Frequency distributions

A frequency distribution shows how many times (the frequency) the values fall into each class. Some terms:

• Class limits: the two ends of a class. In the class 20-30, 20 is the lower limit and 30 the upper limit.
• Class interval (width) = upper limit – lower limit. For 20-30 it is 10.
• Class mark (mid-point) = (upper limit + lower limit) ÷ 2. For 20-30 it is 25. It represents the whole class in calculations.

Before making the table, decide:

• whether the classes should be of equal or unequal width;
• how many classes to have: usually between 6 and 15. The number of classes is roughly the range (largest value – smallest value) divided by the class interval.

Classes can be written in two ways:

• Exclusive classes (0-10, 10-20, 20-30): the upper limit is excluded from the class. A value of exactly 10 goes into the next class, 10-20.
• Inclusive classes (0-9, 10-19, 20-29): both limits are included. This leaves gaps between classes (between 9 and 10). To close them, take half the gap and adjust each limit: 10-19 and 20-29 become 9.5-19.5 and 19.5-29.5.

Then tally: go through the raw data one value at a time, putting a stroke (|) against the class it belongs to. Strokes are grouped in fives: four upright and the fifth across them, so they are easy to count. The number of tallies in each class is its frequency, and all the frequencies add up to the total number of observations.