What you’ll need to know:
In this support activity you’ll become familiar with the following:
- Compare proportions to answer a statistical question.
You will also have an opportunity to refresh the following skills:
- Write a proportion as a simplified fraction.
- Write a proportion as a decimal.
- Write a proportion as a percentage.
Throughout this class, you will need compute fractions, proportions, and percentages and convert from one numeric representation to another.
Fractions, Decimals, and Percentages
Part-to-whole relationships, or proportions, can be represented by fractions, decimals, or percentages. It is often helpful to convert between these three forms to assist with data analysis. To change a fraction to a decimal, divide the numerator by the denominator. To change a decimal to a percentage, move the decimal point two places to the right. See the recall box below for a refresher of these skills.
recall
Core skill:
Core skill:
Core skill:
Core skill:
[link to student resource: Fractions, Decimals, Percentages]
[link to student resource: Rounding and Estimation]
Example
Example: Twenty-four students are enrolled in one section of a statistics course. On Friday, 18 students were present in class. What proportion of the students were present on Friday? Give your answer as a simplified fraction, a decimal rounded to the nearest hundredth, and a percentage.
Solution:
| Reduced Fraction | Decimal | Percentage |
| [latex]\frac{18}{24}= \frac{3}{4}[/latex] | [latex]\frac{3}{4}= \frac{75}{100}= 0.75[/latex] | 0.75 = 75% |
When you use a calculator to convert a fraction to a decimal, you may get a “short” decimal representation like this:
[latex]\frac{15}{25}=0.6[/latex]
Other times, you may get a “long” decimal representation like this:
[latex]\frac{1}{28}=0.03571428571[/latex]
When you get a “long” representation, you can shorten the decimal by rounding.
Round [latex]0.03571428571[/latex] to the nearest thousandth then convert to a percentage.
Round [latex]0.03571428571[/latex] to the nearest hundredth then convert to a percentage.
[/hidden-answer]
Now you try rounding by answering Question 1.
question 1
Convert [latex]\frac{5}{8}[/latex] to a decimal, and then round your answer as follows:
Part A: Round to the nearest tenth.
Part B: Round to the nearest hundredth.
Part C: Round to the nearest thousandth.
Let’s put all of these skills together to make some comparisons about proportions of students enrolled in a large statistics class. Remember a proportion is a part-to-whole relationship. See the summary in the example below to assess your understanding before completing Question 2.
example
A proportion is a part-to-whole relationship that can be expressed as a fraction, a decimal, or a percentage.
Ex. If eight students in a class of 32 students were absent one day, what proportion of students were absent? Give your answer in the form of a simplified fraction, decimal, and percentage.
Now it’s your turn. In Question 2, first fill in the table from information in the given paragraph. Make sure to check the accuracy of your completed table before continuing on! All the rest of the questions depend on it.
question 2
At a certain college, 150 students are enrolled in a statistics class. Of the 150 students, 45 live on campus and 105 live off campus. The professor was curious about whether her students study in the campus library. Of those who live on campus, 20 said they prefer to study in the library. Of those who live off campus, 40 said they prefer to study in the library.
Part A: Organize the data by completing the following table.
| Prefer to study at the library |
Prefer to study elsewhere |
Total | |
| Live on campus | |||
| Live off campus | |||
| Total |
Part B: What proportion of the students enrolled in this statistics class live on campus? Give your answer as a simplified fraction, a decimal, and a percentage rounded to the nearest whole percentage point.
Part C: What proportion of the students enrolled in this statistics class live off campus? Give your answer as a simplified fraction, a decimal, and a percentage rounded to the nearest whole percentage point.
Part D: What proportion of the students enrolled in this statistics class prefer to study at the library? Give your answer as a simplified fraction, a decimal, and a percentage rounded to the nearest whole percentage point.
Part E: What proportion of the students who live on campus prefer to study at the library? Give your answer as a simplified fraction, a decimal rounded to the nearest hundredth, and a percentage rounded to the nearest whole percentage point.
Part F: What proportion of the students who live off campus prefer to study at the library? Give your answer as a simplified fraction, a decimal rounded to the nearest hundredth, and a percentage rounded to the nearest whole percentage point.
Part G: In which group (those who live on campus or those who live off campus) were students more likely to prefer studying at the library?
If you find that you aren’t quite comfortable yet with converting fractions to decimals and percentages, visit the Student Resource Fractions, Decimals, Percentages for more support. Your instructor may also have resources to help. You’ll continue to practice these skills throughout the course though, and they will become less challenging the more you use them. Let’s move on to the What to Know to learn about the powerful benefit of forming study groups in college.
