Question

Sample annual salaries​ (in thousands of​ dollars) for employees at a company are listed. 40  35  44  51  39  39  40  35  44  30  51  40  47 ​(a) Find the sample mean and sample standard deviation. ​(b) Each employee in the sample is given a ​$3000 raise. Find the sample mean and sample standard deviation for the revised data set. ​(c) Each employee in the sample takes a pay cut of ​$2000 from their 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)? ​(a) The sample mean is x overbarequals 41.2 thousand dollars. ​(Round to one decimal place as​ needed.) The sample standard deviation is sequals nothing thousand dollars.

Answer 1

(A)

Following table shows the calculations:

	X	(X-mean)^2
	40	1.44
	35	38.44
	44	7.84
	51	96.04
	39	4.84
	39	4.84
	40	1.44
	35	38.44
	44	7.84
	30	125.44
	51	96.04
	40	1.44
	47	33.64
Total	535	457.72

Sample size: n=13

The sample mean is

The sample standard deviation is

(b)

Now we need to add 3 to each data value. Following table shows the new data set and calculations:

	X	(X-mean)^2
	43	1.44
	38	38.44
	47	7.84
	54	96.04
	42	4.84
	42	4.84
	43	1.44
	38	38.44
	47	7.84
	33	125.44
	54	96.04
	43	1.44
	50	33.64
Total	574	457.72

Sample size: n=13

The sample mean is

The sample standard deviation is

(c)

Now we need to subtract 2 from each data value. Following table shows the new data set and calculations:

	X	(X-mean)^2
	38	1.44
	33	38.44
	42	7.84
	49	96.04
	37	4.84
	37	4.84
	38	1.44
	33	38.44
	42	7.84
	28	125.44
	49	96.04
	38	1.44
	45	33.64
Total	509	457.72

Sample size: n=13

The sample mean is

The sample standard deviation is

(d)

Mean is added or subtracted by same quantity added or subtracted to each data value.

The standard deviation is same in each case.