A frequency distribution table is created by listing each value or class interval, tallying every observation, and recording how often it occurs as the frequency. Finally, check that the frequencies add to the total number of observations.
Method
- Identify the data type. Use individual values for discrete data with few possible outcomes. For continuous data, or data with many values, use class intervals.
- Choose the categories. They must cover the whole data set without overlapping or leaving gaps. For example, write intervals as , , and so on.
- Tally each observation. Place each data value into exactly one category. Tally marks are usually grouped in fives to reduce counting errors.
- Count the tallies. Record each total in the frequency column.
- Check the total. The sum of all frequencies must equal the number of data values: .
For example, consider the data :
| Value | Tally | Frequency, |
|---|---|---|
| I | ||
| II | ||
| III |
For grouped continuous data, the same method applies, but the first column contains intervals rather than individual values. The table should also include a clear heading and units where relevant.
When selecting intervals, use a convenient common width and make the boundaries unambiguous. A value on a boundary enters the interval containing the equality sign; for example, belongs to , not the preceding interval.
A common misconception is that unequal class widths can be used in an ordinary IB frequency histogram without adjustment. In Mathematics: Analysis and Approaches SL 4.2, examination questions use frequency histograms with equal class intervals; frequency-density histograms are not required.
Exam Technique
This skill can be assessed on AA SL Paper 1 or Paper 2. Examiners expect non-overlapping categories, accurate tallies, correct frequencies, and a total-frequency check. If class intervals are given, preserve their boundary notation exactly so no observation can belong to two classes.