# Center of a Distribution

Examples, videos, and solutions to help Algebra I students learn how to describe the Center of a Distribution.

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

Worksheets for Algebra I, Module 2, Lesson 2 (pdf)

Lesson 2 Student Outcomes

• Students construct a dot plot from a data set.
• Students calculate the mean of a data set and the median of a data set.
• Students observe and describe that measures of center (mean and median) are nearly the same for distributions that are nearly symmetrical.
• Students observe and explain why the mean and median are different for distributions that are skewed.
• Students select the mean as an appropriate description of center for a symmetrical distribution and the median as a better description of center for a distribution that is skewed.

Lesson 2 Summary

• A dot plot provides a graphical representation of a data distribution, helping us to visualize the distribution.
• The mean and the median of the distribution are numerical summaries of the center of a data distribution.
• When the distribution is nearly symmetrical, the mean and the median of the distribution are approximately equal. When the distribution is not symmetrical (often described as skewed), the mean and the median are not the same.
• For symmetrical distributions, the mean is an appropriate choice for describing a typical value for the distribution. For skewed data distributions, the median is a better description of a typical value.

Exit Ticket

Each person in a random sample of ten ninth graders was asked two questions:
• How many hours did you spend watching TV last night?
• What is the total value of the coins you have with you today?
Here are the data for these ten students:

1. Construct a dot plot of the data on hours of TV. Would you describe this data distribution as approximately symmetric or as skewed?

2. If you wanted to describe a typical number of hours of TV for these ten students, would you use the mean or the median? Calculate the value of the measure you selected.

3. Here is a dot plot of the data on total value of coins.
Calculate the values of the mean and the median for this data set.

4. Why are the values of the mean and the median that you calculated in question (3) so different? Which of the mean and the median would you use to describe a typical value of coins for these ten students?

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