Module 8.2

Relative Frequency

How can you recognize possible associations and trends between two categories of categorical data?

P. 359

What’s the difference between “Frequency” and “Relative Frequency”?

Frequency is a measure of the raw data. For example: 20 students play basketball.

Relative Frequency compares that frequency to the total. Usually it’s a percent.For example: 25% of all students play basketball.

P. 359

Relative Frequency =

The frequency table below shows the results of a survey Kenesha conducted at school.She asked 80 randomly selected students whether they preferred basketball, football, or soccer.

These numbers are Frequencies.Convert them to Relative Frequencies (percents).For each – in order to convert it – you must answer this question: What percent is it out of the total?

Start with the first – What percent is 20 out of 80?

x 20100 80

=

The solution is always toCross-Multiply and Divide

(80)(x) = (100)(20)80x = 2000

x = 25

Frequency of the categoryTotal of all frequencies

Now calculate the rest.

Grand Total

P. 360

Convert these frequencies to relative frequencies. One from the previous page is done for you.

What percent is 20out of 80? 25%

P. 360

A Joint Relative Frequency is found by dividing a frequency that is not in the Total row or the Total column by the grand total. It tells what portion of the total has both of the two specified characteristics.

Two types of Relative Frequencies are found in a relative frequency table:

A Marginal Relative Frequency is found by dividing a row total or a column total by the grand total. It tells what portion of the total has a specified characteristic.

7.5% 15% 22.5% 45%

17.5% 25% 12.5% 55%

25% 40% 35% 100%

P. 360

7.5% 15% 22.5% 45%

17.5% 25% 12.5% 55%

25% 40% 35% 100%

The joint relative frequencies tell what percent of all those surveyed are in each category:• 7.5% are girls who prefer basketball.• 15% are girls who prefer football.• 22.5% are girls who prefer soccer.• 17.5% are boys who prefer basketball.• 25% are boys who prefer football.• 12.5% are boys who prefer soccer.

The marginal relative frequencies tell what percent of totals has a given single characteristic:• 25% prefer basketball.• 40% prefer football.• 35% prefer soccer.• 45% are girls.• 55% are boys.

P. 361

Joint Relative and Marginal Relative Frequencies (Using Percentages)

The joint relative frequencies:

are girls who selected an apple.

are girls who selected a banana.

are girls who selected an orange.

are boys who selected an apple.

are boys who selected a banana.

are boys who selected an orange.

The marginal relative frequencies:

selected an apple.

selected a banana.

selected an orange.

are girls.

are boys.

P. 362

There’s a 3rd type of relative frequency – it’s called conditional relative frequency. It describes what portion of a group with a given characteristic also has another characteristic. It is the percent of the joint relative frequency (data) out of the marginal relative frequency (total). BOTH NUMBERS WILL EITHER BE FROM THE SAME ROW OR COLUMN.

P. 362

Find the conditional relative frequency that a person prefers soccer, given that the person is a girl.

First – what’s the given? The person must be a girl. How many girls are there? 36.So it’s out of 36.From the girls, how many prefer soccer? 18.So - What percent is 18 (the number that prefer soccer) out of 36 (the number of girls)? 50%

P. 362Find the conditional relative frequency that a student chose an orange, given that the student is a boy.

First – what’s the given? The person must be a boy. How many boys are there? ________From the boys, how many chose an orange? ________So - What percent is ________ out of ________?

Answer: ________

P. 362

P. 363

You do it by comparing conditional relative frequencies.

Here – Is there an association between liking aerobic exercise and liking weight lifting?

What percent is 7 out of 21? 33.3%What percent is 7 out of 19? 36.8%Very close…

P. 367

Can you use gender to predict a preference for taking Spanish?

Conditional relative frequency of taking Spanish, given the student is a girl:What is the percent of 15 out of 25? 60%

Conditional relative frequency of taking Spanish, given the student is a boy:What is the percent of 12 out of 20? 60%

So the answer is no – both genders are equally likely to be taking Spanish.