We want to determine whether Maryann is correct in her reasoning.
Maryann's Statement
If 100 people are surveyed, the frequency table will provide the same information as a total relative frequency table.
If we want to make a total relative frequency table based on a frequency table, we need to divide the value of each cell by the number of respondents and multiply it by 100 %. Let x represent the value of cell in the frequency table and n represent the total number of respondents.
x/n* 100 %
Now let's substitute 100 for n to check whether Maryann is correct.
We can see that when the total number of surveyed people is equal to 100, the value in a total relative frequency table is the same as the value in the frequency table. The only difference is that in the total relative frequency table, all values are in percentages because they are ratios. Therefore, we can agree with Maryann.
Extra
Real-Life Example
Let's take a look at a real-life example. Suppose that we asked 100 people whether they prefer tea or coffee and we gathered our results in the following two-way frequency table.
Tea or Coffee?
Gender
Tea
Coffee
Total
Male
22
26
48
Female
27
25
52
Total
49
51
100
Now let's create the total relative frequency table by using the method described before.
Tea or Coffee?
Gender
Tea
Coffee
Total
Male
22/100* 100 %=22 %
26/100* 100 %=26 %
48/100* 100 %=48 %
Female
27/100* 100 %=27 %
25/100* 100 %=25 %
52/100* 100 %=52 %
Total
49/100* 100 %=49 %
51/100* 100 %=51 %
100/100* 100 %=100 %
We can see that the values in both tables are the same. This means that if the number of respondents is equal to 100, then the frequency table provides the same information as the total relative frequency table.
