ANALYZE: Prom Decisions

The senior class at Evergreen High School is planning their prom! The prom planning committee decides to survey the class on their top options. They ask each senior whether they would prefer to hold prom at Sunset Lodge or the Aquarium and whether they prefer a Under the Sea or Starry Night theme.

Some of the survey results are:

• The survey included 92 different students.

• 20 students said they’d prefer Starry Night at the Aquarium.

• 43 students said they’d prefer Sunset Lodge over the Aquarium.

• 47 students said they’d prefer Under the Sea over Starry Night.

• 18 students said they’d prefer Under the Sea at Sunset Lodge.

Use the above information to answer the following questions. Show all reasoning.

VIDEO: Types of Data: Categorical vs Numerical Data

In the INTRO, you looked at a survey that gathered categorical data about prom options. Watch the video to learn about the different types of data. Then, answer the questions

VIDEO: Two-Way Tables

We can organize data on two categorical variables by using a two-way table. A two-way table uses rows to represent one categorical variable and columns to represent the second categorical variable. Each cell of the table tells us how many data points fall into that particular intersection and totals are often included at the end of each row and column. Watch the video walkthrough and answer the questions.

Complete the two-way table using the data from the Intro.

Some of the survey results are:

• The survey included 92 different students.

• 20 students said they’d prefer Starry Night at the Aquarium.

• 43 students said they’d prefer Sunset Lodge over the Aquarium.

• 47 students said they’d prefer Under the Sea over Starry Night.

• 18 students said they’d prefer Under the Sea at Sunset Lodge.

High School Graduates: 6 Months Later

You’ve finally made it - you’ve graduated from high school! But what comes next? Let’s look at some data to see what recent high school graduates are doing

The table below shows observational data about the education and employment of recent high school graduates. It is based on the nationally representative sample from the Current Population Survey. Study the table and answer the questions.

Relative Frequency Table

The table below shows the same data about recent high school graduates. However, it is organized differently to show the percentage of people who gave each response, instead of the number.

This is called a relative frequency table. It is a type of two-way table that shows percentages rather than counts. It is helpful for seeing if there is an association between two variables.

Represented Another Way

Mahlet wanted to find out if educational enrollment was associated with employment. Using the same data set about recent high school graduates, she built a different relative frequency table to compare the percentage of people who were employed, unemployed, or not in the labor force across each educational group.

Associations Between Variables

You’ve learned about correlation in previous lessons; when we talk about two-way tables, we use the term association to mean something similar.

Association refers to a relationship between two variables: when one variable changes, so does the other one. Correlation is a type of association that tells us more about the shape and strength of the relationship.

We can use relative frequency tables to determine whether two variables have an association. One of the easiest ways to know if there is an association is to work backwards: check if the variables have NO association. If there’s no association, the relative frequency values should be very similar across each column or row.

Part 1: No Association

The table below is an example of two variables with no association; it shows the percentage of American children with health insurance by age. You can see that the percentage of children with health insurance stays approximately the same in each age group.

Part 2: Association

The table below shows the percentage of American adults with health insurance by education level. Study the table and answer the questions.

Level 1

Part 1: Graduation Rates and College Type

Of students who enroll at 4-year colleges, how many graduate? Let’s explore some data about the graduation rates at different types of 4-year colleges: public, private non-profit, and private for-profit.

The table below based on a nationally representative sample of full-time students at 4-year colleges[1].

Part 2: Student Loan Associations

Level 2

Part 1: Education and Employment

How does education level relate to unemployment rates? Explore the data below to find out.

The relative frequency table shows the percentage of adults who are employed by level of education. The data focuses on adults over 25 years old who are in the labor force (looking for work).

Part 2: Comparing Occupations

Different jobs have different educational requirements. Some careers require a specific degree, while others have more flexible requirements. Let’s explore 5 careers where workers have similar levels of education.