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5/19 FA 8.4 Histograms

Last updated over 2 years ago
17 questions
Note from the author:

OBJECTIVES & STANDARDS

Math Objectives
  • Create a histogram given a data set
  • Analyze the distribution, center, and variability of a histogram
  • Identify the similarities and dissimilarities between a dot plot, box plot, and histogram that represent the same data set
  • Compare two histograms that represent related data sets
Common Core Math Standards
  • Link to all CCSS Math
  • CCSS.HSS.ID.A.1
  • CCSS.HSS.ID.A.2
  • CCSS.HSS.ID.A.3
Personal Finance Objectives
  • Represent and analyze real-world personal finance data, including student debt, credit scores, and housing costs, using histograms.
National Standards for Personal Financial Education
Spending
  • 6b: Compare the short-term and long-term costs and benefits of renting versus buying a home in their city of residence

Distribute to students
  • Student Activity Packet
  • Application Problems
  • Histogram Jigsaw Data Sets

OBJECTIVES & STANDARDS

Math Objectives
  • Create a histogram given a data set
  • Analyze the distribution, center, and variability of a histogram
  • Identify the similarities and dissimilarities between a dot plot, box plot, and histogram that represent the same data set
  • Compare two histograms that represent related data sets
Common Core Math Standards
  • Link to all CCSS Math
  • CCSS.HSS.ID.A.1
  • CCSS.HSS.ID.A.2
  • CCSS.HSS.ID.A.3
Personal Finance Objectives
  • Represent and analyze real-world personal finance data, including student debt, credit scores, and housing costs, using histograms.
National Standards for Personal Financial Education
Spending
  • 6b: Compare the short-term and long-term costs and benefits of renting versus buying a home in their city of residence

Distribute to students
  • Student Activity Packet
  • Application Problems
  • Histogram Jigsaw Data Sets
Intro

CALCULATE: Phone Battery Life

A college class with 25 students completes a survey about how long the battery life on their phone lasts.
Here are their responses, given in number of hours and sorted from least to greatest: 6, 6, 7, 7.5, 8, 8, 8, 9, 9, 9.5, 10, 10, 10, 10.5, 10.5, 10.5, 11.5, 13, 13.5, 13.5, 14.5, 15, 16, 16.5, 22

1
What is the average phone battery life in this class?_______
1
Which box plot represents the data set shown? _______


Explain your reasoning._______
1

Which value do you think is a better measure of the typical phone battery life in the class - the mean or the median? Explain your reasoning.

Learn It
VIDEO: Create a Histogram
We can also represent the phone battery data in the Intro using a histogram. A histogram is a graph that displays data using bars of different heights. The height of each bar represents how many data points fall into that range. To make a histogram, we start by grouping the data into a frequency table. Watch the video walkthrough and answer the questions.
14

Desmos Activity: Create a Histogram https://student.desmos.com/activitybuilder/student-greeting/64677fd44f0a7158dff914fc

Once Complete answer the following question: What is a histogram?

CREATE: Histogram Jigsaw
CREATE: Histogram Jigsaw
Data can be a great way to understand the world around us. But it can also be confusing! Histograms are one way that we can make sense of data; they make it easier to make observations and summarize trends.
In this activity, you’ll work with your group to uncover more about your focus topic using data. You’ll turn a data set into a histogram about student loans, car prices, mortgages, or credit scores.
10

Part I: Create Your Histogram

Your teacher will assign you to a group to work on one of the Data Sets. Create a poster that includes the following information:
____A histogram of your data set
____The mean and median of your data set
____The bin size you chose and why
____One sentence summarizing the data shown

Part II: Compare

Follow your teacher’s instructions to explore the other groups’ histograms. Then, answer the questions.
1

Which histogram(s) have a mean that is greater than the median? What do you notice about those histograms?

1

Which data set(s) have at least one outlier?

1

Choose one histogram and sketch the corresponding box plot.

Practice it
10

DESMOS: Polygraph: Guess the Distribution

In this activity, you’ll be paired with another student for a guessing game about histograms. Use your math vocabulary to try to find the correct histogram using the fewest guesses possible! Follow your teacher’s instructions to complete this Desmos activity.
https://student.desmos.com/activitybuilder/student-greeting/6467850be1b950726ae0fef4
Desmos link to Practice it: Complete with a partner (each on your own computer)
What helped you "guess" the correct histogram?

Application Problems
APPLICATION: Histograms for Student Loans, Housing, and High-Cost Lenders

Level 1

Federal Student Loan Balance by Age

Let’s use histograms to analyze student loan balances for different age groups.
The histograms below show the student loan balances of borrowers under 25 and borrowers aged 35-49. Both histograms pull a representative sample of 100 borrowers using data from Federal Student Aid.


1

Summarize: How does student loan debt compare for borrowers aged 35-49 and borrowers below 25?

For each of the following statements, respond true, false, or can’t be determined. Then, write one sentence using math vocabulary and/or numbers to support your response.
1

For each of the following statements, respond true, false, or can’t be determined. Then, write one sentence using math vocabulary and/or numbers to support your response.

The median student debt is higher for borrowers aged 35-49 than borrowers under 25.

1

For each of the following statements, respond true, false, or can’t be determined. Then, write one sentence using math vocabulary and/or numbers to support your response.

The standard deviation of student debt for borrowers under 25 is higher than the standard deviation of student debt for borrowers aged 35-49.

1

For each of the following statements, respond true, false, or can’t be determined. Then, write one sentence using math vocabulary and/or numbers to support your response.

There was one borrower aged 35-49 with a loan balance of exactly $300,000.

1

For each of the following statements, respond true, false, or can’t be determined. Then, write one sentence using math vocabulary and/or numbers to support your response.

For borrowers aged 35 - 49, the mean loan balance is greater than the median loan balance.

1

Make an inference: Why is the mean student debt higher for borrowers aged 34-49 year olds than for borrowers under 25?

20

Level 2

Part 1: Representing and Comparing Housing Costs

Let’s use data analysis to look at the cost of housing in different states. We’re going to compare the monthly costs of renting and owning a home in Michigan and California, using a representative sample from the US Census’ 2020 American Community Survey.

Desmos Link: https://student.desmos.com/activitybuilder/student-greeting/6467872ce1b950726ae0ff6f


1
  • Click the graph tab.
  • Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.
The End