Corequisite Support Activity for Comparing Quantitative Distributions: 3E – 13

What you’ll need to know

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

In the next section of the course material and in the following activity, you will need to compare the distributions of a single variable between groups. In this corequisite support activity, we will practice describing the distributions when presented with a histogram.

Describing Histograms

In the the section What to Know About Applications of Histograms: 3D  you defined the shape, center, spread, and the presence of outliers in the distribution of a quantitative variable. You learned about the skewness and modality of a distribution and saw how to use the range as a possible representation of spread. Then, in the activity, Forming Connections in Applications of Histograms: 3D, you used these statistical terms in summary to thoroughly describe the distribution of a quantitative variable.   In the upcoming section and activity, you’ll need to display a comfortable understanding of this statistical language so we’ll spend some time analyzing some histograms and possible descriptions in this support activity.

In Questions 1–3 below, you will be presented with a histogram and a description of the distribution of the variable to analyze. The recall box below contains the descriptions of each of the four characteristics of a thorough description.

Recall

Recall, from Forming Connection in Applications of Histograms: 3D, that a complete description of the distribution of a quantitative variable will include a discussion of shape, center, spread, and the presence of outliers. Refresh your understanding of the definitions of these characteristics if needed.

Core skill:

Using the language of statistics to describe the distribution of a quantitative variable.

For each histogram in the questions below, identify if the description of the distribution is complete and addresses the appropriate features of a distribution. If not, identify the missing elements. Use the guidelines presented in Forming Connections in Applications of Histograms: 3D: shape, center, spread, and the presence of outliers.

question 1

The distribution of per capita CO2 emissions for 28 European countries is roughly symmetric and unimodal. The emissions range from 2.5 to about 22.5 metric tons.

A bar chart showing the per capita carbon dioxide emissions of EU countries in metric tons. The data primarily lies on the left side of the chart, with one symmetrical peak on the left, and one data point off to the far right.

question 2

The number of hours watching TV per week in 2018 ranged from about 0 to 25 hours per week. There are a few respondents who watched an unusually high amount of TV (20 hours and 25 hours) compared to the rest.

A bar chart showing the number of hours spent watching television per week in 2018. The data primarily lies on the far left of the chart, with a peak on the far left that steeply decreases as you move to the right.

question 3

The average SAT score for the 50 states does not have any extreme observations.

A bar chart showing the Average SAT scores for the 50 states. The data has two distinct peaks, with one trough separating the peaks.

question 4

Provide a complete description for the movie runtimes for all G-rated movies.

A bar graph shows the run time in minutes for G-rated movies. The data primarily lies in the center of the chart, with only a few data points off to the far left and right of the chart.

Hopefully, you have started to become more comfortable using the language of statistics to describe the distribution of a quantitative variable. It’s time to move on to the next section.