CREATING A RELATIVE FREQUENCY TABLE

Relative frequency of a class is defined as the ratio of the class frequency to the total frequency. Percentage frequency of a class is defined as the ratio of class frequency to the total frequency, expressed as a percentage.  

For example, if the class frequency is 8 and the total frequency is 80, then the relative frequency is 

=  8/80 

=  1/10 or 0.10

Percentage frequency is 

=  0.10 x 100 %

=  10 %

Solved Examples

Example 1 :

A survey is conducted among school students. 50 students are randomly selected and they are asked, whether they prefer dogs, cats or other pets. Convert this table to a relative frequency table that uses decimals as well as one that uses percents.

Solution :

Step 1 :

Divide the numbers in the frequency table by the total to obtain relative frequencies as decimals. Record the results in the table below.

Step 2 :

Multiply the decimals in the above table by 100 to convert them into percentages. 

Example 2 :

100 students in a middle school are asked, how they travel to school. The table given below shows the different types of transport they use and their corresponding frequencies. Convert this table to a relative frequency table that uses decimals as well as one that uses percents.

Solution :

Step 1 :

Divide the numbers in the frequency table by the total to obtain relative frequencies as decimals. Record the results in the table below.

Step 2 :

Multiply the decimals in the above table by 100 to convert them into percentages. 

Reflect

1. How can we check that we have correctly converted frequencies to relative frequencies ?

The sum of the relative frequencies as decimals should be 1; the sum of the relative frequencies as percents should be 100%.

2. Explain why the number in the Total column of a relative frequency table is always 1 or 100%.

To obtain a relative frequency from a frequency, we have to divide the frequency by the total. The total divided by itself will always be equal to 1 or 100%.

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