Question

Sample annual salaries (in thousands of dollars) for employees at a company are listed.

55 38 53 58 41 41 55 38 53 29 58 55 43

(a) Find the sample mean and the sample standard deviation.

(b) Each employee in the sample is given a $5000 raise. Find the sample mean and the sample standard deviation for the revised data set.

(c) each employee in the sample takes a pay cut of $2000 from the original salary. Find the sample mean and the sample standard deviation for the revised data set.

(d) What can you conclude from the results of (a), (b), and (c)?

Answer 1

The calculations in excel is given below

salary(x)	(x-xbar)^2	y=X+5	(y-ybar)^2	z=x-2	(z-zbar)^2
55	56.829	60	56.829	53	56.829
38	89.52	43	89.52	36	89.52
53	30.675	58	30.675	51	30.675
58	111.06	63	111.06	56	111.06
41	41.751	46	41.751	39	41.751
41	41.751	46	41.751	39	41.751
55	56.829	60	56.829	53	56.829
38	89.52	43	89.52	36	89.52
53	30.675	58	30.675	51	30.675
29	340.827	34	340.827	27	340.827
58	111.06	63	111.06	56	111.06
55	56.829	60	56.829	53	56.829
43	19.905	48	19.905	41	19.905
xbar	Sx	ybar	Sy	zbar	Sz
47.4615	9.4747	52.4615	9.4747	45.4615	9.4747

(a) Find the sample mean and the sample standard deviation.

The sample mean is $47.4615 and sample standard deviation is $9.4747

b) Each employee in the sample is given a $5000 raise. Find the sample mean and the sample standard deviation .

The sample mean is $52.1615 K and sample standard deviation is $9.4747

(c) each employee in the sample takes a pay cut of $2000 from the original salary. Find the sample mean and the sample standard deviation for the revised data set.

The sample mean is $45.1615 K and sample standard deviation is $9.4747

D) From resulta a, b and c,we conclude that if the increment/ decrement in the salary implies that sample mean is also get increased/decreased but no change in sample standard deviation.

In short the sample mean is affected by change in origin whereas sample standard deviation does not affected.