**Finding associations between variables :**

We can use conditional relative frequency to check whether there is an association between two variables.

**Example 1 :**

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 results of the survey to investigate possible influences of gender on transport preferences.

**Solution :**

**Step 1 :**

Identify the percent of all students surveyed who are girls.

Required percent is

= Total no. of girls / Total no. of students

= 50/100

= 50%

**Step 2 :**

Determine each conditional relative frequency.

(i) Of the 47 students who prefer car, 22 are girls.

Percent who are girls, given a preference for car is

= 22/47 ≈ 47%

(ii) Of the 72 students who prefer bus, 38 are girls.

Percent who are girls, given a preference for car is

= 38/72 ≈ 53%

(iii) Of the 81 students who prefer other transport, 40 are girls.

Percent who are girls, given a preference for car is

= 40/81 ≈ 49%

**Step 3 :**

Interpret the results by comparing each conditional relative frequency to the percent of all students surveyed who are girls.

The percent of girls among students who prefer car is less than 50%, so boys are more likely than girls to prefer car.

The percent of girls among students who prefer bus is greater than 50%, so girls are more likely than boys to prefer bus.

The percent of girls among students who prefer other transport is close to 50%, so gender does not appear to influence preference for other transport.

**Example 2 :**

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 results of the survey to investigate possible influences of gender on pet preferences.

**Solution :**

**Step 1 :**

Identify the percent of all students surveyed who are girls.

Required percent is

= Total no. of girls / Total no. of students

= 28/50

= 56%

**Step 2 :**

Determine each conditional relative frequency.

(i) Of the 22 students who prefer dogs as pets, 12 are girls.

Percent who are girls, given a preference for dogs as pets is

= 12/22 ≈ 55%

(ii) Of the 15 students who prefer cats as pets, 6 are girls.

Percent who are girls, given a preference for cats as pets is

= 6/15 = 40%

(iii) Of the 13 students who prefer other pets. 10 are girls.

Percent who are girls, given a preference for other pets is

= 10/13 ≈ 77%

**Step 3 :**

Interpret the results by comparing each conditional relative frequency to the percent of all students surveyed who are girls.

The percent of girls among students who prefer dogs is close to 56%, so gender does not appear to influence preference for dogs.

The percent of girls among students who prefer cats is much less than 56%, so boys are more likely than girls to prefer cats.

The percent of girls among students who prefer cats is much greater than 56%, so girls are more likely than boys to prefer other pets.

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