Wiki Page, Math 13 - Perez Sandbox : ANSWER(S): Module 4 – Dotplots (2b of 2 discussion 1)

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2026-01-17T21:14:51-08:00

Here are the dotplots. We are suppose to compare the distribution of calories in child and adult cereals.

Here are our observations about these two distributions:

Compare the shapes: The calorie distributions for both adult and child cereals have a similar shape. Both are symmetric with a central peak.

Compare the centers: We chose the center of the calorie distribution for child cereals as 110 calories in a serving. For adult cereals we chose 100 calories.

(Remember that this is an judgement call at this point. You might choose a different value for center, but it should be a value that represents the distribution well. We will learn more precise ways to define and calculate the center soon.)

Compare the spreads: There is more variability in the calorie distribution for adult cereals. Adult cereals vary from 50 to 160 calories, which is an overall range of 110 calories. The calories in child cereals vary from 90 to 120 calories, which gives a much smaller range of 30.

Typical adult cereals have 90 to 120 calories. All child cereals fall within this same interval. Almost all child cereals have 110 calories in a serving.

Now we need to write a paragraph comparing the two distributions. Here are two sample paragraphs. Both are good answers.

Version 1 - paragraph comparing the two distributions without formal vocabulary:

In this sample, child cereals vary in calorie content from 90 to 120 calories, with most at 110 calories in a bell-shaped pattern. The calories in adult cereals can vary widely, ranging from 50 to 160 calories, but the distribution is also somewhat bell-shaped with a center at about 100 calories. Despite the greater variability, typical adult cereals vary in calories from 90 to 120 per serving, which is similar to child cereals.

Version 2 - paragraph comparing the distributions with more formal vocabulary:

When we compare adult and child cereals in this sample, both calorie distributions are symmetric with a central peak. The peak in the child cereal distribution is at 110 calories in a serving and there is little variability. The calorie content in child cereals varies from 90 to 120 calories, with an overall range of only 30 calories. The peak in the adult cereal distribution is a little lower at 100 calories with more variability about the peak than in child cereals. Adult cereals vary from a minimum of 50 calories to a maximum of 160 calories with a much larger overall range of 110 calories. However, the calories in typical adult cereals fall between 90 to 120. Therefore, despite the greater variability in calories for adult cereals, child cereals and typical adult cereals have similar calorie content.

What makes a good description and comparison? In other words, what should we look for in our answers?

Compare characteristics of the two distributions, instead of just listing observations about the distributions.

Compare shape, center and spread.

Describe the numbers in the context of the problem; include units (in this case calories per serving). Somewhere in the paragraph (or multiple places), describe the variable (in this case calories) and individuals (in this case adult and child cereals).