 Collecting and Analyzing Data

The Soda Survey

Surveys are an excellent way to integrate a variety of mathematical concepts. Surveys enable students to compute basic statistics like the mean, median, and mode as well as chart results in the form of frequency (or bar) charts and pie charts. Also, students can calculate the ratio of those surveyed to a larger group such as the entire school. For example, if 25 of the 100 students surveyed liked 7-Up, then you could expect that 200 of the 800 students in the school would also like 7-Up if you surveyed a representative sample of students in the first place. What constitutes a good sample is another issue that you can discuss as part these lessons.

This file contains 3 lessons for the soda survey data. Each lesson may take more than one day. Lesson 1 gets students to create a survey and plan who will be surveyed. Lesson 2 requires students to organize the data and discuss how it will be analyzed. Lesson 3 allows students to analyze the data and make charts. The degree to which students analyze data will depend upon their knowledge of specific math concepts. For example, it is possible for students to use ratios as a basis for estimating how many students in the school might prefer a particular soda.

 Math Objective Collect and analyze data Compute fractions, decimals and percents, ratios. Compute the mean, median, and mode. Skills/Outcomes Ability to design a survey Organize survey data on a spreadsheet Create charts that represent the data Apply math concepts in the context of the survey data Materials survey forms calculators Files to Use Download Info/Instructions Grid Worksheets (math concepts lesson) soda.xls Pie Charts (math concepts lesson)

Lesson 1

Lesson 2

Lesson 3

Lesson 1 - Creating the Survey

 Teacher Note: This lesson will culminate in a survey that students will use outside of class. The next lesson, Lesson 2, is based on analyzing the survey data. Please allow time for students to conduct the survey as you plan these lessons.

Classroom Discussion and Activities (Whole Group or Teams)

Design the Survey

Begin class by discussing students' favorite food, soda, clothing, or music. Discuss ways in which these things change in their popularity. Give an example of how there may be a big difference between the number of students who like the most popular soda and those who like the second most popular soda. Suveys are a way to explore these issues systematically.

In making a survey, it is very important that you first decide what questions you want answered. Make sure that you are asking all of the questions that interest you. There won't be time to go back to those surveyed to get more information.

• Create a survey that lists all of the popular sodas. Be sure to create an "other" option.

• Ask how much soda each student drinks per day. You can define soda consumption around a common quantity such as a 12 oz. can or cup.

• Below is one possible survey form. You can make it as long as you think is reasonable. Be sure to discuss with the students the importance of getting a range of students to answer the survey. Just getting their friends or one "type" or grade level of students may not be a good indicator of how everyone in the school feels about a certain soda.

Once the class has determined what type of students they are going to ask, how many, and when they will ask them (in class, during lunch, etc.), they are ready to conduct the survey.

Lesson 2 - Organizing the Data and Planning the Analysis

 Teacher Note: Make sure that students fill out a chart with all of the data before they go to the lab. You can use Grid Worksheets as a template for creating column and row names as well as entering the data. Also, you will need to work as a group if different students have collected survey data. Also, it is critical to this lesson that students understand how key math concepts apply to the data. Stress the concepts as you discuss the data. Review the relationship between fractions and decimals as different ways to express the same number.

• Organize the data by using a master survey form to combine all of the information. This will allow you to list how many students preferred each of the different kinds of sodas and how much soda students drank. It is very important at this step to be clear about how to combine and record the data. With soft drinks, we want to know the total number of first choices, how many students drank a certain quantity of sodas per day, and so forth. Students may want to combine the data in ways that won't make sense. Therefore, work with them on representing the data in ways that are clear and help the class understand the data. The table below shows how first preference of sodas and total number of sodas drank per day could be represented. • Now discuss the different ways in which the data could be analyzed. Depending upon what math concepts you have taught, you could get students to first find the total or sum, and then generate what fraction of the students liked Coke as their first choice, Pepsi, and so forth. The second source of information, how many sodas students drink per day, could be analyzed in a similar fashion. Converting the data into fractions would allow you to show how the same numbers could be expressed as decimals and percents. The data also lends itself to different kinds of charts (e.g., column or bar charts, pie charts). Discuss all of these possibilities with students after they have organized their data on their worksheets. Again, Grid Worksheets is a template that you can use for this kind of in-class planning. Finally, students could even write some of the formulas that they will use when they go to the lab (e.g., = sum(B2:B6)).

• One of the most ambitious concepts that you can use in this lesson is the concept of ratio. If the students surveyed represent the student body as a whole, then how many students in the school would we expect to like Coke, Pepsi, etc., as their first choice? We can determine this through a ratio. In the example above, 70 students were surveyed, and 23 liked Pepsi as their first choce. If there are 800 students in the school, we can find out how many would like Pepsi as a first choice by using a ratio. There are various ways to teach ratios, and the display below is one example of how you could set it up. • Students can use calculators to determine what decimal number goes in the denominator and use the same decimal number on top as the numerator. (For example, the number that represents both the numerator and the denominator above is 11.43.) Be sure to discuss with students how and why ratios work in this way. This number or constant can be used as part of a formula for all of the numbers in a spreadsheet. This will be described in the next lesson.

• At the end of the lesson, students should have an organized data sheet and some formulas they can use for the lab.

Lesson 3 - Analyzing the Data

 Teacher Note: Once students have completed their data sheets, they are ready to enter the data in a spreadsheet and analyze it. You may want to have the students enter the data themselves or create your own "master" data file that they use in the lab. All of this depends on your objectives (e.g., learning how to set up spreadsheet files, how to make charts, use percents and decimals).

• Students should apply a variety of functions to the data in the table below. They could use functions to find: • Formulas will also be useful in finding fractions (e.g., =B2/70). You will have to remind students how to format the different columns so that the numbers in that column are expressed as fractions, decimals, or percents.

• Finally, the students need to make sure to set up the data correctly so that they can create charts. The file soda.xls is an example of how a student file might look once it is complete. It is just one of many possibilities for analysis of soda data.

• Be sure that students can explain their analyses once they have completed them. This will provide an important assessment of student understanding.