Question

So the question is saying to find the mean and the standard deviation for these numbers: 4,8,5,12,3,9,5,2. I know how to get the mean, but im completely lost with the standard deviation. could someone help me?

Answer 1

what did you get for the mean

Answer 2

6

Answer 3

your first step is to subtract the 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 4

The differences are: -2, 2, -1, 6, -3, 3, -1, -4

Square these differences to get

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

Then add up these squares

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

Answer 5

If you're looking for the population standard deviation, then divide by n = 8 (since there are 8 original data values)

80/8 = 10

So the population variance is 10

Take the square root of this to get the population standard deviation

sqrt(10) = 3.16227766016838


So the population standard deviation is roughly 3.16227766016838

Answer 6

oh my goodness, this was so helpful. thank you so much!!

Answer 7

you're welcome, this is a pain to do by hand (esp for large sets which are more common in the real world), so calculators are very handy since most can calculate the standard deviations in one step

Answer 8

but it helps to know how to do it step by step like this

Answer 9

yeah thank you so much for working it out for me.

Answer 10

sure thing