Comparing Quantitative Distributions: Background You’ll Need 1

Learning Goals

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 Applications of Histograms: What to Know 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, Applications of Histograms: Forming Connections, 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:

Describing a Distribution

Use the guidelines presented in Applications of Histograms: Forming Connections: shape, center, spread, and the presence of outliers to assist you with each histogram in the questions below.

question 1

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

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

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

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.