Question

1. A.) Survey on the “Leadership Behavior” of 15 managers was conducted. Twenty-five employee respondents were taken. The results are found below using an instrument with how frequently the manager engages in the behavior described by them.

	5 Always (A)	4 Often (Oft)	3 Occasionally (Occ)	2 Seldom (S)	1 Never (N)
1. He makes his attitude clear to the group	4	13	3	3	2
2. He is easy to understand.	3	12	6	2	2
3. He schedules the work to be done.	5	13	3	2	2
4. He maintains definite standards of performance.	6	12	4	2	1
5. He is willing to make changes.	2	16	3	2	2

Question:

1. How did the manager behave in each statement as perceived by the employee respondents?
2. Determine also the standard deviation.

2. The same instrument was administered by the 15 managers and resulted into the data below.

	5 Always (A)	4 Often (Oft)	3 Occasionally (Occ)	2 Seldom (S)	1 Never (N)
1. He makes his attitude clear to the group.	4	5	3	2	1
2. He is easy to understand.	3	7	2	2	1
3. He schedules the work to be done.	4	5	2	2	2
4. He maintains definite standards of performance.	4	7	2	1	1
5. He is willing to make changes.	2	8	2	2	1

Questions 1.) How did the managers rate themselves in each of the statement?

    2.) Compute also the standard deviation.

Answer 1

From Employee survey-

For Question 1

Mean = (4*5+13*4+3*3+3*2+2*1)/25 = 3.56

Variance = (4*(3.56-5)^2+13*(3.56-4)^2+3*(3.56-3)^2+3*(3.56-2)^2+2*(3.56-1)^2)/25 = 1.2864

Std Dev = Sqrt(1.2864) = 1.1342

For Question 2

Mean = (3*5+12*4+6*3+2*2+2*1)/25 = 3.48

Variance = (3*(3.48-5)^2+12*(3.48-4)^2+6*(3.48-3)^2+2*(3.48-2)^2+2*(3.48-1)^2)/25 = 1.1296

Std Dev = Sqrt(Variance) = 1.0628

For Question 3

Mean = (5*5+13*4+3*3+2*2+2*1)/25 = 3.68

Variance = (5*(3.68-5)^2+13*(3.68-4)^2+3*(3.68-3)^2+2*(3.68-2)^2+2*(3.68-1)^2)/25 = 1.2576

Std Dev = Sqrt(Variance) = 1.121

For Question 4

Mean = (6*5+12*4+4*3+2*2+1*1)/25 = 3.8

Variance = (6*(3.8-5)^2+12*(3.8-4)^2+4*(3.8-3)^2+2*(3.8-2)^2+1*(3.8-1)^2)/25 = 1.04

Std Dev = Sqrt(Variance) = 1.0198

For Question 5

Mean = (2*5+16*4+3*3+2*2+2*1)/25 = 3.56

Variance = (2*(3.56-5)^2+16*(3.56-4)^2+3*(3.56-3)^2+2*(3.56-2)^2+2*(3.56-1)^2)/25 = 1.0464

Std Dev = Sqrt(Variance) = 1.0229

Tabulating all the results, we get

	Question 1	Question 2	Question 3	Question 4	Question 5
Mean	3.56	3.48	3.68	3.8	3.56
Variance	1.2864	1.1296	1.2576	1.04	1.0464
Std Dev	1.134196	1.062826	1.121428	1.019804	1.022937

Considering the low Std Dev and the closeness of Mean for Question 4 to value 4, we can definitely say that the employees rate their managers "He often maintains definite standards of performance.". For other question, they have rate their managers in between "Often" to "Occasionally"

From Manager Survey-

For Question 1

Mean = (4*5+5*4+3*3+2*2+1*1)/15 = 3.6

Variance = (4*(3.6-5)^2+5*(3.6-4)^2+3*(3.6-3)^2+2*(3.6-2)^2+1*(3.6-1)^2)/15 = 1.44

Std Dev = Sqrt(Variance) = 1.2

For Question 2

Mean = (3*5+7*4+2*3+2*2+1*1)/15 = 3.6

Variance = (3*(3.6-5)^2+7*(3.6-4)^2+2*(3.6-3)^2+2*(3.6-2)^2+1*(3.6-1)^2)/15 = 1.3067

Std Dev = Sqrt(Variance) = 1.1431

For Question 3

Mean = (4*5+5*4+2*3+2*2+2*1)/15 = 3.4667

Variance = (4*(3.4667-5)^2+5*(3.4667-4)^2+2*(3.4667-3)^2+2*(3.4667-2)^2+2*(3.4667-1)^2)/15 = 1.8489

Std Dev = Sqrt(Variance) = 1.3597

For Question 4

Mean = (4*5+7*4+2*3+1*2+1*1)/15 = 3.8

Variance = (4*(3.8-5)^2+7*(3.8-4)^2+2*(3.8-3)^2+1*(3.8-2)^2+1*(3.8-1)^2)/15 = 1.2266

Std Dev = Sqrt(Variance) = 1.1075

For Question 5

Mean = (2*5+8*4+2*3+2*2+1*1)/15 = 3.5333

Variance = (2*(3.5333-5)^2+8*(3.5333-4)^2+2*(3.5333-3)^2+2*(3.5333-2)^2+1*(3.5333-1)^2)/15 = 1.1822

Std Dev = Sqrt(Variance) = 1.0873

Tabulating all the results, we get,

	Question 1	Question 2	Question 3	Question 4	Question 5
Mean	3.6	3.6	3.466667	3.8	3.533333
Variance	1.44	1.306667	1.848889	1.226667	1.182222
Std Dev	1.2	1.143095	1.359739	1.10755	1.0873

In this case too, the manager rate themselves as "He often maintains definite standards of performance." and for the other question they rate themselves between "Often" to "Occasionally"

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