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?
Stacey Warren - Expert brainly.com
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what did you get for the mean
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
Not the answer you are looking for? Search for more explanations.
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
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
oh my goodness, this was so helpful. thank you so much!!
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
but it helps to know how to do it step by step like this