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Unformatted text preview: Introduction to Statistics Project #2: Best Catapult Ever Built Introduction You have been hired to construct the most accurate and precise catapult ever created. You will analyze the hurling capabilities of your catapult by using the measures of central tendency (mean, median, mode, midrange) and measures of variation (range, variance, standard deviation, coefficient of variation). A quality catapult must have a balance of large average distance with high consistency. You will be competing with your classmates for the title of "Best Catapult Ever Built". The project will have three phases. Phase I is the catapult construction. Phase II is the performance data gathering. Phase III is the data organization and analysis. Objectives You will be able to summarize data using measures of central tendency including the mean, median, mode, and midrange You will be able to determine which measure of central tendency most appropriately summarizes the data. You will be able to describe data using measures of variation such as the range, variance, standard deviation, and coefficient of variation Technical Specifications You will construct your catapult from the following materials provided: 40 wooden popsicle sticks Masking Tape 1 Rubber Bands Puff Ball Operation Specifications The catapult must be used only to launch the puff balls The catapult must be able be free standing and easily transportable The catapult must be able to be launched by one person with one finger (not allowed to use another person or a second hand to hold the catapult down while launching) Tips You can google "popsicle stick catapult" to find a few sample catapult plans Refer to your textbook for key formulas Procedures 1. Construct your catapult using the materials provided. Your construction deadline will be ______________ (determined by your teacher) 2. Have an independent investigator (a classmate) measure the distances (centimeters) of 20 throws. 3. Organize your 20 throws into a data table 4. Create a dot plot, or histogram, of your data to examine the distribution of your data 5. Create a summary table that includes o All measures of central tendency (mean, median, mode, and midrange) o All measures of spread (range, sample variance, sample standard deviation, coefficient of variance) 6. Mark the measures of central tendency on your dot plot or histogram and 7. Answer the summary questions that follow Questions 1. What is the best measure of central tendency that represents the throwing distance of your catapult? Explain. Note: Mark and label your measures of central tendency on your dot plot or histogram to clarify your answer. 2. Why might the coefficient of variance be more helpful than the standard deviation in comparing different catapults? 3. Why might manufacturers be interested in measures of spread when analyzing the performance of their products? 4. Describe a real life example where someone might use a measure of spread to help make an informed decision. Introduction to Statistics Project #2: Best Catapult Ever Built Rubric Element Name Date Title Catapult Construction Process Raw Data Table The name of each student in the group, the date, and the title of the project is clearly indicated on the project Catapult is constructed within guidelines. Safety has been a high priority throughout entire manufacturing process. A very neat and organized data table shows at least 20 measurements of the throwing distances. Columns and rows are neatly labeled and units (centimeters) are included. Information is easily legible. A neat and organized dot plot or histogram is accurately created. All axes are labeled, appropriately scaled, and units are included. The shape and distribution of the data is very clear. The mean, median, mode, and midrange are clearly marked on the graph Mean, median, mode, and midrange are correctly calculated and presented in a clearly labeled summary table. Midrange, Population Variance, Population Standard Deviation, and Coefficient of Variance are all calculated correctly. The information is neatly presented in the summary table. The work involved to produce these calculations neatly shows all major steps. All questions have been clearly answered. Catapult construction has been completed on time. Data analysis and summary reports have been completed by the start of class on 10/3/08. Catapult is constructed mostly within guidelines. Safety has been a priority throughout most of the manufacturing process. A mostly neat and organized data table shows at least 20 measurements of the throwing distances. Columns and rows are labeled and units (centimeters) are included. Information is mostly legible. A dot plot or histogram is created with one or two inaccuracies. Most axes are labeled, appropriately scaled, and units are included. The shape and distribution of the data is clear. The mean, median, mode, and midrange are marked on the graph. Mean, median, mode, and midrange are calculated with one mistake. The information is presented in a labeled summary table. Midrange, Population Variance, Population Standard Deviation, and Coefficient of Variance are calculated with one or two mistakes. Most information is presented in the summary table. The work involved to produce these calculations neatly shows most major steps. Most questions have been answered Catapult construction has been completed on time. Data analysis and summary reports have been completed within two days of the due date 10/3/08. The name of each student in the group, the date, and the title of the project is indicated on the project 4 3 2
Some information from the name of each student in the group, the date, and the title of the project is indicated on the project Catapult is constructed but some guidelines have been violated. Safety has been compromised two or more times. A data table shows 20 measurements of the throwing distances. Most Labels and units are missing. Information is somewhat legible. 1 No name, date, and title information is included in the project Catapult has not been constructed. Safety has been severely neglected. Data table is incomplete, illegible, or not present. Graph: Dot Plot or Histogram A dot plot or histogram is created with more than two inaccuracies. Labels, appropriate scaling, or units may need improvement. The mean, median, mode, or midrange are missing. A dot plot or histogram is not created or contains more than four inaccuracies. Labels, scaling, and units are missing. No mean, median, mode, or midranges are marked. Measures of Central Tendency Measures of Variance Questions On Time Mean, median, mode, and midrange are calculated with two or more mistakes. The information is presented in a summary table, but proper labels may be missing Midrange, Population Variance, Population Standard Deviation, and Coefficient of Variance are calculated with more than two mistakes. Some information is presented in the summary table. The work involved to produce these calculations shows some steps. Some questions have been answered. Catapult construction has been completed with delay Data analysis and summary reports have been completed within four days of the due date 10/3/08. Mean, median, mode, and midrange are not calculated. Midrange, Population Variance, Population Standard Deviation, or Coefficient of Variance are not calculated. Questions have not been answered Catapult construction has been completed with delay Data analysis and summary reports have been completed More than four days of the due date 10/3/08. ...
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 Spring '11
 Lee
 Statistics, Mean, Median, Mode

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