#### Introduction:

#### Two-way Relative Frequency Table:

Data can be organized in a two-way frequency table and then used to construct a two-way relative frequency table. Relative frequency can be determined for the rows and the columns as well as for the whole table.

A relative frequency table shows the ratio of the number of data in each category to the total number of data items. The ratio can be expressed as a fraction, decimal, or percent.

**Example:**

#### 4.5.1 Construction of Two-Way Relative Frequency Table

**Example 1:**

Ann conducted a survey on 40 randomly selected students on whether they preferred dogs, cats, or other pets. She recorded the gender of each student surveyed.

What percent of students surveyed were girls who preferred dogs?

**Solution:**

**Step 1:**

Make a two-way frequency table.

**Step 2:**

Make a two-way relative frequency table.

Twenty percent of students surveyed were girls who preferred dogs.

#### 4.5.2 Comparing Relative Frequency by Rows

**Example 2:**

Ann asked 40 randomly selected students whether they preferred dogs, cats, or other pets and made the following two-way frequency table.

Find the conditional relative frequency that a student surveyed prefers cats as pets, given the student is a girl.

**Solution:**

#### 4.5.3 Comparing Relative Frequency by Columns

**Example 3:**

Ann asked 40 randomly selected students whether they preferred dogs, cats, or other pets and made the following two-way frequency table.

Find the conditional relative frequency that a student surveyed is a boy, given that the student prefers dogs as pets.

**Solution:**

**Example 4:**

Henry surveyed twenty students from ninth grade and thirty students from twelfth grade at random. He asked the students whether they were involved in school clubs and created the following two-way frequency table of his results.

Create a two-way relative frequency table for the columns in the frequency table.

**Solution:**

To create a two-way relative frequency table based on columns, divide each value in a column by the total frequency for that column.

#### Exercise:

- A _____________________ shows the ratio of the number of data in each category to the total number of data items.
- Use the table below and find what percent of the people surveyed have the artistic ability. Round to the nearest percent.

3. Men and women are asked what type of car they own. The table shows the relative frequencies with respect to the total population asked in the survey. Which type of car is more popular?

4. The following two-way frequency table shows the results of a survey conducted on a group of 120 people. Each person has a dog, a cat, or a bird.

Complete the two-way relative frequency table to show the distribution of the data with respect to all 120 people. Round to the nearest tenth of a percent.

5. Students were asked if they liked raspberries. The two-way relative frequency table shows the relative frequencies with respect to the response. What percent of students who do not like raspberries are girls?

#### Concept Map:

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