1. Report your findings regarding “Diesel Generator Demands” (Data file diesel.c
ID: 3273595 • Letter: 1
Question
1. Report your findings regarding “Diesel Generator Demands” (Data file diesel.csv). Give a short description of the data and the variable(s) in the data file. Construct a relative frequency histogram and a boxplot for the data, and describe the shape of distribution. Calculate the mean and the median of the successful demands between failures. Calculate the IQR and standard deviation.
(a) Are there any outliers?
(b) Discuss the relative sensitivity of mean and median to extreme values.
(c) Which measure of center appears to best represent the center of the data?
C1 28 26 50 15 193 226 54 4 46 128 147 4 76 105 10 40 0) 4 10 273 84 164 0) 41 0) 26 62 6Explanation / Answer
Solution
The given data is arranged in ascending order as shown below:
i
x(i)
1
0
2
0
3
0
4
1
5
4
6
4
7
4
8
6
9
7
10
7
11
9
12
10
13
10
14
15
15
26
16
26
17
28
18
40
19
41
20
46
21
50
22
54
23
55
24
55
25
62
26
76
27
84
28
105
29
128
30
147
31
164
32
193
33
226
34
273
n
34
33
mean
57.52
51
SD
69.16
58.97
Mean + 3SD
265.01
227.91
Let x(i) denote the ith observation in the above ordered set.
Mean = 57.52 and Standard deviation (SD) = 69.16 based on all 34 observations.
Since the largest value, 273 is greater than (mean + 3SD,) 273 is an outlier. ANSWER 1
Eliminating this outlier, Mean = 51 ANSWER 2
and Standard deviation (SD) = 58.97 ANSWER 3 based on all 33 observations. Now, all observations are within (mean +/- 3SD).
With 33 observations, the median is the 17th value [i.e., x(17)]. So, median = 28 ANSWER 4
First quartile, Q1 = (33/4) = 8.25th ordered value. x(8) = 6 and x(9) = 7 and hence x(8.25) = 6.25. Similarly, third quartile, Q3 = (3x33)/4 = 24.75th ordered value. x(24) = 55 and x(25) = 62 and hence x(24.75) = 60.25. Thus, Q3 – Q1 = IQR = 54 ANSWER 5
i
x(i)
1
0
2
0
3
0
4
1
5
4
6
4
7
4
8
6
9
7
10
7
11
9
12
10
13
10
14
15
15
26
16
26
17
28
18
40
19
41
20
46
21
50
22
54
23
55
24
55
25
62
26
76
27
84
28
105
29
128
30
147
31
164
32
193
33
226
34
273
n
34
33
mean
57.52
51
SD
69.16
58.97
Mean + 3SD
265.01
227.91
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