Calculating Deceptive Statistics, business and finance homework help

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Question Description

Refer to the Excel file Salary (attached to the assignment) 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 Rating 85 8 80 7 75 5 100 16 90 16 70 12 100 8 90 9 100 10 80 7 100 19 95 22 100 2 90 12 80 8 90 4 55 3 80 11 85 1 70 16 95 13 65 6 65 6 75 9 70 4 95 2 80 7 95 9 95 5 90 18 60 4 95 4 90 9 80 2 90 4 75 3 95 2 95 11 90 6 90 2 Gender 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 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 Raise Degree Gender1 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 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 Grade 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 thousan Age – Age in years Performance Rating - App Service – Years of service (rounded) Gender – 0 = male, 1 = fem Midpoint – salary grade midpoint Raise – percent of last rais Grade – job/pay grade Degree (0= BS\BA 1 = MS Gender1 (Male or Female) Compa - salary divided by 4,3 5,7 5,5 5,2 5,2 3,9 5,5 5,3 6,6 4,6 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 Performance Rating - Appraisal rating (employee evaluation score) Data Type Salary Compa Midpoint Age Ratio Scale Ratio Scale Ratio Scale Ratio Scale Performance Rating Ordnal Scale Salary: Salary data is ratio level as this satisifies satisfies all properties of the data measurement inclduing identity Compa: Compa salary data is ratio level as this satisifies satisfies all properties of the data measurement inclduing Midpoint Salary: Midpoint salary data is ratio level as this satisifies satisfies all properties of the data measuremen Age: Age data is ratio level as this satisifies satisfies first three properties of the data measurement inclduing ident Performance Rating: Performance Rating data is ordinal scale as this satisfies firrst two properties of the data mea Service Lenght: Service length data is ratio level as this satisifies all properties of the data measurement inclduing Gender: Gender data is nominal level as this satisifies only first property of the data measurement. Based on the da Percentage of Last Raise: Percentage of Last Raise: data is ratio level as this satisifies all properties of the data me Degree: Degree data is nominal level as this satisifies only first property of the data measurement. Based on the da Gender1: Gender 1 data is nominal level as this satisifies only first property of the data measurement. Based on th Grade: Grade data is ordinal scale as this satisfies firrst two properties of the data measurement inclduing identity, Service Gender Length Ratio Scale Nominal Scale Raise Ratio Scale Degree Gender 1 Nominal Scale Nominal Scale Grade Ordinal Scale asurement inclduing identity, magnitude, equal intervals, and meaningful zero value. data measurement inclduing identity, magnitude, equal intervals, and meaningful zero value. rties of the data measurement inclduing identity, magnitude, equal intervals, and meaningful zero value. measurement inclduing identity, magnitude, equal intervals. This this data zero value is not meaningful. o properties of the data measurement inclduing identity, and magnitude. data measurement inclduing identity, magnitude, equal intervals, and