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.
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:
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.
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