We have given data with variable Gender , Age , Prior Experience , Beta Experience , Education and Annual salary in $
Now we need to find Mean ,Median and Standard deviation of salary based on different categories
1) Based on Gender ( here given 0 , 1 for Female or Male )
2) Based on Education ( Less than 4 , 4 , greater than 4 )
3) Based on Age ( Young (age<34) , Middle age (34 Age < 50) , Older(Age 50) )
{ Print data for required labels only }
Employee | Gender | Age | Education | Annual Salary |
1 | 1 | 39 | 4 | 63900 |
2 | 0 | 44 | 6 | 84000 |
3 | 0 | 24 | 4 | 45600 |
4 | 1 | 25 | 4 | 44200 |
5 | 0 | 56 | 8 | 156100 |
6 | 1 | 41 | 4 | 80300 |
7 | 1 | 33 | 6 | 50900 |
8 | 0 | 37 | 4 | 67100 |
9 | 1 | 51 | 6 | 137800 |
10 | 0 | 23 | 4 | 36600 |
11 | 0 | 31 | 6 | 61500 |
12 | 1 | 27 | 0 | 34800 |
13 | 0 | 47 | 4 | 67700 |
14 | 1 | 35 | 6 | 66200 |
15 | 1 | 29 | 0 | 28400 |
16 | 0 | 46 | 6 | 75900 |
17 | 1 | 50 | 4 | 106200 |
18 | 0 | 30 | 4 | 66200 |
19 | 1 | 34 | 4 | 58400 |
20 | 1 | 42 | 4 | 83900 |
21 | 1 | 51 | 8 | 134900 |
22 | 0 | 63 | 4 | 144600 |
23 | 0 | 28 | 4 | 55600 |
24 | 1 | 32 | 4 | 56500 |
25 | 0 | 55 | 6 | 143200 |
26 | 1 | 45 | 4 | 68700 |
27 | 0 | 34 | 2 | 34300 |
28 | 0 | 33 | 4 | 58600 |
29 | 1 | 23 | 4 | 48900 |
30 | 0 | 40 | 6 | 75800 |
31 | 1 | 48 | 4 | 88300 |
32 | 1 | 27 | 0 | 23000 |
For Q1
First we will find which observation represents male.
Male = 0
Sr no
Sr.No |
Male Obs No. |
Annual Salary |
|
1 |
2 |
84000 |
|
2 |
3 |
45600 |
|
3 |
5 |
156100 |
|
4 |
8 |
67100 |
|
5 |
10 |
36600 |
|
6 |
11 |
61500 |
|
7 |
13 |
67700 |
|
8 |
16 |
75900 |
|
9 |
18 |
66200 |
|
10 |
22 |
144600 |
|
11 |
23 |
55600 |
|
12 |
25 |
143200 |
|
13 |
27 |
34300 |
|
14 |
28 |
58600 |
|
15 |
30 |
75800 |
We sort Salary of males in Ascending Order
[1] 34300 36600 45600 55600 58600 61500 66200
67100 67700 75800
[11] 75900 84000 143200 144600 156100
Thus Mean Salary for Male = = (34300 + 36600 + .... +143200 +144600 + 156100) / 15
= 1172800 / 15
= 78186.67
Mean Salary for Male = 78187
Median Salary = ( n + 1 )/ 2 Obsn = 8th Obs ( As n= 15 is odd number )
Median Salary = 67100
Standard deviation =
Where = =
= [ (34300 -78187 )2 + ( 36600- 78187)2 + .... +(143200-78187)2 +(144600 -78187)2 +
(156100 -78187) 2 ]/ (15-1)
= 21018857333 / 14
= 1501346952
Hence Standard deviation = = 38747.22
Hence using similar formulas we will find mean , median and Standard deviation for every group
Mean (xi) =
Median =( n + 1 )/ 2 Obsn { if Observations (n ) are odd }
= ( [n/2 ]+ [n/2+1] )/ 2 { if Observations (n ) are even }
Standard deviation =
Where =
Now we will find which observation represents Female.
