Problem 3 - Algebra 1

Question

You took a survey of your class and found that 18 out of the 31 students have a pet at home. Explain how you can use your results to make a prediction for the 1746 students in your school.

Step-by-Step Solution

Answer

Based on the class survey, it can be predicted that approximately 1015 students in the school have a pet.

Step 1: Calculate the Proportion of Students who have a Pet

To find the ratio of students who have a pet in class, divide the number of students who have a pet (18 students) by the total number of students (31 students). This proportion is represented as \(\frac{18}{31}\).

Step 2: Predict the number of Students in School having a Pet

To estimate the number of students who have a pet in the entire school, one must relate the proportion of students with a pet to the total number of students in the school, which is 1746 students. This can be done by multiplying the ratio \(\frac{18}{31}\) by the school's total student population, 1746: \(\frac{18}{31} * 1746\).

Step 3: Round off to the nearest Whole Number

As the number of students must be a whole number, the resulting figure ought to be rounded to the closest whole number: \(1015\).

Key Concepts

Proportion

When we discuss proportion, we are essentially comparing one part of a group to the whole group. In the context of the exercise, we are interested in the proportion of students who have pets. To find this, we divide the number of students owning pets by the total number of students surveyed.
The formula looks like this:

• Number of students with pets = 18
• Total number of students = 31
• Proportion = \( \frac{18}{31} \)

This proportion helps us consistently represent the data, showing a relationship between the part (students with pets) and the whole (total students in the class). It's a handy way to understand and communicate such data effectively.

Survey Results

Survey results give us valuable information about a sample group, which can be used to make predictions about a larger population. In statistical terms, this is known as using a sample to infer about the population.
First, ensure you have correctly interpreted your survey results. For instance:

• Your class survey shows that 18 out of 31 students have a pet.

When you aim to apply this information to a larger group, such as the whole school with 1746 students, you use the proportion from your survey. By multiplying the proportion by the school population, you adjust the findings to reflect the larger group:

• Predicted number of students with pets = \( \frac{18}{31} \times 1746 \)

This provides an estimate of how many students in the entire school are likely to have pets, based on your survey data.

Whole Numbers

In statistics, whole numbers are often necessary when talking about people or other discrete items. You can’t have 1014.6 students having pets; students are whole people, so you need a whole number.
When you calculate using proportions, you might end up with a decimal that represents an average or estimated number. Here’s how:

• After multiplying the proportion by the total school population, you might get a decimal like 1014.6.
• To sensibly present this data, round to the nearest whole number, since the number of people cannot include a fraction.

In this exercise, you would round 1014.6 to 1015. This is because rounding conforms to the rules of representing whole numbers in a realistic and understandable form.