August 4, 2010

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In this lesson, students will gather data for their class and analyze it using the measures of central tendency they learned in the last section.

- Mathematics > General
- Mathematics > Applied Mathematics
- Mathematics > Data Analysis & Probability
- Mathematics > Number Sense & Operations
- Mathematics > Problem Solving
- Mathematics > Statistics

- Grade 6
- Grade 7
- Grade 8

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**Materials needed for this lesson:**

1. *Gathering and Analyzing Data* worksheet (see Lesson 9 Resources folder).

2. *Class Data *Excel spreadsheet (see Lesson 9 Resources folder).

3. Identify the Area Median Household Income for your class' area by following the link: http://www.ers.usda.gov/data/unemployment/

**Procedure:**

In this section of the lesson, students will apply what they learned in the last section to the "real" data of their class' economy. Begin the lesson by a brief discussion introducing the study of statistics. In particular, highlight that statistics is the domain of mathematics that is interested in both describing characteristics of a **population **(i.e. a particular group under study) and in making predictions about that population. The branch of statistics that is used to actually *describe* the population is called (not surprisingly) **descriptive statistics**, whereas the branch that attempts to make mathematical predictions for the population is called** inferential statistics**. We're only going to be focusing on descriptive statistics in this lesson. In other words, we're going to be describing what is actually there, rather than trying to use that information to make predictions.

Highlight the fact that the students have actually already learned almost all of the tools they will need for descriptive statistics: the measures of central tendency and scatterplots and relationships. There will be one more tool (and a couple more measures) that they will learn tomorrow, but they are well on their way! Today, we will be focusing more on the process of *doing* statistics than on any new content of statistics.

Distribute the *Gathering and Analyzing Data* worksheet and pull up the *Class Data* spreadsheet on the projector. Work through the *Gathering Class Data* section together as a class, filling in the appropriate sheets on the spreadsheet. (The spreadsheet can then be posted to a class folder on a server for future reference.) Go over the key definitions to ensure that all members of the class understand what each indicator measures. They should have already found all but two of the indicators for their own family in previous lessons during this unit. The two indicators that they have not seen are as follows:

*Household Savings Rate:* This is simply the percentage of net income that a household saves. In order to compute it, have the students look at their monthly savings (if they have any) on their *Family Budget Worksheet*. They simply need to find that amount as a **percentage **of their Net Monthly Income.

*Percentage of Area Median Household Income:* This is a slightly more conceptually difficult indicator. Essentially, the students will compare their household income to the *median* household in their area. In order to do this, they simply need to find their **Annual Gross Income** as a percentage of the **Area Median Household Income**. You can find this value by following the link given in the materials section for this lesson. For Orange County, Virginia in 2008, this value was $52,158. Thus, a student with a $75,000 annual gross income would be at 144% of AMHI. (Note that percentages can be more than 100%).

Have students find (or calculate) all necessary values for their own family before proceeding to the data collection phase for the whole class. Circulate and double-check what the students are calculating. When they are done, have them check their partner's values. Then, proceed to the class data collection phase. Have students report their values, and fill them in simultaneously on the spreadsheet. DO NOT arrange them from least to greatest yet (leave that for the students to do).

After gathering all the data, have students work through the rest of the *Gathering and Analyzing Data* worksheet individually. As they do this, use the Excel sorting function to provide the sorted list for each of the indicators (without projecting this). As students complete their sorts, they will come to your computer to check them (as the worksheet instructs them to). Alternatively, you can put the *Class Data* spreadsheet on the class folder on the server and have students check it from there.

At either the end of this class period, or the beginning of the next (if you choose to assign the remainder of the worksheet for homework), review all of the answers for the measures of central tendency for each of the indicators, as well as the appropriate one to select. Highlight the fact that the choice of mean, median, or mode is NOT a personal choice, rather it is a reasoned choice based on the distribution of the data (i.e. if there are outliers, the median should be chosen, if the data is centralized, the mean should be chosen, if there is no discernible pattern at all, the mode should be chosen).

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