Question

HELP?!
mean and standard deviation for ...
2,3,4,5,5,8,9,12

mean = 6

Answer 1

The mean is 6, yes. Do you know how to find the standard deviation?

Answer 2

not really

Answer 3

There are two different versions of the standard deviation: there's the sample standard deviation, and the population standard deviation. My guess is that the population version is the one to be used, but I'll tell you both versions.

Having found the mean of the values, take each value, subtract the mean, and square the result. Sum all of those together, and divide by the number of samples. Take the square root of the result and you've got the population SD.

For the sample SD, the procedure is similar, except you divide by the number of samples - 1.

Have you done any of these problems in class? If you have, and got nice round numbers for your answers, my guess is this problem should be done with the population SD, because you will get a nice round number. If you do it with the sample SD, you'll end up with a square root in the answer, and not a nice round number.

Answer 4

i did all that i think but not sure. the answer i got for that was 3.16

Answer 5

Yeah, the sum of the squared differences is 16+9+4+1+1+4+9+36 = 80. Divide that by 8 samples = 10, and \(\sqrt{10} \approx 3.1623\)

Answer 6

If you were doing the sample SD, you'd have
\[\sqrt{\frac{80}{7}}\approx 3.38062\]

Answer 7

it says just standard deviation and to round to the nearest hundredth

Answer 8

where do u get the '7' from?

Answer 9

Number of samples - 1

Answer 10

No, I can't explain in any convincing fashion why that makes it better (and I think with that one you also subtract the mean of the entire population, not the sample)...

Answer 11

i just need to know how to do it so i can finish the rest of my assignment ... no clue about the "number of samples"

Answer 12

Your samples are 2,3,4,5,5,8,9,12, so you have 8 of them, right? The population standard deviation assumes that you are taking the standard deviation of all of the data. If instead you had just a sampling of the data (say there are thousands of test scores, but you've just got 10 of them, and want to use them to find some statistics about the whole set) then you would use the sample standard deviation. If you haven't been taught about both versions, then the population standard deviation (the one where you got 3.16) is probably the right one to use.

Answer 13

i still dont understand where you got the 7 from

Answer 14

Well, the definition of the sample standard deviation has you divide the sum of the squared differences by (number of samples - 1) instead of (number of samples). But probably best to just forget about it entirely if it doesn't look familiar, and stick to the population standard deviation, where you divide by the number of samples.