Frequency

The frequency of something is the amount of times that it appears in a situation. So the frequency of getting a black car in the previous example is 2 as we found two black cars that travelled down the road out of the total of ten. To count the frequency of certain events we use a ‘tally chart.’ This lets us know the amount of times that something has happened without having a long list. Putting the ‘raw data’ from our example of car colours into a tally chart we get the following results.

This tally chart uses lines to represent an event happening; each vertical line is counted as one car and the amount of lines for each colour tells us the frequency of this car coming down the road. One of the colours is marked as ‘other’ and has a tally for this which is the car that was green. This is a good thing to use as we will then also know the total number of cars that do not fit into the categories that we set.

When we get to five tally marks we tend to use a horizontal line that cuts through the first four verticals. This just makes it easier when we come to adding up the frequencies later.

When adding up the tally marks to get a total we simply add the number of fives and the singles to give us the total answer. For example:

By adding up the tally marks in this way we get the total frequency for an event, which we will look at using later in this lesson to draw conclusions from the data we have gathered.

Grouped frequency tables

Another way to use a frequency table is to group the findings rather than having individual parts. This is usually done for numerical data and allows us to cut down on the number of segments we have. Say we have some raw data that may be any number from 0 to 100, rather than having 100 different parts we may want to separate the data into groups of 10. When doing this, the main thing to avoid is ambiguity. This means when we can have two different ways of doing something: so we need to make sure that any piece of data can only go into one group.

If we have a score for how people perform on a test with marks being whole numbers out of 40, we may want to group this data. The example below shows what NOT to do.

Clearly, this way of grouping the data will result in trouble if someone scores exactly 10, 20 or 30 points. For each of these scores there are two possible places where it can be recorded.

A much better way is to group the data so that this ‘ambiguity’ is avoided. This has been done for this case in the table below.

Here we have made sure that each individual score can only be correctly put into one group.