Activity 3.5 Applied Statistics



Applied Statistics Answer KeyIn this activity you will collect data and then perform statistical analyses to determine measures of central tendency and variation of the data. You will also represent the data using a histogram.EquipmentEngineering notebookPencilDial caliperProcedurePart of the manufacturing quality control testing for a toy is to measure the depth of 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 data was 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, 3.8Calculate each of the following measures of central tendency. Show your work.Mean: ___8.07 cm__________ μ = x =xin=48.812 = 4.0667Median: ____8.05 cm________ 7.8, 7.9, 7.9, 8.0, 8.0, 8.0, 8.1, 8.1, 8.1, 8.2, 8.3, 8.4Average=8.0+8.12=8.05Mode: _____Bimodal 8.0 cm_and 8.1 cm________Calculate each of the following measures of variation for the data set. Show your work. A table has been provided to help you calculate the standard deviations. In the table round values in the last two columns to four decimal places. Report the standard deviation statistics to four decimal places.Range: ____0.6 cm___ Range = max – min = 8.4 – 7.8 = 0.6 cmxx - ?(x - ?)27.8-0.26670.07117.9-0.16670.02787.9-0.16670.02788.0-0.06670.00448.0-0.06670.00448.0-0.06670.00448.10.03330.00118.10.03330.00118.10.13330.00118.20.13330.01788.30.23330.05448.40.33330.1111SUM0.3265Standard Deviation of this data: ___0.17 cm_ σ =xi-μ2n=0.326512= 0.0272 = 0.1650 ≈ 0.17 cmCreate a histogram for the data using the grid below. The horizontal axis should display each length measurement from the minimum to maximum recorded lengths. You may choose to begin with a dot plot and then fill in the bars. Be sure to label your axes.What class interval is appropriate for the measurement values reported as 8.1 cm? 8.05 cm ≤ x < 8.15 cmThe class interval boundaries should include one more decimal place than the pare your results to a teammate’s calculations. Make corrections to your work as necessary. ConclusionHow can statistics of a product’s dimensions be used to assess the quality of the product?Quality of a product can often be related to whether or not the product (or parts of the product) is within specific limits that allow the product to function properly. Statistics are often used in quality control of raw materials or product output. For instance, in mass production, random products from the production line can be inspected or measured. Statistical analyses are performed on these measurements to determine if the product is being produced within allowable tolerances and to indicate when corrections in the production process are necessary. ................
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