Corequisite Support Activity for Applications of Histograms: 3D – 10

What you’ll need to know

In this support activity you’ll become familiar with the following:

You will also have an opportunity to refresh the following skills:

In the next section, What to Know about Applications of Histograms: 3D, and in the following activity, you will need to be able to use technology to visualize the distribution of quantitative variables and use the visualization to answer questions about the distribution.

Analyzing Course Evaluations

In this corequisite support activity, you will use the evals dataset,[1] which includes information collected from student evaluations for a sample of 463 courses taught by 94 professors at The University of Texas at Austin. Each row is a different course, and the columns have information about the professor and summary information from the course.

The objective of this analysis is to explore the distribution of age of the professor for the 463 courses. To do so, you’ll use technology to make a histogram to visualize the distribution of professor ages.

Read and interpret a data table and data dictionary

The first 10 observations of the selected variables within the “Teaching Evaluations” dataset are displayed in the following table.

Teaching Evaluations
score rank cls_profs cls_students age
4.7 tenure track single 43 36
4.1 tenure track single 125 36
3.9 tenure track single 125 36
4.8 tenure track single 123 36
4.6 tenured multiple 20 59
4.3 tenured multiple 40 59
2.8 tenured multiple 44 59
4.1 tenured single 55 51
3.4 tenured single 195 51
4.5 tenured single 46 40

The following is a data dictionary of the selected variables:

score: Average professor evaluation score
rank: Rank of professor (teaching, tenure track, tenured)
cls_profs: Number of professors teaching sections in course in sample (single, multiple)
cls_students: Number of students in the class
age: Age of professor in years

question 1

What are the observational units in the dataset?

question 2

Which of the following variables are quantitative? Select all that apply.

  1. score
  2. rank
  3. cls_profs
  4. cls_students
  5. age

Now let’s examine the distribution of the variable age.

Create a histogram from a dataset using technology

Go to the Describing and Exploring Quantitative Variables tool at https://dcmathpathways.shinyapps.io/EDA_quantitative/ and select the dataset Teaching Evaluations – Age” to make a histogram of the distribution of professor ages. Select Binwidth to 5.

question 3

Use a histogram to answer questions about a variable

Use the histogram to answer the following questions. You may wish to refresh the mathematical skill needed for Question 4 in the recall box before beginning. Also see the Student Resources: Fractions, Decimals, Percentages and Ratios and Fractions.

Recall

For question 4 below, recall from 1E and 2D Corequisite Activities how to write a proportion.

Core Skill:

question 4

About what proportion of courses are taught by a professor who is younger than 40 years old?

Hint: The number of observations in each group can be easily seen by hovering over the bar on the histogram.

question 5

About 50% of the courses in the data were taught by professors older than what age? Select the closest response.

  1. 30
  2. 45
  3. 50
  4. 55

question 6

What is the approximate difference between the maximum and minimum values in the distribution? Select the closest response.

  1. 40
  2. 45
  3. 40
  4. 55

question 7

Based on these data, is a course at The University of Texas at Austin more likely to be taught by a professor who is close to 37 years old or close to 52 years old? Explain.

Now that you’ve gained some valuable practice creating and interpreting a histogram, it’s time to move on to the next section and activity.

  1. Professor evaluations and beauty. (n.d.). OpenIntro. Retrieved from https://www.openintro.org/data/index.php?data=evals ↵