Statistics project & Quiz 6

Statistics Project (10% of course grade, due ___)

For this assignment, you will implement a project involving statistical procedures. The topic may

be something that is related to your work, a hobby, or something you found interesting. If you

choose, you may use the example described below.

The project report must include

• name of project and your name

• purpose of project

• data (provide the raw data used, and cite the source)—the sample size must be at least

10. (The project example uses a random sample. Your sample does not have to be

random. You could be collecting personal data, such as your own bowling scores, and in

that case, the source is just your personal records.) Post a summary of your topic and your data here in the Statistics Project class conference (as a new topic). Include a brief informative description in the title of your posting.

• frequency distribution

• histogram • median, sample mean, range, sample variance, and sample standard deviation (show

work)

• percentage of data within one standard deviation of the mean, percentage of data

within two standard deviations of the mean, percentage of data within three standard

deviations of the mean (include explanation and interpretation --- do your percentages

imply that the histogram is approximately bell-shaped?)

• conclusion (several paragraphs interpreting your statistics and graphs; relate to the

purpose of the project)

If you choose, you may use the following example for your data.

• Purpose: Compare the amount of sugar in a standard serving size of different brands of

cereal. (You may instead choose to compare the amount of fat, protein, salt, or any other

category in cereal or some other food.)

• Procedure: Go to the grocery store (or your pantry) and pick at least 10 different brands

of cereal. (Instead of choosing a random sample, you might purposely pick from both the

"healthy" cereal types and the "sugary" ones.)

From the cereal box, record the suggested serving size and the amount of sugar per serving. The

raw data is the serving size and amount of sugar per serving for each of the 10 boxes of cereal.

Before calculating the statistics on the amount of sugar in each cereal, be sure you are comparing

the same serving size.

If you use a serving size of 50 grams, you must calculate how much sugar is in 50 grams of each

cereal. For example, if the box states that there are 9 grams of sugar in 43 grams of cereal, there

would be 50 times 9 divided by 43, or 10.5 grams in 50 grams of cereal. The result of this simple

calculation (for each of 10 boxes) is the data you will use in the project statistics and charts.

Here is a Statistics Project Checklist:

* Title

* Your Name

* Purpose

* Data (A set of at least 10 data values of a numeric quantity, such as sugar per serving. Cite the source. Label data as appropriate. For instance, Brand X: 10.5g per serving.)

*

Summary of Topic, and Data (posted in the Statistics Project conference.) The idea here is two-fold: (1) To share your interesting project idea with your classmates, and (2)

To give me a chance to give you a brief thumbs-up or thumbs-down before you finish the

project. Sometimes students get off on the wrong foot or misunderstand the intent of the

project, and your posting provides an opportunity for some feedback. Remark: Students may

use similar topics, but must have different data sets. For example, several students may be

interested in points scored by a particular team, and that is fine, but they must collect different

data, perhaps from different years.

* Frequency Distribution (used for histogram; can do by hand, or by using statistical software)

* Histogram (can do by hand, or by using statistical software)

* Median (SHOW WORK/EXPLANATION)

* Sample Mean (SHOW WORK/EXPLANATION; result can be confirmed by using by using statistical software)

* Range (SHOW WORK/EXPLANATION)

*

Sample Variance (SHOW WORK/EXPLANATION; result can be confirmed by using by using statistical software) Make sure you are using the correct sample variance formula when showing your calculations.

* Sample Standard Deviation (SHOW WORK/EXPLANATION; result can be confirmed by using by using statistical software)

*

Distribution of data: Calculate the percentage of data within one standard deviation of the mean, percentage of data within two standard deviations of the mean, percentage of

data within three standard deviations of the mean (include explanation and

interpretation). For a bell-shaped distribution, the respective percentages are approximately 68%,

95%, and 100%. Do your percentages imply that your data distribution is approximately bell-

shaped? Note that the answer could be Yes or No, depending on your data. You can also look

at the shape of your histogram (is it roughly bell-shaped?) as well as the percentages when

making your judgment.

* Conclusion (A short narrative summary) Interpret your results in a narrative summary consisting of several paragraphs. Be sure to describe features of the graphs and measurements

that you find to be important or interesting. )

You may submit all of your project in one document or a combination of documents, which may consist of word processing documents or spreadsheets or scanned handwritten work, provided it is clearly labeled where each checklist item can be found. Projects are graded on the basis of completeness, correctness, ease in locating all of the checklist items, and strength of the narrative portions.

Please see additional topics for Statistics Project Suggestions and Tips, and for a completely-worked Statistics Project Example.

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Project Suggestions and Tips

Suggestions for Topics: Look to your own experience and interests for sample topics. Here are some popular variables of interest, and data are relatively easy to collect:

• Temperatures (ex: set of high temperatures for a particular location)

• Sports-related data or hobby-related data (ex: your most recent 12 bowling scores, points/runs scored by a particular team for games in a specified time period)

• Gas prices in different geographic locations

• Breakfast cereal attribute (ex: calories per serving, or cost per serving, carbohydrates per serving, etc.)

• Milk prices

• Stock price or Dow-Jones index for selected days

• Mileage rating (miles per gallon) for various vehicles

• Unemployment rates in various locales

• Salaries for a particular type of job (ex: teacher salary) in various geographic locations

• Data compiled for some feature of an item (example: prices of 4&5-megapixel digital cameras reviewed in Consumer Reports)

Tips:

• Remember that a sample size of at least 10 is required.

• If all of the data are virtually the same (example: 10 gas prices and 8 of them nearly identical), then there is little interest in carrying out descriptive statistics techniques -- there isn't anything interesting to learn from the analysis! So, your data should have some variability.

• Make sure you are analyzing data related to a single variable. For example, if your data consists of 15 unemployment rates for males and 15 unemployment rates for females in 15 selected cities, then you are working with two variables (male unemployment rate and female unemployment rate), NOT one variable as specified.

• For this project, it is NOT necessary that the data be drawn as a random sample. (In the Statistics Project example, the data do happen to be randomly selected, to show you how it can be done, but random sampling is not a requirement for this project.)

• Be sure that your graphs/charts are labeled appropriately, with the axes, scales, and title easy to interpret.

• Use the Statistics Project Checklist as an aid in making sure your project meets all of the specifications.