Lesson 6 Food for Thought Develop Understanding

Learning Focus

Represent data with box plots, dot plots, and histograms.

Analyze data represented in different ways.

How can we describe differences in data sets? What features should we look for in different representations?

Open Up the Math: Launch, Explore, Discuss

Aaliyah loves to cook and collect recipes. She started her own food blog to share her love of food and passion for cooking. She hopes to build up a following and to eventually get sponsors, so that her blog can become a source of income.

The web service that hosts her site provides some data analytics that she likes to look at to make decisions about future posts.

Last week she collected this data. The first set of data shows the number of visits to the site each day, starting with Monday. The second set of data shows how many recipes of each type were downloaded during the week.

1.

Compare the two displays of data. What similarities and differences do you observe?

Aaliyah found that her most popular recipe was for her special, chewy, moist brownies. She checked the analytics and found that during the week, $30$ people had checked out the brownie page. The next two diagrams both represent the data for the number of minutes that people spent on the brownie page.

2.

Compare the two representations of the data.

a.

What do you observe about the number of minutes spent on the brownie page?

b.

What aspects of the data are highlighted or obscured by each representation?

Aaliyah’s math teacher said that there is one more representation that she should see, the box plot, sometimes called the box and whisker plot.

3.

Compare the two representations of the data. What aspects of the data are highlighted or obscured by each representation?

Aaliyah likes histograms and wants to use them more. She asked her math teacher what she should be looking for when she examines a representation of numerical data. Her teacher said that she should look for:

Center: Measures of center include the mean and median.

Shape: There are many possible shapes, but some of the most common are:

Spread: Tells us something about how wide, or disperse, the data are. Measures include the range and the mean absolute deviation. (We’ll talk more about spread in the next lesson.)

4.

Without using technology, sketch a data distribution with the following characteristics:

a.

A histogram with seven bins that is skewed right.

b.

A box plot with a median of $5$ and a range of $15$ .

c.

A dot plot that is mostly uniform and has an outlier.

d.

A bimodal histogram that is not symmetric.

5.

Aaliyah found data for the number of minutes that people spent browsing her recipes blog. Use technology to create a histogram with $5$ bins, and describe the center, shape, and spread.

$2$	$3$	$3$	$5$	$5$	$6$	$6$	$6$
$6$	$10$	$10$	$10$	$12$	$12$	$12$	$13$
$13$	$15$	$15$	$15$	$15$	$16$	$16$	$16$
$16$	$16$	$16$	$16$	$17$	$17$	$17$	$18$
$18$	$18$	$18$	$19$	$19$	$20$	$20$	$20$

Ready for More?

You’re surrounded by data in your life! Think of contexts that would produce histograms with the following shapes.

a.

Bimodal:

b.

Symmetric and unimodal:

c.

Skewed right:

Takeaways

Single-variable quantitative data:

Representations
Features

Lesson Summary

In this lesson, we focused on single-variable quantitative data. We compared histograms, dot plots, and box plots to consider what aspects of the data are highlighted in each. We learned to look for the center, the shape, and the spread of the data.

Retrieval

1.

___
$r = - 0.44$
___
$r = 0.89$
___
$r = 0.27$
___
$r = - 0.95$

Strong, positive correlation
Moderate, positive correlation
Weak, positive correlation
Weak, negative correlation
Moderate, negative correlation
Strong, negative correlation
No correlation at all