The population standard deviation of the numbers 3, 8, 12, 17, and 25 is 7.563 correct to 3 decimal places. what happens if each of the five numbers is multiplied by 3

Let's figure this out as though we have no idea what the answer would be.

Step One
Find the new five numbers.
3*3, 8*3, 12*3, 17*3, 25*3
9 , 24 , 36, 51, 75

Step 2
Find the average
(9 + 24 + 36 + 51 + 75)/5 = 195/5 = 39

Step 3
Subtract the individual numbers from the average
(39 - 9) = 30
(39 -24) = 15
(39 - 36) = 3
(39 - 51) = - 12
(39 - 75) = -36

Step 4 
Square the results from Step 3
30^2 = 900
15^2 = 225
3^2 = 9
(-12)^2 = 144
(-36)^2 = 1296

Step 5
Take the average of the results from step 4
(900 + 225 + 9 + 144 + 1296)/5
2574 / 5 = 514.8

Step 6
Take the square root of the result from step 5
deviation = sqrt(514.8)
deviation = 22.689

Step seven 
Compare the two standard deviations.
s2/s1 = 22.689 / 7.563 = 3

Conclusion
If you are given 1 set of numbers to find a population standard deviation and you multiply each member by a, then the result will be a * the standard population deviation of the first set of numbers.

Note
Your calculator will do this as well, but you have to know how to enter the data into your calculator. That requires that you follow the directions carefully.