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.

a histogram comparing days and numbers of visits 222444666# of Visits555101010151515202020000Day
a bar graph comparing types of foods and their frequency 222444666888101010000

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, 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 histogram 222444666888101010121212141414161616181818222444666888101010121212141414000
a dot plot where the mean is 11.6 and the median is 15 111222333444555666777888999101010111111121212131313141414151515161616171717181818191919000

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?

a histogram 222444666888101010121212141414161616181818222444666888101010121212141414000
a box plot 222444666888101010121212141414161616181818000

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:

skewed right: A histogram with six bins descending in height to the right. The tallest bin is on the left and the shortest bin is on the right. Skewed right:
skewed left: A histogram with six bins ascending in height to the right. The shortest bin is on the left and the tallest bin is on the right. mmm222Skewed left:
symmetric: A histogram with six bins. The first 3 bins ascend in height to the right. The next 3 bins descend in height to the right. The tallest bin or bin is in the middle. Symmetric:
Bimodal: A histogram with six bins. The two middle bins are the shortest. The two tallest bins are each side of the two smallest bins. Bimodal
uniform: A histogram with six bins, all have the same height Uniform:

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 and a range of .

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 bins, and describe the center, shape, and spread.

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.

Match the correlation coefficient with its description.

  1. ___

  2. ___

  3. ___

  4. ___

  1. Strong, positive correlation

  2. Moderate, positive correlation

  3. Weak, positive correlation

  4. Weak, negative correlation

  5. Moderate, negative correlation

  6. Strong, negative correlation

  7. No correlation at all