8. (25 points) A manufacturing process at your company produces a polymer film t

Question

8. (25 points) A manufacturing process at your company produces a polymer film that is in the shape of a rectangle. For each film produced, as a quality control measure the thickness (in microns) is measured in four specified locations, "Bottom Left", "Bottom Right", "Top Left" and "Top Right", labeled 1,2, 3 and 4, respectively. From a production run of 3000 pieces, 160 films were randomly selected and the four thickness measurements were made for each of those selected. Thus, the outcome of this set of measurements was four sets of 160 thickness measurements, each set corresponding to a specific location on the films. 1500 1250 1000 n 750 500 250 8a.) (10 points) Box plots for the four data sets, 1,2, 3 and 4, are shown above. These plots were generated in Matlab using the same convention that we discussed in class. Answer the following questions for data set 4, corresponding to a position on the "Top Right" of each film Indicate on the plot the value of the median, the 25th percentile, 75th percentile and the Inter- quartile range (IQR) Does the upper whisker appear to extend to its maximal value of (75th percentile 1.5 IQR)? Does the lower whisker appear to extend to its minimal value of (25th percential 1.5*IQR)? Circle or otherwise identify any outliers.

Explanation / Answer

answer related to box-plot

a) the length upon y -axis each 1unit=50 unit

the red line is indicating median so the median is 550 unit

the upper portion that is the upper line of the box is indicating 75 percentile so it is 700

the lower line of the box indicating 25 percentile and it is 400 unit

IQR is 700-400=300

b) 75th perentile +1.5*IQR=1150

and it is clesr from the picture

c) 25th percentile -1.5*IQR=-50

that should be 0 and it is extend to 0

d) the samll blue circle is indicating the outliers .........above the whiscar

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