Statics process control and improvements, Basic Statistics

1. Warm-up Exercise

Volumes I, II, III, and IV of Shakespeare are in sequence next to one another in the library bookcase.  Each volume has 2" of pages and the front and back covers of each of the volumes are each ¼" thick.

If a bookworm starts at Page 1 of Volume I and eats its way through the volumes (following the shortest route) to the last page of volume IV, how many inches did the bookworm travel?

Answer the following three questions based on what you know about statistics now.

2. What is Statistics?

3. How is it abused?

4. How should it be used in decision-making?

5. Find the errors in the following mean, median, and mode matrix and correct them:

                                                Mean                                                    Median                                     Mode

a.  5, 3, 4, 1, 2?                    3                                                                  3                                            3

b.  5, 5, 5, 5, 5?                    5                                                                  5                                            5

c.  3, 3, 3, 1, 3, 5?                3                                                                  3                                            3

d.  8, 6, 4, 5, 8, 11?           7.5                                                                  8                                            8

e.  1, 1, 7, 1, 1?                2.2                                                                  1.5                                          1

6. Refer to the run chart on page 6.  Why is there no solid black vertical line at data point #4 = 8?

7. Calculate the variance and standard deviation of problems b-e below, using problem a as a guide:

a. 1, 2, 3, 4, 5

    Step 1     Step 2                 Step 3

      1     -3  =    -2     x   -2 =   4

      2     -3  =    -1      x  -1 =   1

      3     -3  =     0      x   0 =   0

      4     -3  =     1      x   1 =   1

      5     -3  =     2      x   2 =   4

Sum       15                                           Sum     10 (Step 4) / (5-1) = 10/4 = 2.5 (Step 5) = V

Number    5

Average   3                                                          Step 6 = the square root of V = 1.58 = SD

Now you do the following four:

b. 5, 5, 5, 5, 5

c. 1, 3, 3, 3, 3, 3, 5

d. 2, 5, 4, 5, 8, 6

e. 1, 1, 7, 1, 1

8. Using the x-axis given at the bottom of this page, construct the frequency histogram for the data set: 8, 10, 5, 11, 6, 6, 9, 12, 6, 8, 8, 20, 7, 8, 9, 7, 8, 7, 7, 13, 9, 8, 10, 8, 7, 8

5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20

Posted Date: 2/25/2013 1:42:23 AM | Location : United States







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