# Comparing Distributions

Videos, lessons, examples and solutions to help Algebra I students learn how to compare two or more distributions in terms of center, variability, and shape.
Students interpret a measure of center as a typical value.
Students interpret the IQR as a description of the variability of the data.
Students answer questions that address differences and similarities for two or more distributions.

### New York State Common Core Math Algebra I, Module 2, Lesson 8

Lesson 8 Summary

Histograms show the general shape of a distribution.

Box plots are created from the 5-number summary of a data set.

A box plot identifies the median, minimum and maximum values, and the upper and lower quartiles.

The interquartile range (IQR) describes how the data is spread around the median; it is the length of the interval that contains 50% of the data values.

The median is used as a measure of the center when a distribution is skewed or contains outliers.

Example 1: Country Data

A science museum has a “Traveling Around the World” exhibit. Using 3D technology, participants can make a virtual tour of cities and towns around the world. Students at Waldo High School registered with the museum to participate in a virtual tour of Kenya, visiting the capital city of Nairobi and several small towns. Before they take the tour, however, their mathematics class decided to study Kenya using demographic data from 2010 provided by the United States Census Bureau. They also obtained data for the United States from 2010 to compare to data for Kenya.

The following histograms represent the age distributions of the two countries:

Exercises 1–8

1. How do the shapes of the two histograms differ?
2. Approximately what percent of people in Kenya are between the ages of 0 and 10 years?
3. Approximately what percent of people in the United States are between the ages of 0 and 10 years?
4. Approximately what percent of people in Kenya are 60 years or older?

1. Approximately what percent of people in the United States are 60 years or older?
2. The population of Kenya in 2010 was approximately 41 million people. What is the approximate number of people in Kenya between the ages of 0 and 10 years?
3. The population of the United States in 2010 was approximately 309 million people. What is the approximate number of people in the United States between the ages of 0 and 10 years?
4. The Waldo High School students started planning for their virtual visit of the neighborhoods in Nairobi and several towns in Kenya. Do you think they will see many teenagers? Will they see many senior citizens who are 70 or older? Explain your answer based on the histogram.

Example 2: Learning More about the Countries using Box Plots and Histograms

A random sample of 200 people from Kenya in 2010 was discussed in previous lessons. A random sample of 200 people from the United States is also available for study. Box plots constructed using the ages of the people in these two samples are shown below.

1. Estimate the median age of a person in Kenya and the median age of a person in the United States using the box plots.
2. Using the box plot, 25% of the people in the United States are younger than what age? How did you determine that age?
3. Using the box plots, approximately what percent of people in Kenya are younger than 18 years old?
4. Could you have estimated the mean age of a person from Kenya using the box plot? Explain your answer.

Exit Ticket

1. Using the histograms of the population distributions of the United States and Kenya in 2010, approximately what percent of the people in the United States were between 15 and 50 years old? Approximately what percent of the people in Kenya were between 15 and 50 years old?
2. What 5-year interval of ages represented in the 2010 histogram of the United States age distribution has the most people?
3. Why is the mean age greater than the median age for people in Kenya?

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