What is the standard deviation for 37, 50, 81, 57, 43, 36, 75, 57, 51?

Answer 1

37, 50, 81, 57, 43, 36, 75, 57, 51

Mean = (37 + 50 + 81 + 57 + 43 + 36 + 75 + 57 + 51)/9
Mean = (487/9)
Mean = 54.11

SD = sqrt(σ)
Variance = σ^2

σ^2 = ((37 - 54.11)^2 + (50 - 54.11)^2 + (81 - 54.11)^2 + (57 - 54.11)^2 + (43 - 54.11)^2 + (36 - 54.11)^2 + (75 - 54.11)^2 + (57 - 54.11)^2 + (51 - 54.11)^2)/9

σ^2 = ((-17.11)^2 + (-4.11)^2 + (26.89)^2 + (2.89)^2 + (-11.11)^2 + (-18.11)^2 + (20.89)^2 + (2.89)^2 + (-3.11)^2)/9

σ^2 = (292.7521 + 16.8921 + 723.0721 + 8.3521 + 123.4321 + 327.9721 + 436.3921 + 8.3521 + 9.6721)/9

σ^2 = (1946.8889)/9

σ^2 = 216.3209889

SD = 14.71

Answer 2

First, calculate the mean and determine N.
Remember, the mean is the sum of scores divided by N where N is the number of scores.

mean = (37+50+81+57+43+36+75+57+51)/9 = 54.11

Then, square the difference of the mean and the score
note: get the absolute value

ex.
37 - 54.11 = 17.11 sqrd = 292.7521
50 - 54.11 = 4.11 sqrd = 16.8921
81 - 54.11 =
57 - 54.11 =
43 - 54.11 =
36 - 54.11 =
75 - 54.11 =
57 - 54.11 =
51 - 54.11 =

add these up and divide by N-1
ex.
(292.7521 + 16.8921 + .... ) / (N -1)
(292.7521 + 16.8921 + .... ) / (9 -1)

then get the square root of the answer...

sorry i dont have a calcu right here now so i cant compute it for you. hope it helps...

Answer 3

standard dev = 14.707