Grouping and frequency distribution

To make sense of a long list of numbers, we group them into classes. The steps:

• Decide the classes: look at the range (lowest to highest value), and choose the number of classes and the class interval. For values from 3 to 98, you might use ten classes of 10: 0-10, 10-20, and so on.
• Classify each value using tally marks: four strokes and a fifth across them for every five (the 'four and cross' method).
• Count the simple frequency (f) of each class. The total of all frequencies, Σf, equals N, the number of values.
• Work out the cumulative frequency: add the frequencies one after another (for example, 3, 3 + 6 = 9, 9 + 8 = 17, ...). The last one equals N.

Two ways to write classes:

• Exclusive: 20-30, 30-40. The upper limit is excluded: a value of 30 goes in 30-40.
• Inclusive: 20-29, 30-39. Both limits are included.