HOW TO CALCULATE MARGINAL RELATIVE FREQUENCY

Marginal relative frequency is one of the types of relative frequency that we can obtain from a two-way frequency table.

A marginal relative frequency can be calculated by dividing a row total or a column total by the Grand total. 

Let us look at some examples to understand how to calculate marginal relative frequency.  

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. The table given below shows the results of the survey. 

Use the above table to find each marginal relative frequency.

(i) Find the marginal relative frequency of the students who prefer cats as pets.

(ii) Find the marginal relative frequency of boys.

(iii) Find the marginal relative frequency of girls.

(iv) Find the marginal relative frequency of the students who prefer dogs as pets.

Solution (i) : 

Divide the total number of students who prefer cats as pets by the grand total. Express your answer as a decimal and as a percent.

15/50  =  0.30  =  30%

Solution (ii) : 

Divide the total number of boys by the grand total. Express your answer as a decimal and as a percent.

22/50  =  0.44  =  44%

Solution (iii) : 

Divide the total number of girls by the grand total. Express your answer as a decimal and as a percent.

28/50  =  0.56  =  56%

Solution (iv) : 

Divide the total number of students who prefer dogs as pets by the grand total. Express your answer as a decimal and as a percent.

22/50  =  0.44  =  44%

Example 2 :

A survey is made among 100 students in a middle school. They are asked, how they travel to school. The table given below shows the results of the survey. 

Use the above table to find each conditional relative frequency.

(i) Find the marginal relative frequency of the students who prefer car.

(ii) Find the marginal relative frequency of boys.

(iii) Find the marginal relative frequency of girls.

(iv) Find the marginal relative frequency of the students who prefer bus.

Solution (i) : 

Divide the total number of students who prefer car by the grand total. Express your answer as a decimal and as a percent.

47/200  ≈  0.24  =  24%

Solution (ii) : 

Divide the total number of boys by the grand total. Express your answer as a decimal and as a percent.

100/200  =  0.50  =  50%

Solution (iii) : 

Divide the total number of girls by the grand total. Express your answer as a decimal and as a percent.

100/200  =  0.50  =  50%

Solution (iv) : 

Divide the total number of students who prefer bus by the grand total. Express your answer as a decimal and as a percent.

72/200  =  0.36  =  36%

Example 3 :

You conduct a technology survey to publish on your school’s website. You survey students in the school cafeteria about the technological devices they own. The results are shown in the two-way table. Find and interpret the marginal frequencies.

Solution :

Number of students used cellphones and tablet computer 

= 34

Number of students used cellphones and not tablet computer 

= 124

Number of students not using cellphones and tablet computer 

= 18

Number of students not using cellphones and tablet computer 

= 67

total number of students = 34 + 124 + 18 + 67

= 243

Percentage of students who use cellphones and tablet computer

= (34/243) x 100%

= 0.1399 x 100%

= 13.99%

Percentage of students used cellphones and not tablet computer 

= (124/243) x 100%

= 0.51 x 100%

= 51%

Percentage of students not using cellphones and tablet computer 

= (18/243) x 100%

= 0.07 x 100%

= 70%

Percentage of students not using cellphones and tablet computer 

= (67/243) x 100%

= 0.27 x 100%

= 27%

Example 4 :

You conduct a survey that asks 286 students in your freshman class whether they play a sport or a musical instrument. One hundred eighteen of the students play a sport, and 64 of those students play an instrument. Ninety-three of the students do not play a sport or an instrument. Organize the results in a two-way table. Include the marginal frequencies.

total number of students surveyed = 286

number of students who play sport = 118

Number of students who play instruments = 64

Number of students who do not play a sport or an instrument = 93

Applying the known values in the table.

118 - 64 ==> 54

Number of students dont play sport and instruments

= 286 - 118

= 168

Number of students who dont play sport = 168 - 93

= 75

Total number of students who play sport and instrument

= 64 + 75

= 139

Total number of students who dont play sport and instrument

= 54 + 93

= 147

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