Statistics and Quality



Statistics and Quality Answer KeyIn this activity you will collect data and then perform a statistical analysis to estimate measures of central tendency and variation of a product (wooden cubes). You will represent the data using a histogram. EquipmentNotebook, JournalPencilDial caliper27 wooden cubes per studentProcedureObtain a set of 27 wooden cubes (3/4 in.) from your instructor. Label each cube (1 through 27) lightly in pencil. Measure the side length of each block along the grain. When taking a measurement, position the block so the caliper measuring surfaces are touching the end grain faces. Record the measurements to create a data set. For this analysis a precision of .001 is necessary; therefore, record each measurement to the nearest one thousandth of an inch (.001 in).Wood cube 1:0.754Wood cube 15:0.741Wood cube 2:0.748Wood cube 16:0.758Wood cube 3:0.745Wood cube 17:0.747Wood cube 4:0.747Wood cube 18:0.762Wood cube 5:0.756Wood cube 19:0.745Wood cube 6:0.741Wood cube 20:0.754Wood cube 7:0.747Wood cube 21:0.751Wood cube 8:0.752Wood cube 22:0.742Wood cube 9:0.752Wood cube 23:0.749Wood cube 10:0.763Wood cube 24:0.756Wood cube 11:0.742Wood cube 25:0.745Wood cube 12:0.754Wood cube 26:0.755Wood cube 13:0.758Wood cube 27:0.741Wood cube 14:0.746Use Excel to perform a statistical analysis of the data to determine each of the following.Mean: 0.750Median: 0.749Mode: 0.754Range: 0.022Sample Standard Deviation: 0.006472Create a histogram to represent the data. Use seven to ten class intervals (bin values). Be sure to label your axes and define units where appropriate. Print a copy of the Excel worksheet that shows your data, the summary statistics, and your histogram.Does your data appear to be normally distributed? Justify your answer. Answers will varyConclusionYou have calculated statistics related to your 27 wooden cubes. Consider how your statistical analysis results would change if all of the data values for all of the cubes measured by all of the students in your class were compiled and used for analysis. Then answer the following questions.How would the histogram of the entire class’ data change compared to your histogram?It would change because different people have different sized cubes and the statistics will be very different.What value would you expect for the mean of the length measurements if the data from the entire class were used? Explain.Answers will varyWould you expect the standard deviation of the class’ measurements be larger, smaller, or about the same as the standard deviation of your measurements? Why? Answers will vary ................
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