Find the standard deviation of the data set below. Round your answer to three decimal places.

Question

3,5,7,7,9,11,12,13,15,17,18,19,19,19

Answer 1

The steps to find standard deviation are:

1) Find mean of the set (arithmetic average)

2) For each original # subtract the mean from it and square the result

3) Find the mean of the new set of #'s

4) Take the square roof of the new mean...

This last number is the standard deviation of the set

 

1) This set adds to 174... divide by 14 since there are 14 numbers in the original set

    174/14 = 12.42857

2)  (3-12.42857)² = (-9.42857)² = 88.89793

     (5-12.42857)² = (-7.42857)² = 55.18365

     (7-12.42857)² = (-5.42857)² = 29.46937

     (7-12.42857)² = (-5.42857)² = 29.46937

     (9-12.42857)² = (-3.42857)² = 11.75509

    (11-12.42857)² = (-1.42857)² = 2.04081

    (12-12.42857)² = (-0.42857)² = 0.18367

    (13-12.42857)² = 0.57143²    =  0.32653

    (15-12.42857)² = 2.57143²    =  6.61225

    (17-12.42857)² = 4.57143²    =  20.89797

    (18-12.42857)² = 5.57143²   =  31.04083

    (19-12.42857)² = 6.57143²   = 43.18369

    (19-12.42857)² = 6.57143²   = 43.18369

    (19-12.42857)² = 6.57143²   = 43.18369

                                                 __________

                                                  405.42854 /14 = 28.95918

 

4) √28.95918 = 5.38137

 

Rounding to 3 decimal places the standard deviation is 5.381

 

Answer 2

To determine the standard deviation, σ:

 

1. Calculate the mean (average) of all of the numbers. This is μ.

2. Calculate the difference between each number and the mean, μ

3. Square each of the numbers calculated in #2.

4. Calculate the mean (average) of the numbers in #3.

5. Take the square root of the number calculated in #4, this is the standard deviation, σ