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 m

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Home>Business & Finance homework help>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 m

Data

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

Requirement 1

Salary Compa Midpoint Age Performance Rating Service Length Gender Raise Degree Gender 1 Grade
Data Type Ratio Scale Ratio Scale Ratio Scale Ratio Scale Ordnal Scale Ratio Scale Nominal Scale Ratio Scale Nominal Scale Nominal Scale Ordinal Scale
Salary: Salary data is ratio level as this satisifies satisfies all properties of the data measurement inclduing identity, magnitude, equal intervals, and meaningful zero value.
Compa: Compa salary data is ratio level as this satisifies satisfies all properties of the data measurement inclduing identity, magnitude, equal intervals, and meaningful zero value.
Midpoint Salary: Midpoint salary data is ratio level as this satisifies satisfies all properties of the data measurement inclduing identity, magnitude, equal intervals, and meaningful zero value.
Age: Age data is ratio level as this satisifies satisfies first three properties of the data measurement inclduing identity, magnitude, equal intervals. This this data zero value is not meaningful.
Performance Rating: Performance Rating data is ordinal scale as this satisfies firrst two properties of the data measurement inclduing identity, and magnitude.
Service Lenght: Service length data is ratio level as this satisifies all properties of the data measurement inclduing identity, magnitude, equal intervals, and meaningful zero value.
Gender: Gender data is nominal level as this satisifies only first property of the data measurement. Based on the data, ranking among the observation cannot be made here.
Percentage of Last Raise: Percentage of Last Raise: data is ratio level as this satisifies all properties of the data measurement inclduing identity, magnitude, equal intervals, and meaningful zero value.
Degree: Degree data is nominal level as this satisifies only first property of the data measurement. Based on the data, ranking among the observation cannot be made here.
Gender1: Gender 1 data is nominal level as this satisifies only first property of the data measurement. Based on the data, ranking among the observation cannot be made here.
Grade: Grade data is ordinal scale as this satisfies firrst two properties of the data measurement inclduing identity, and magnitude.

Requirement 2(a)

Mean, Standrd Deviation, and Range of Entire Salary Data Set
ID Salary Gender The mean, standrd deviation, and range of entire (male and female employees) salary data set are $45.57, $19.381, and $56.90 respectively.
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 45.8 M
42 22.4 F
43 75.6 F
44 61.3 M
45 59.7 F
46 55.1 M
47 63.8 M
48 62.8 F
49 64 M
50 66.3 M
Mean 45.57
Standard Deviation 19.381
Range 56.90

Requirement 2(b)

Mean, Standrd Deviation, and Range of Salary of Male Employees
ID Salary Gender The mean, standrd deviation, and range of male employees salary data set are $52.792, $17.992, and $54.20 respectively.
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

Requirement 2(c)

Mean, Standrd Deviation, and Range of Salary of Female Employees
ID Salary Gender The mean, standrd deviation, and range of female employees salary data set are $38.348, $18.289, and $53.80 respectively.
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

Requirement 3(a)

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 45.8 M
42 22.4 F
43 75.6 F
44 61.3 M
45 59.7 F
46 55.1 M
47 63.8 M
48 62.8 F
49 64 M
50 66.3 M
First Quartile Range 24.6
Second Quartile Range 43.55
Third Quartile Range 61.3
Interquartile Range 36.70

Requirement 3(b)

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

Requirement 3(c)

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

Requirement 3(d)

Comparison of the First, Second & Third Quartiles and Interquartile Range of the Male and Female Salary Data: Whereas the first, second & third quartiles and interquartile range of female salary are 23.8, 34.4, 55.1 and 31.30 respectively, the first, second & third quartiles and interquartile range of male salary are 45.3, 60.8, 64, and 18.70 respectively. Here, from the observation of the first, second & third quartiles and interquartile range of male and female salary, it can be said that as compared to that of female’s salary, male’s salary is more dispersed.

Requirement 4(a)

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 Lower Range Upper Rage
Mean Plus Minus One Standard Deviation 34.80 17.99
Mean Plus Minus Two Standard Deviation 16.81 88.78
Mean Plus Minus Three Standard Deviation -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 normally distributed.

Requirement 4(b)

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 Lower Range Upper Rage
Mean Plus Minus One Standard Deviation 20.06 56.64
Mean Plus Minus Two Standard Deviation 1.77 74.93
Mean Plus Minus Three Standard Deviation -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.

Sheet1

5
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?