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# Elementary Statistics: Projects: Univariate Data

Summary: In this project, students will design and carry out a survey, analyze the data, and graphically display the results. Note: This module is currently under revision, and its content is subject to change. This module is being prepared as part of a statistics textbook that will be available for the Fall 2008 semester.

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## Student Learning Objectives

• The student will design and carry out a survey.
• The student will analyze and graphically display the results of the survey.

## Instructions

• ____: Decide what data you are going to study.

### Examples:

Here are two examples, but you may NOT use them: number of M&M's per small bag, number of pencils students have in their backpacks.
• ____: Is your data discrete or continuous? How do you know?
• ____: Decide how you are going to collect the data (for instance, buy 30 bags of M&M's; collect data from the World Wide Web).
• ____: Describe your sampling technique in detail. Use cluster, stratified, systematic, or simple random (using a random number generator) sampling. Do not use convenience sampling. What method did you use? Why did you pick that method?
• ____: Conduct your survey. Your data size must be at least 30.
• ____: Summarize your data in a chart with columns showing data value, frequency, relative frequency and cumulative relative frequency.
• ____: Answer the following (rounded to 2 decimal places):
• x¯ x =
• ss =
• First quartile =
• Median =
• 70th percentile =
• ____: What value is 2 standard deviations above the mean?
• ____: What value is 1.5 standard deviations below the mean?
• ____: Construct a histogram displaying your data.
• ____: In complete sentences, describe the shape of your graph.
• ____: Do you notice any potential outliers? If so, what values are they? Show your work in how you used the potential outlier formula in Chapter 2 (since you have univariate data) to determine whether or not the values might be outliers.
• ____: Construct a box plot displaying your data.
• ____: Does the middle 50% of the data appear to be concentrated together or spread apart? Explain how you determined this.
• ____: Looking at both the histogram and the box plot, discuss the distribution of your data.

## Assignment Checklist

You need to turn in the following typed and stapled packet, with pages in the following order:

• ____ Cover sheet: name, class time, and name of your study
• ____ Summary page: This should contain paragraphs written with complete sentences. It should include answers to all the questions above. It should also include statements describing the population under study, the sample, a parameter or parameters being studied, and the statistic or statistics produced.
• ____ URL for data, if your data are from the World Wide Web.
• ____ Chart of data, frequency, relative frequency and cumulative relative frequency.
• ____ Page(s) of graphs: histogram and box plot.

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