Question

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

43, 54, 55, 51, 33, 33, 43, 54, 55, 26, 51, 43, 46

​(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)?

Answer 1

a)

X	(X - X̄)²
43	4.64
54	78.25
55	96.95
51	34.18
33	147.72
33	147.72
43	4.639
54	78.254
55	96.947
26	366.870
51	34.178
43	4.639
46	0.716

	X	(X - X̄)²
total sum	587	1095.69
n	13	13

mean =    ΣX/n =    587.000   /   13   =   45.1538(thousands of​ dollars) = $45153.85

                      
  
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (1095.6923/12)   =       9.5551(thousands of​ dollars) = $9555.1

b) new sample mean = 45153.85 - 3000 = 42153.85

std dev remain unchanged = 9555.1

c)

new sample mean = 45153.85 -2000 = 43153.85

std dev remain unchanged = 9555.1

d)

if each data value is increase/ decrease by a value , Sample mean decreases/ increases by same value resp.

but std dev do not change