Question

Find the mean and standard deviation of each data set. Round to the nearst hundredth.

1. 4 8 5 12 3 9 5 2

Answer 1

i already know the mean i just dont know how to find the standard deviation.

Answer 2

You should have found that the mean is 6.


Now subtract the sample mean from EVERY data value:

4-6 = -2
8-6 = 2
5-6 = -1
12-6 = 6
3-6 = -3
9-6 = 3
5-6 = -1
2-6 = -4

Answer 3

So the differences are: -2, 2, -1, 6, -3, 3, -1, -4

Answer 4

Now square each difference:

(-2)^2 = 4
(2)^2 = 4
(-1)^2 = 1
(6)^2 = 36
(-3)^2 = 9
(3)^2 = 9
(-1)^2 = 1
(-4)^2 = 16

Answer 5

So we have the squares 4, 4, 1, 36, 9, 9, 1, 16

Answer 6

Now add up each square:

4+4+1+36+9+9+1+16 = 80

Answer 7

Next, divide that sum by n-1 = 8-1 = 7 to get 80/7 = 11.4285714285714



So the sample variance is roughly 11.4285714285714


To find the sample standard deviation, just take the square root of the sample variance.

Answer 8

Oooh... Thanks! I think I understand now

Answer 9

Yes, there are a lot of steps, but that's great.

Answer 10

To speed things up, you can just use a calculator (which should be allowed)

Answer 11

KK :)