midpoint | Frequency | Cumulative Freq. | Relative Freq. | Density |
|---|
Calculator Input
Example Data Table
| Class Interval | Lower | Upper | Frequency |
|---|---|---|---|
| 0 - 10 | 0 | 10 | 4 |
| 10 - 20 | 10 | 20 | 7 |
| 20 - 30 | 20 | 30 | 12 |
| 30 - 40 | 30 | 40 | 15 |
| 40 - 50 | 40 | 50 | 9 |
| 50 - 60 | 50 | 60 | 5 |
Formula Used
1) Class width
h = Upper boundary - Lower boundary
2) Midpoint
Midpoint = (Lower + Upper) / 2
3) Frequency density
Density = Frequency / Class width
4) Mean for grouped data
Mean = Σ(f × midpoint) / Σf
5) Median for grouped data
Median = L + [((N / 2) - Cprev) / fm] × h
Here, L is the lower boundary of the median class,
Cprev is the cumulative frequency before it,
fm is that class frequency, and h is class width.
6) Mode for grouped data
Mode = L + [(f1 - f0) / (2f1 - f0 - f2)] × h
Here, f1 is the modal class frequency,
f0 is the previous class frequency,
and f2 is the next class frequency.
7) Variance and standard deviation
Variance = Σ[f × (midpoint - mean)2] / Σf
Standard deviation = √Variance
8) Quartiles
The calculator estimates Q1 at position N / 4 and Q3 at position 3N / 4 using grouped interpolation inside the matching classes.
How to Use This Calculator
Step 1
Enter each class interval on a new line using the format: lower, upper, frequency.
Step 2
Choose whether the histogram bars should represent raw frequency or frequency density.
Step 3
Set decimal places, chart labels, export name, and cumulative line preference.
Step 4
Press Calculate Histogram. The result section appears above the form automatically.
Step 5
Review the summary cards, grouped table, and Plotly graph to inspect the distribution.
Step 6
Download the results as CSV or PDF whenever you need a record or report.
FAQs
1) What is a histogram for grouped data?
It is a graph for frequency distributions built from class intervals instead of raw observations. Each bar represents an interval, and bar height reflects frequency or density.
2) When should I use frequency density?
Use frequency density when class widths are unequal. Density corrects bar heights so the histogram reflects area properly and compares intervals more fairly.
3) Does this calculator estimate the mean correctly?
It estimates the grouped mean using class midpoints. That is the standard method for grouped distributions when individual raw observations are unavailable.
4) How is the grouped median calculated?
The calculator finds the class containing the middle position, then applies linear interpolation inside that class using its lower boundary, width, and cumulative frequency.
5) Can I use decimal values in intervals or frequencies?
Yes. Decimal lower bounds, upper bounds, and frequencies are accepted. This helps with scientific, financial, and engineering grouped datasets.
6) What happens if my classes are out of order?
Enable automatic sorting. The calculator will reorder classes by lower boundary before computing results and drawing the histogram.
7) Can I export the analysis?
Yes. After calculation, you can download a CSV file for spreadsheet work and a PDF report for documentation or sharing.
8) Are open-ended classes supported?
No. Open-ended classes do not have a fixed width, and width is needed for midpoint, density, histogram bars, and several grouped statistics.