meaningful zero value. measurement. Based on the data, ranking among the observation cannot be made here. all properties of the data measurement inclduing identity, magnitude, equal intervals, and meaningful zero value. easurement. Based on the data, ranking among the observation cannot be made here. a measurement. Based on the data, ranking among the observation cannot be made here. surement inclduing identity, and magnitude. Mean, Standrd Deviation, and Range of Entire Salary Data Set ID Salary Gender 1 62,9 M 2 27,2 M 3 34,9 F 4 64,6 M 5 49,2 M 6 77,7 M 7 41,2 F 8 22 F 9 73,4 M 10 23,9 F 11 21,8 F 12 60,8 M 13 41,8 F 14 23,3 F 15 24,6 F 16 47,4 M 17 66,6 F 18 34,8 F 19 24,5 M 20 35,9 F 21 77,1 M 22 58,9 F 23 23,8 F 24 55,1 F 25 24,6 M 26 24,1 F 27 45,3 M 28 75,2 F 29 78,7 M 30 48,3 M 31 24,2 F 32 27,6 M 33 61,2 M 34 27 M 35 23,8 F 36 24,4 F 37 23,5 F 38 61,3 M 39 34,4 F 40 24,7 M The mean, standrd deviation, and range of entire (male and fe set are $45.57, $19.381, and $56.90 respectively. 41 42 43 44 45 46 47 48 49 50 Mean Standard Deviation Range 45,8 22,4 75,6 61,3 59,7 55,1 63,8 62,8 64 66,3 45,57 19,381 56,90 M F F M F M M F M M range of entire (male and female employees) salary data 90 respectively. Mean, Standrd Deviation, and Range of Salary of Male Employees ID Salary Gender 1 62,9 M 2 27,2 M 4 64,6 M 5 49,2 M 6 77,7 M 9 73,4 M 12 60,8 M 16 47,4 M 19 24,5 M 21 77,1 M 25 24,6 M 27 45,3 M 29 78,7 M 30 48,3 M 32 27,6 M 33 61,2 M 34 27 M 38 61,3 M 40 24,7 M 41 45,8 M 44 61,3 M 46 55,1 M 47 63,8 M 49 64 M 50 66,3 M Mean 52,792 Standard Deviation 17,992 Range 54,20 The mean, standrd deviation, and range of male em $17.992, and $54.20 respectively. viation, and range of male employees salary data set are $52.792, espectively. Mean, Standrd Deviation, and Range of Salary of Female Employees ID Salary Gender 3 34,9 F 7 41,2 F 8 22 F 10 23,9 F 11 21,8 F 13 41,8 F 14 23,3 F 15 24,6 F 17 66,6 F 18 34,8 F 20 35,9 F 22 58,9 F 23 23,8 F 24 55,1 F 26 24,1 F 28 75,2 F 31 24,2 F 35 23,8 F 36 24,4 F 37 23,5 F 39 34,4 F 42 22,4 F 43 75,6 F 45 59,7 F 48 62,8 F Mean 38,348 Standard Deviation 18,289 Range 53,800 The mean, standrd deviation, and range of f $18.289, and $53.80 respectively. standrd deviation, and range of female employees salary data set are $38.348, nd $53.80 respectively. First, Second & Third Quartiles and Interquartile Range of Entire Salary Data Set ID Salary Gender 1 62,9 M 2 27,2 M 3 34,9 F 4 64,6 M 5 49,2 M 6 77,7 M 7 41,2 F 8 22 F 9 73,4 M 10 23,9 F 11 21,8 F 12 60,8 M 13 41,8 F 14 23,3 F 15 24,6 F 16 47,4 M 17 66,6 F 18 34,8 F 19 24,5 M 20 35,9 F 21 77,1 M 22 58,9 F 23 23,8 F 24 55,1 F 25 24,6 M 26 24,1 F 27 45,3 M 28 75,2 F 29 78,7 M 30 48,3 M 31 24,2 F 32 27,6 M 33 61,2 M 34 27 M 35 23,8 F 36 24,4 F 37 23,5 F 38 61,3 M 39 34,4 F 40 24,7 M 41 42 43 44 45 46 47 48 49 50 First Quartile Range Second Quartile Range Third Quartile Range Interquartile Range 45,8 22,4 75,6 61,3 59,7 55,1 63,8 62,8 64 66,3 24,6 43,55 61,3 36,70 M F F M F M M F M M First, Second & Third Quartiles and Interquartile Range of Male Salary Data ID Salary Gender 1 62,9 M 2 27,2 M 4 64,6 M 5 49,2 M 6 77,7 M 9 73,4 M 12 60,8 M 16 47,4 M 19 24,5 M 21 77,1 M 25 24,6 M 27 45,3 M 29 78,7 M 30 48,3 M 32 27,6 M 33 61,2 M 34 27 M 38 61,3 M 40 24,7 M 41 45,8 M 44 61,3 M 46 