# Descriptive Statistics

## Objective

Define categorical and numerical data. Create two-way tables to organize bivariate categorical data.

## Common Core Standards

### Core Standards

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• HSS-ID.B.5 — Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

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• 8.SP.A.4

## Criteria for Success

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1. Identify the graphs that are used for univariate data as bar graphs, circle graphs, histograms, box plots, and dot plots. Describe that they all measure the frequency of that one variable.
2. Describe bivariate data as comparing or combining two variables.
3. Identify the graphs that are used for bivariate data as scatterplots, line graphs, and two-way frequency tables.
4. Describe that two-way tables organize information that compare two categorical variables.
5. Describe the ways we can use two-way tables to compare.
6. Use given information to create a two-way table.

## Tips for Teachers

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• This lesson has a lot of parallels to 8th grade but is focused much more on the variables and quantities represented as well as the idea of choosing an appropriate data representation (or kind of representation) before data is even collected or as a way to organize the data collected.
• Students will need notes that allow them to organize their thinking around bivariate data. Over this set of lessons, up through lesson 19, students will need to think about how categorical data analysis is different from and similar to numerical analysis.

## Anchor Problems

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### Problem 1

A sandwich shop owner asked the following statistical question:

“Is there a relationship between when people buy sandwiches and the type of sandwich they buy?”

Which of these two situations discusses one variable, and which discusses two variables?

### Problem 2

The sandwich shop owner collected some data but did not take your advice for organizing it. Here’s what he recorded:

• 500 people came in over the week.
• 200 people came in for breakfast (7:30–9:00).
• 250 people came in during lunch hours (11:00–1:30).
• 50 people came in between these times (9:00–11:00, 1:30–3:00).
• Of the people who came in for breakfast, 100 people had a sandwich with egg.
• Of the people who came in for breakfast, 50 people had a vegetarian sandwich (without egg or meat).
• Of the people who came in for lunch, 20 had a sandwich with egg.
• 230 people total had a sandwich with a lunch meat on it.
• 40 of the 50 people who came in for a snack (not lunch and not breakfast) had a vegetarian sandwich
• 175 people had lunch meat during lunchtime.
• The sandwich shop went through 250 eggs (and each egg sandwich requires 2 eggs) over the week.

Organize this information for the sandwich shop owner so he has a better understanding of the data he has collected.

## Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

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### Problem 1

A survey asked the question, “How tall are you to the nearest inch?” A second question on this survey asked, “What sports do you play?” Indicate what type of data (numerical or categorical) would be collected from the first question. What type of data would be collected from the second question?

#### References

EngageNY Mathematics Algebra I > Module 2 > Topic C > Lesson 9Exit Ticket and Question #1

Algebra I > Module 2 > Topic C > Lesson 9 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

### Problem 2

Another random sample of 100 surveys was selected. Jill had a copy of the frequency table that summarized these 100 surveys. Unfortunately, she spilled part of her lunch on the copy. The following summaries were still readable:

#### References

EngageNY Mathematics Algebra I > Module 2 > Topic C > Lesson 9Exit Ticket and Question #2

Algebra I > Module 2 > Topic C > Lesson 9 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..