Frequency tables

A frequency table records how often each value appears. It is the step between a raw list of numbers and any chart or summary made from them, and doing it carelessly poisons everything downstream.

Building one

Here are twenty test scores out of ten.

The frequencies add to twenty, which is the number of scores you started with. That check takes two seconds and catches almost every counting error.

Grouped data

When values spread over a wide range, listing every one produces a table as long as the data. Group them into equal intervals instead.

Intervals must be equal in width and must not overlap. An interval of 130 to 140 followed by 140 to 150 leaves nowhere to put a height of exactly 140. Between five and eight intervals is usually right: fewer hides the shape, more scatters it back into noise.

Reading the table

The score table says the most common score was 7, that 30 percent of the class scored 7, and that only one student scored below 6. Each of those is a sentence about the class, and the point of the table is to make such sentences available at a glance.

Common mistakes

Not checking the total

Frequencies must add to the number of data values. If they do not, something was counted twice or missed.

Overlapping intervals

Every value must belong to exactly one interval.

Leaving out an empty value

If no one scored 4 and the table runs from 3 to 10, the row for 4 should appear with a frequency of zero. Deleting it makes the distribution look different from what it is.

Check yourself