Descriptive Statistics

User Generated

zpnfgvyyb

Mathematics

Description

Refer to the Excel file Salary (attached) to address all the questions below:

  1. What is the probability for:

a.) Randomly selecting a person being a male in Grade E?

b.) Given that we picked a random person and he was a male, what is the probability of being in grade E?

c.) Why the results different?

2. Consider each group (Male and Female separately) and assume the salaries follow a Normal Probability distribution:

a.) What is the top 75th percentile of salary for Males?

b.) What is the top 75th percentile of salary for Females?

c.) What is the probability that a male picked at random makes more than 50K?

d.) What is the probability that a female picked at random makes between 30K and 40K?

Unformatted Attachment Preview

ID Salary Compa Midpoint Age 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 62.9 27.2 34.9 64.6 49.2 77.7 41.2 22 73.4 23.9 21.8 60.8 41.8 23.3 24.6 47.4 66.6 34.8 24.5 35.9 77.1 58.9 23.8 55.1 24.6 24.1 45.3 75.2 78.7 48.3 24.2 27.6 61.2 27 23.8 24.4 23.5 61.3 34.4 24.7 1.104 57 31 31 57 48 67 40 23 67 23 23 57 40 23 23 40 57 31 23 31 67 48 23 48 23 23 40 67 67 48 23 31 57 31 23 23 23 57 31 23 34 52 30 42 36 36 32 32 49 30 41 52 30 32 32 44 27 31 32 44 43 48 36 30 41 22 35 44 52 45 29 25 35 26 23 27 22 45 27 24 0.879 1.127 1.134 1.026 1.160 1.029 0.956 1.095 1.039 0.947 1.066 1.044 1.012 1.070 1.186 1.169 1.124 1.065 1.159 1.150 1.228 1.036 1.147 1.069 1.047 1.133 1.122 1.175 1.006 1.050 0.889 1.074 0.872 1.036 1.060 1.023 1.075 1.109 1.076 Performance Service Gende Raise Rating r 85 80 75 100 90 70 100 90 100 80 100 95 100 90 80 90 55 80 85 70 95 65 65 75 70 95 80 95 95 90 60 95 90 80 90 75 95 95 90 90 8 7 5 16 16 12 8 9 10 7 19 22 2 12 8 4 3 11 1 16 13 6 6 9 4 2 7 9 5 18 4 4 9 2 4 3 2 11 6 2 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 5.7 3.9 3.6 5.5 5.7 4.5 5.7 5.8 4 4.7 4.8 4.5 4.7 6 4.9 5.7 3 5.6 4.6 4.8 6.3 3.8 3.3 3.8 4 6.2 3.9 4.4 5.4 4.3 3.9 5.6 5.5 4.9 5.3 4.3 6.2 4.5 5.5 6.3 41 42 43 44 45 46 47 48 49 50 45.8 22.4 75.6 61.3 59.7 55.1 63.8 62.8 64 66.3 1.145 0.975 1.129 1.075 1.244 0.967 1.119 1.101 1.122 1.163 40 23 67 57 48 57 57 57 57 57 25 32 42 45 36 39 37 34 41 38 80 100 95 90 95 75 95 90 95 80 5 8 20 16 8 20 5 11 21 12 0 1 1 0 1 0 0 1 0 0 4.3 5.7 5.5 5.2 5.2 3.9 5.5 5.3 6.6 4.6 Degree Gender 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 M M F M M M F F M F F M F F F M F F M F M F F F M F M F M M F M M M F F F M F M Gr E B B E D F C A F A A E C A A C E B A B F D A D A A C F F D A B E B A A A E B A The column labels in the table mean: ID – Employee sample number Salary – Salary in thousands Age – Age in years Performance Rating - Appraisal rating (em Service – Years of service (rounded) Gender – 0 = male, 1 = female Midpoint – salary grade midpoint Raise – percent of last raise Grade – job/pay grade Degree (0= BS\BA 1 = MS) Gender1 (Male or Female) Compa - salary divided by midpoint 0 1 0 1 1 1 1 1 0 0 M F F M F M M F M M C A F E D E E E E E ance Rating - Appraisal rating (employee evaluation score)
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Explanation & Answer

Attached.

ID

Salary

Compa

Midpoint

Age

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40

62.9
27.2
34.9
64.6
49.2
77.7
41.2
22
73.4
23.9
21.8
60.8
41.8
23.3
24.6
47.4
66.6
34.8
24.5
35.9
77.1
58.9
23.8
55.1
24.6
24.1
45.3
75.2
78.7
48.3
24.2
27.6
61.2
27
23.8
24.4
23.5
61.3
34.4
24.7

1.104

57
31
31
57
48
67
40
23
67
23
23
57
40
23
23
40
57
31
23
31
67
48
23
48
23
23
40
67
67
48
23
31
57
31
23
23
23
57
31
23

34
52
30
42
36
36
32
32
49
30
41
52
30
32
32
44
27
31
32
44
43
48
36
30
41
22
35
44
52
45
29
25
35
26
23
27
22
45
27
24

0.879
1.127
1.134
1.026
1.160
1.029
0.956
1.095
1.039
0.947
1.066
1.044
1.012
1.070
1.186
1.169
1.124
1.065
1.159
1.150
1.228
1.036
1.147
1.069
1.047
1.133
1.122
1.175
1.006
1.050
0.889
1.074
0.872
1.036
1.060
1.023
1.075
1.109
1.076

Performance Service Gende Raise
Rating
r
85
80
75
100
90
70
100
90
100
80
100
95
100
90
80
90
55
80
85
70
95
65
65
75
70
95
80
95
95
90
60
95
90
80
90
75
95
95
90
90

8
7
5
16
16
12
8
9
10
7
19
22
2
12
8
4
3
11
1
16
13
6
6
9
4
2
7
9
5
18
4
4
9
2
4
3
2
11
6
2

0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0

5.7
3.9
3.6
5.5
5.7
4.5
5.7
5.8
4
4.7
4.8
4.5
4.7
6
4.9
5.7
3
5.6
4.6
4.8
6.3
3.8
3.3
3.8
4
6.2
3.9
4.4
5.4
4.3
3.9
5.6
5.5
4.9
5.3
4.3
6.2
4.5
5.5
6.3

41
42
43
44
45
46
47
48
49
50

45.8
22.4
75.6
61.3
59.7
55.1
63.8
62.8
64
66.3

1.145
0.975
1.129
1.075
1.244
0.967
1.119
1.101
1.122
1.163

40
23
67
57
48
57
57
57
57
57

25
32
42
45
36
39
37
34
41
38

80
100
95
90
95
75
95
90
95
80

5
8
20
16
8
20
5
11
21
12

0
1
1
0
1
0
0
1
0
0

4.3
5.7
5.5
5.2
5.2
3.9
5.5
5.3
6.6
4.6

Degree Gender
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0

M
M
F
M
M
M
F
F
M
F
F
M
F
F
F
M
F
F
M
F
M
F
F
F
M
F
M
F
M
M
F
M
M
M
F
F
F
M
F
M

Gr
E
B
B
E
D
F
C
A
F
A
A
E
C
A
A
C
E
B
A
B
F
D
A
D
A
A
C
F
F
D
A
B
E
B
A
A
A
E
B
A

The column labels in the table mean:
ID – Employee sample number
Salary – Salary in thousands
Age – Age in years
Performance Rating - Appraisal rating (em
Service – Years of service (rounded) Gender – 0 = male, 1 = female
Midpoint – salary grade midpoint
Raise – percent of last raise
Grade – job/pay gra...


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