Question

4. Consider a large company where the average wage of workers is $15 per hour, but there is a spread of wages from minimum wage to $35 per hour.

(a) After a contract negotiation, all workers receive a $2 per hour raise. What happens to the standard deviation of hourly wages?

A) No change

B) It goes up by $2 per hour

C) It goes up by $4 per hour

D) It goes up by 4 dollars-square per hour

E) It goes up by $4 per hour-square

F) Can't tell from the information given.

(b) The annual cost-of-living adjustment is 3%. After the cost-of-living adjustment, what happens to the standard deviation of hourly wages?

A) No change

B) It goes up by 3%

C) It goes up by 9%

D) Can't tell from the information given.

5. To exercise your ability to calculate groupwise quantities, use the swimming records in SwimRecords in MosaicData and calculate the mean and minimum swimming time for the subset. (Answers have been rounded to one decimal place.)

(a) Record times for women: • Mean: 47.8 53.5 54.7 57.3 61.4 63.4 65.2 73.8 84.2

• Minimum: 47.8 53.5 54.7 57.3 61.4 63.4 65.2 73.8 84.2

(b) All records before 1920. Hint: You can construct a new variable by running the command Old = SwimRecords$year <20

• Mean: 47.8 53.5 54.7 57.3 61.4 63.4 65.2 73.8 84.2

• Minimum: 47.8 53.5 54.7 57.3 61.4 63.4 65.2 73.8 84.2

(c) All records that are slower than 60 seconds.

(Hint: Think what “slower" means in terms of the swimming times.)

• Mean: 47.8 53.8 54.7 60.2 61.6 63.4 65.2 69.6 84.2

• Minimum: 47.8 53.8 54.7 60.2 61.6 63.4 65.2 69.6 84.2

Answer 1

4a )

as $2 is added to each workers salary, nothing would happen to the standard deviation
Hence the correct choice is A

b)

In this case all values would change by 3% of thier original values , hence the standard deviation would also increase by 3%

This can easily be proved in excel, please see the screenshots below

Please note that we can answer only 1 question at a time , as per the answering guidelines