Question

The following is the age distribution of 1000 working employees working in an organization

Age(years)	20-25	25-30	30-35	35-40	40-45	45-50	50-55	55-60	60-65
Number of persons	30	160	210	180	145	105	70	60	40

Due to continuous losses, it is desired to bring down the manpower according the following scheme

1. Retrench the first 15% from the lower age group

2. Absorb the next 45% in the other branches.

3. Make 10% from the highest age group permanently retire, if necessary.

a) Calculate the age limits of the persons retained and those transferred to other departments.

b) Find the average age of those retained and those transferred to other branches

c) Calculate the standard deviation of the employee retained and transferred

d) Compute the coefficient of skewness of the employees retained and transferred

Comment on your result

Answer 1

Age(years)	20-25	25-30	30-35	35-40	40-45	45-50	50-55	55-60	60-65
Number of persons	30	160	210	180	145	105	70	60	40
cumulative	30	190	400	580	725	830	900	960	1000

we are retrenching, that is, laying off first 15% from the lower age group

thus 150 of the 1000 employee are cut off starting from the lower age group

so the lowest income group is gone.

and we are left with the following

Age(years)	25-30	30-35	35-40	40-45	45-50	50-55	55-60	60-65
Number of persons	40	210	180	145	105	70	60	40

the next 45% is transferred

thus 450 of the next employees are transfered which looks like this

Age(years)	25-30	30-35	35-40	40-45
Number of persons	40	210	180	20

and we are left with the following

Age(years)	40-45	45-50	50-55	55-60	60-65
Number of persons	125	105	70	60	40

also we are permanently retiring 10% from the highest age group,that is 4 persons, so we are left with

Age(years)	40-45	45-50	50-55	55-60	60-65
Number of persons	125	105	70	60	36

a)the transfered employees are

Age(years)	25-30	30-35	35-40	40-45
Number of persons	40	210	180	20

the retained employees are

Age(years)	40-45	45-50	50-55	55-60	60-65
Number of persons	125	105	70	60	36

b)for finding the average we calculate the midpoint of every class and we get the following

Age(years)	20-25	25-30	30-35	35-40	40-45	45-50	50-55	55-60	60-65
mid point	22.5	27.5	32.5	37.5	42.5	47.5	52.5	57.5	62.5

Thus the average=$\sum (mid\ point*frequency\ of\ that\ class)/total\ frequency$

therefore average of the transfered employee= 34.5

average of the retained employees=49.68

c)Standard deviation=$\sqrt{1/n\sum(m.p-mean)^2*freq}$ , m.p=mid point of class, n=total frequency

therefore standard deviation of retained employees=6.56

standard deviation of transfered employees=3.56

d)skewness=

skewness of retained employee=(49.68-42.5)/6.56 = 1.09

skewness of transfered employee=(34.5-32.5)/3.56= 0.56

we can see that both the data set are positively skewed with retained employee being more positively skewed than transfered employee and transfered employee is quite close to symmetry