Since it is calcualted
Mean Median and Std Dev using above formulas
For females
Mean =69135.29 = 69135
Median = 63900
Standard deviation = 33321.52
part 2)
Based on Education ( Less than 4 , 4 , greater than 4 )
i ) Less than 4 ( Education < 4 )
Sr No. |
Less than 4 Obs No. |
Salary |
1 |
12 |
34800 |
2 |
15 |
28400 |
3 |
27 |
34300 |
4 |
32 |
23000 |
Sorted data
Xi = 23000 28400 34300 34800
Mean = = 30125
Median = 31350 { here n = 4 }
Standard deviation = 5568.587
ii ) Equal to 4
Sr . no |
4 Obs No. |
Salary |
1 |
1 |
63900 |
2 |
3 |
45600 |
3 |
4 |
44200 |
4 |
6 |
80300 |
5 |
8 |
67100 |
6 |
10 |
36600 |
7 |
13 |
67700 |
8 |
17 |
106200 |
9 |
18 |
66200 |
10 |
19 |
58400 |
11 |
20 |
83900 |
12 |
22 |
144600 |
13 |
23 |
55600 |
14 |
24 |
56500 |
15 |
26 |
68700 |
16 |
28 |
58600 |
17 |
29 |
48900 |
18 |
31 |
88300 |
Sorted data
Xi =
36600 44200 45600 48900 55600 56500 58400 58600 63900
66200
67100 67700 68700 80300 83900 88300 106200 144600
Mean = = 68961.11 = 68961
Median = 65050 { here n = 18 }
Standard deviation = 25475.83
i ) Greater than 4 ( Education > 4 )
Sr No |
Greater than 4 Obs No. |
Salary |
1 |
2 |
84000 |
2 |
5 |
156100 |
3 |
7 |
50900 |
4 |
9 |
137800 |
5 |
11 |
61500 |
6 |
14 |
66200 |
7 |
16 |
75900 |
8 |
21 |
134900 |
9 |
25 |
143200 |
10 |
30 |
75800 |
Sorted data
Xi = 50900 61500 66200 75800 75900 84000 134900 137800 143200 156100
Mean = = 98630
Median = 79950 { here n = 10 }
Standard deviation = 39580.41
part 3)
Based on Age ( Young (age<34) , Middle age (34 Age < 50) , Older(Age 50) )
i) Young (age<34)
Sr No |
age Obs No. |
age |
Salary |
1 |
3 |
24 |
45600 |
2 |
4 |
25 |
44200 |
3 |
7 |
33 |
50900 |
4 |
10 |
23 |
36600 |
5 |
11 |
31 |
61500 |
6 |
12 |
27 |
34800 |
7 |
15 |
29 |
28400 |
8 |
18 |
30 |
66200 |
9 |
23 |
28 |
55600 |
10 |
24 |
32 |
56500 |
11 |
28 |
33 |
58600 |
12 |
29 |
23 |
48900 |
13 |
32 |
27 |
23000 |
Sorted Data
Xi - 23000 28400 34800 36600 44200 45600 48900 50900 55600 56500 58600 61500 66200
Mean = = 46984.62
Median = 48900 { here n = 13 }
Standard deviation = 13182.18
ii) Middle age (34 Age < 50)
Sr No |
age Obs No. |
age |
Annually Salary |
1 |
1 |
39 |
63900 |
2 |
2 |
44 |
84000 |
3 |
6 |
41 |
80300 |
4 |
8 |
37 |
67100 |
5 |
13 |
47 |
67700 |
6 |
14 |
35 |
66200 |
7 |
16 |
46 |
75900 |
8 |
19 |
34 |
58400 |
9 |
20 |
42 |
83900 |
10 |
26 |
45 |
68700 |
11 |
27 |
34 |
34300 |
12 |
30 |
40 |
75800 |
13 |
31 |
48 |
88300 |
Sorted Data
Xi - 34300 58400 63900 66200 67100 67700 68700 75800 75900 80300 83900 84000 88300
Mean = = 70346.15
Median = 68700
Standard deviation = 14062.87
iii) Older ( Age 50)
Sr No |
age Obs No. |
age |
Annually Salary |
1 |
5 |
56 |
156100 |
2 |
9 |
51 |
137800 |
3 |
17 |
50 |
106200 |
4 |
21 |
51 |
134900 |
5 |
22 |
63 |
144600 |
6 |
25 |
55 |
143200 |
Sorted Data
Xi - 106200 134900 137800 143200 144600 156100
Mean = = 137133.3
Median = 140500
Standard deviation = 16820.19
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