Cumulative Frequency

The cumulative frequency is obtained by adding each frequency in the table, to the cumulative frequency in the row above it.

Example:

Insert a cumulative frequency column into the table below.

Recall, cumulative frequency is obtained by adding the frequency in each row, to the cumulative frequency in the row above it.

It should be noted that when a question asks that the cumulative frequency should be determined, it is also the norm that questions will ask candidates to determine from the cumulative frequency table, the proportion and/or percentage of the sample above or below a given value.

This information can be determined from a cumulative frequency table by inserting a Less than or Equal to column.

For example, in the solution to the example above, we can insert a Length Less than or Equal to column as shown below.

Note the values in the Less than or Equal to column are the values in the Length column, and this information is interpreted as for example:

-When the length is 9cm, the values less than or equal to 9cm, is the cumulative frequency, that is 17.

Note: If the cumulative frequency is to be calculated for a table with grouped data, then the less than or equal to value for each class will be the upper class boundary.

Example:

How many lengths in the table above are less than or equal to 10cm?

Identify 10 in the less than or equal to column, the answer is the cumulative frequency amount in that row, that is, 27.

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