Frequency distribution table calculator
Choose the number of classes or the class width and the table fills in, with a histogram and ogive drawn from the same numbers.
| Class | Midpoint | Frequency | Relative | Cumulative | Cum. relative |
|---|---|---|---|---|---|
| 58 – 65 | 61.5 | 4 | 0.200 | 4 | 0.200 |
| 66 – 73 | 69.5 | 6 | 0.300 | 10 | 0.500 |
| 74 – 81 | 77.5 | 5 | 0.250 | 15 | 0.750 |
| 82 – 89 | 85.5 | 3 | 0.150 | 18 | 0.900 |
| 90 – 97 | 93.5 | 2 | 0.100 | 20 | 1.000 |
| Total | 20 | 1.000 |
Histogram
Ogive (cumulative frequency)
Estimated mean from the table: Σ(midpoint × f) / n = 74.7 (the exact mean of the raw data is 74.75).
Building a grouped frequency table by hand
- Range: largest − smallest value.
- Choose the number of classes, usually 5 to 20. Fewer for small data sets.
- Class width: range ÷ number of classes, then round up (for whole-number data, to the next whole number) so the last value still fits.
- Class limits: start at the minimum (or a convenient number below it) and add the width repeatedly.
- Tally the values in each class, then add the relative (f / n) and cumulative columns.
For whole-number data the table uses inclusive limits, such as 58 – 65 and 66 – 73, like most textbooks. For decimal data each class includes its lower limit and excludes its upper limit.
What the ogive is for
The ogive plots cumulative frequency against each class's upper boundary. Read across from n/2 to the curve and down to the axis to estimate the median; do the same at n/4 and 3n/4 for the quartiles. The exact values from the raw data are on the quartile calculator.
Still not clicking? Ask the tutor
An AI tutor that sees the numbers you entered above and explains them. It can make mistakes, so check anything important against the worked steps.
Questions students ask
How do you make a frequency distribution table?
Find the range, choose how many classes (5 to 20 is typical), set the class width to range ÷ classes rounded up, list the class limits starting at or below the minimum, then count how many values fall in each class.
What is relative frequency?
The class frequency divided by the total count. It shows the proportion of the data in each class, and all relative frequencies add up to 1 (or 100%).
What is cumulative frequency?
The running total of frequencies up to and including each class. Plotted against upper class boundaries it makes an ogive, from which you can read medians and percentiles.
How do you find the mean of grouped data?
Multiply each class midpoint by its frequency, add these products, and divide by the total frequency. It is an estimate because it assumes values sit at the midpoints.