55,1 M 47 63,8 M 49 64 M 50 66,3 M First Quartile Range 45,3 Second Quartile Range 60,8 Third Quartile Range 64 Interquartile Range 18,70 First, Second & Third Quartiles and Interquartile Range of Female Salary Data ID Salary Gender 3 34,9 F 7 41,2 F 8 22 F 10 23,9 F 11 21,8 F 13 41,8 F 14 23,3 F 15 24,6 F 17 66,6 F 18 34,8 F 20 35,9 F 22 58,9 F 23 23,8 F 24 55,1 F 26 24,1 F 28 75,2 F 31 24,2 F 35 23,8 F 36 24,4 F 37 23,5 F 39 34,4 F 42 22,4 F 43 75,6 F 45 59,7 F 48 62,8 F First Quartile Range 23,8 Second Quartile Range 34,4 Third Quartile Range 55,1 Interquartile Range 31,30 Comparison of the First, Second & Third Quartiles and Interquartile Range of the Male and Female Salar Whereas the first, second & third quartiles and interquartile range of female salary are 23.8, 34.4, 55.1 a 31.30 respectively, the first, second & third quartiles and interquartile range of male salary are 45.3, 60.8 and 18.70 respectively. Here, from the observation of the first, second & third quartiles and interquartile r male and female salary, it can be said that as compared to that of female’s salary, male’s salary is more dispersed. Male and Female Salary Data: are 23.8, 34.4, 55.1 and e salary are 45.3, 60.8, 64, tiles and interquartile range of male’s salary is more Mean and Standard Deviation of Male Salary Data ID Salary Gender 1 62,9 M 2 27,2 M 4 64,6 M 5 49,2 M 6 77,7 M 9 73,4 M 12 60,8 M 16 47,4 M 19 24,5 M 21 77,1 M 25 24,6 M 27 45,3 M 29 78,7 M 30 48,3 M 32 27,6 M 33 61,2 M 34 27 M 38 61,3 M 40 24,7 M 41 45,8 M 44 61,3 M 46 55,1 M 47 63,8 M 49 64 M 50 66,3 M First Quartile Range 52,79 Second Quartile Range 17,99 Test Nomality of Male Salary Data Criteria Mean Plus Minus One Standard Deviation Mean Plus Minus Two Standard Deviation Mean Plus Minus Three Standard Deviation Lower Range Upper Rage 34,80 17,99 16,81 88,78 -1,18 2849,55 Here, the maximum nad minimum data of the salary of the male is within the range of mean+-3 stnadard deviation. Thus, male salary can be considered as Mean and Standard of Female Salary Data ID Salary Gender 3 34,9 F 7 41,2 F 8 22 F 10 23,9 F 11 21,8 F 13 41,8 F 14 23,3 F 15 24,6 F 17 66,6 F 18 34,8 F 20 35,9 F 22 58,9 F 23 23,8 F 24 55,1 F 26 24,1 F 28 75,2 F 31 24,2 F 35 23,8 F 36 24,4 F 37 23,5 F 39 34,4 F 42 22,4 F 43 75,6 F 45 59,7 F 48 62,8 F Mean 38,35 Standard Deviation 18,29 Test Nomality of Female Salary Data Criteria Mean Plus Minus One Standard Deviation Mean Plus Minus Two Standard Deviation Mean Plus Minus Three Standard Deviation Lower Range Upper Rage 20,06 56,64 1,77 74,93 -16,52 93,22 Here, the maximum nad minimum data of the salary of the female is within the range of mean+-3 stnadard deviation. Thus, female salary can be considered as normally distributed. ...
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Tutor Answer

FinAccGuru
School: University of Maryland

Here is the answer. Thanks

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
Rating
85
8
80
7
75
5
100
16
90
16
70
12
100
8
90
9
100
10
80
7
100
19
95
22
100
2
90
12
80
8
90
4
55
3
80
11
85
1
70
16
95
13
65
6
65
6
75
9
70
4
95
2
80
7
95
9
95
5
90
18
60
4
95
4
90
9
80
2
90
4
75
3
95
2
95
11
90
6
90
2

Gender
0
0
1
0
0
0
1
1...

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Anonymous
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