Question 9 A small IT consulting firm has the following sala

Question 9

A small IT consulting firm has the following salaries (in thousands of dollars):

{21,33,57,49,41}.

Compute the standard deviation of the salaries to three decimal places.

Solution

21,33,57,49,41
Step 1:Add them up:
21+33+57+49+41 = 201

Step 2: Square your answer:
201 × 201 = 40401
…and divide by the number of items. We have 5 items in our example so:
40401 / 5 = 8080.2
Set this number aside for a moment.

Step 3: Take your set of original numbers from Step 1, and square them individually this time:
21^2+33^2+57^2+49^2+41^2= 8861

Step 4: Subtract the amount in Step 2 from the amount in Step 3.
8861 – 8080.2 = 780.8
Set this number aside for a moment.

Step 5: Subtract 1 from the number of items in your data set. For our example:
5 – 1 = 4

Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance:
780.8 / 4 = 195.2
How to find the sample variance and standard deviation: Standard Deviation

Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation:

195.2 = 13.971