Question

Sample annual salaries​ (in thousands of​ dollars) for employees at a company are listed. 43  44  55  50  38  38  43  44  55  32  50  43  53 ​(a) Find the sample mean and sample standard deviation. ​(b) Each employee in the sample is given a ​$5,000 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 ​$3,000 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

SolutionA:

Rcode:salaries <- c(
43000,
44000,
55000,
50000,
38000,
38000,
43000,
44000,
55000,
32000,
50000,
43000,
53000)
mean(salaries)
sd(salaries)

sample mean=50230.77

samplesd=7037.446

Solutionb:

Rcode:Salaryraise <- salaries+5000
print(Salaryraise)
mean(Salaryraise)
sd(Salaryraise)

sample mean_revised=50230.77

sample_sd_Revised=7037.446

sample mean and sample standard deviation for the revised data set. ​ are 50230.77 and 7037.446

Solutionc:

Rcode:

pay_cut <- salaries-3000
print(pay_cut)
mean(pay_cut)
sd(pay_cut)

sample mean=42230.77

samplesd=7037.446

Solutiond:

if we increase by orginal amount by a constant number mean increases and increase=orignial mean+increase

if we decrease by orginal amount by a constant number mean decreases =orignial mean-decrease

But Standard deviation remains same .in the above three cases sd remained constant 7037.446