Frequency Distribution
A frequency distribution counts how often each value or class occurs. It is the bridge between a list of numbers and a picture of the data, and it is usually the first table a statistics course asks for.
A frequency table for individual values
| Value | Frequency | Relative | Cumulative |
|---|---|---|---|
| −10 | 1 | 0.1667 | 1 |
| −5 | 2 | 0.3333 | 3 |
| 3.5 | 1 | 0.1667 | 4 |
| 7 | 2 | 0.3333 | 6 |
The relative frequency is the proportion of the dataset, so the column adds up to 1. The cumulative column keeps a running total, which is what you read to find a median or a percentile.
Grouped class intervals
When values are spread across a wide range, they are grouped into classes such as 10-20, 20-30 and 30-40. Enter them in the grouped mode as one class per line, like 10-20 5, and the calculator works from the class midpoints and interpolates the median and quartiles inside their class, stating the method on the result.
Choosing a class width
- Aim for between five and ten classes for a class-sized dataset.
- Keep the width the same for every class, so the histogram bars are comparable.
- Make the classes meet without gaps, so no value falls between two of them.
From a table to a histogram
The calculator draws a simple histogram beside the table: one bar per class, with the length showing the frequency. Read it for the shape of the data. A single tall bar in the middle suggests a symmetrical dataset; a long tail on the right suggests a few unusually large values, which is the moment to prefer the median to the mean.