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Activity 3.5 Applied StatisticsIntroductionToday’s consumers are constantly trying to judge the quality of products. But what isquality? How and by whom is quality determined? Some would say the designercreates specifications, which in turn dictate the quality of a product. That quality isalso based on the acceptable value of a part within a whole product. Statistics arecommonly used in manufacturing processes to control and maintain quality. Thisactivity will allow you to apply statistics in order to analyze and determine the qualityof a set of wooded cubes.In this activity you will collect data and then perform statistical analyses to determinemeasures of central tendency and variation of the data. You will also represent thedata using a histogram.EquipmentEngineering notebookPencilDial caliperProcedure1. Part of the manufacturing quality control testing for a toy is to measure the depthof a connector piece that must fit into another part. The designed depth is 4.1 cm.Every tenth part produced on the production line is measured. The following datawas collected during a two minute production period.4.1, 4.1, 4.0, 4.1, 3.9, 4.4, 3.9, 4.3, 4.0, 4.2, 4.0, 3.8a. Calculate each of the following measures of central tendency. Show yourwork.Mean: _____________Median: ____________Mode: _____________b. Calculate each of the following measures of variation for the data set.Show your work. A table has been provided to help you calculate thestandard deviations. In the table round values in the last two columns tofour decimal places. Report the standard deviation statistics to fourdecimal places. Range: _____________© 2012 Project Lead The Way, Inc.IED Activity 3.5 Applied Statistics – Page 1xx-µ(x - µ)2SUMStandard Deviation of this data: _____________c. Create a histogram for the data using the grid below. The horizontal axisshould display each length measurement from the minimum to maximumrecorded lengths. You may choose to begin with a dot plot and then fill inthe bars. Be sure to label your axes.d. What class interval is appropriate for the measurement values reported as4.1 cm?© 2012 Project Lead The Way, Inc.IED Activity 3.5 Applied Statistics – Page 22. Gather measurement data taken by your teammates on Activity 3.3 MakingLinear Measurements for the largest outside diameter of the wheel. You shouldcollect at least 5 measurements. In your engineering notebook, list eachmeasurement value recorded by your team (including yours) and showcalculations for the mean, median, mode, range and standard deviation.Remember the rules for rounding in statistics. Show your work.3. Compare your results to a teammate’s calculations. Make corrections to yourwork as necessary.Conclusion1. How can statistics of a product’s dimensions be used to assess the quality of theproduct?2. In which phase(s) of a design process might statistics be most useful? Why?© 2012 Project Lead The Way, Inc.IED Activity 3.5 Applied Statistics – Page 3