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# Statistics problems

Please do # 2, 3 and 5.

2. In a 2-week study of the productivity of workers, the following data were obtained on the total number of acceptable pieces:

65 36 49 84 79 56 28 43 67 36
43 78 37 40 68 72 55 62 22 82
88 50 60 56 57 46 39 57 73 65
59 48 76 74 70 51 40 75 56 45
35 62 52 63 32 80 64 53 74 34
76 60 48 55 51 54 45 44 35 51
21 35 61 45 33 61 77 60 85 68
45 53 34 67 42 69 52 68 52 47
62 65 55 61 73 50 53 59 41 54
41 74 82 58 26 35 47 50 38 70

a. Calculate the sample average.
b. Calculate the sample standard deviation
c. Find the median for these data.
d. Construct a stem-and-leaf plot for these data.
e. Construct a histogram for these data.

The following data represent the yield on 90 consecutive batches of ceramic substrate to which a metal coating has been applied by a vapor-deposition process.
94.1 87.3 94.1 92.4 84.6 85.4 93.2 84.1 94.7
92.1 90.6 83.6 86.6 90.6 90.1 96.4 89.1 98.0
85.4 91.7 91.4 95.2 88.2 88.8 89.7 87.5 82.6
88.2 86.1 86.4 86.4 87.6 84.2 86.1 94.3 84.5
85.0 85.1 85.1 85.1 95.1 93.2 84.9 84.0 96.1
89.6 90.5 90.0 86.7 87.3 93.7 90.0 95.6 86.4
92.4 83.0 89.6 87.7 90.1 88.3 87.3 95.3 89.1
90.3 90.6 94.3 84.1 86.6 94.1 93.1 89.4 87.6
97.3 83.7 91.2 97.8 94.6 88.6 96.8 82.9 91.1
86.1 93.1 96.3 84.1 94.4 87.3 90.4 86.4 83.1

a. Compute the mean yield.
b. Compute the standard deviation and the variance of the yield
c. Compute the median yield.
d. Construct a histogram.
e. Construct a boxplot for the yield.

5. Two different methods are used for predicting the shear strength for steel plate girders. Nine specific girders are randomly selected, and the shear strength measurement is made using each method. The data are shown below:

Girder Karlsruch Method Lehigh Method
1 1.186 1.061
2 1.151 0.992
3 1,322 1.063
4 1.339 1.062
5 1.200 1.065
6 1.402 1.178
7 1.365 1.037
8 1.537 1.068
9 1.559 1.052

Determine whether there is any difference (on the average) between the two methods.

#### Solution Preview

Calculations are done in excel

1. In a 2-week study of the productivity of workers, the following data were obtained on the total number of acceptable pieces:

65 36 49 84 79 56 28 43 67 36
43 78 37 40 68 72 55 62 22 82
88 50 60 56 57 46 39 57 73 65
59 48 76 74 70 51 40 75 56 45
35 62 52 63 32 80 64 53 74 34
76 60 48 55 51 54 45 44 35 51
21 35 61 45 33 61 77 60 85 68
45 53 34 67 42 69 52 68 52 47
62 65 55 61 73 50 53 59 41 54
41 74 82 58 26 35 47 50 38 70

a. Calculate the sample average.
=5524/100=55.24

b. Calculate the sample standard deviation
Standard deviation = = =15.2624
c. Find the median for these data.

Median is the middle value in the series =mean of 50 and 51st observation =55
d. Construct a stem-and-leaf plot for these data.

Stem-and-Leaf Display: Data

Stem-and-leaf of Data N = 100
Leaf Unit = 1.0

2 2 12
4 2 68
8 3 2344
17 3 555566789
25 4 00112334
35 4 5555677889
49 5 ...

#### Solution Summary

This solution gives the step by step method for computing descriptive statistics, normal probability plots, histogram etc

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