# Thread: how to calculate a z score

1. ## how to calculate a z score

hi,

well i have a question regarding a z-score calculation.

i have an array of values like this:

(23,45,32,12,65,34,67,22)

and a population of such arrays

(21,35,2,12,5,34,57,12)
(28,46,92,15,54,44,87,32)
(43,41,12,82,52,54,67,52)
(63,5,52,19,61,74,97,2)

to calculate a z score i would need to somehow derive a single number from my sample and a mean from my population. but the problem is i'm quite insecure in calculating an average from a single array like:

(23,45,32,12,65,34,67,22) -> avrg == mean =37.5

to get this single number and then doing the same thing for every single outcome in my population. is there an alternative??

how to calculate a z score for such a case ?

thank you!

ps

this is basically a type of vector manipulation that i'm not very familiar with ..

so what i want to do is to calculate a z-score for my experiment that has a set of outcomes compared to a population of experiments where every exper. in my population is consisted of also a set of outcomes

2. First, the numbers in your arrays are all integers, so they clearly aren't normally distributed.

Ignoring that problem, what exactly are you trying to test? Do the eight entries in your array follow the same distribution, or do they each have individual distributions? Assuming the latter, read up about the Multivariate normal distribution and Hotelling's T-square distribution.

And when you talk about "doing the same thing for every single outcome in my population," are you implying that the population is finite?

3. ok,

an array represents a field trip in which i did some sampling. every sample produced some quantity that is an integer value. samples are totally independent from each other, meaning first number represents the number of smokers in my sample, the second represents the number of birds i saw in that trip and so on.... but in every field trip i monitored the same things so my question now is (IF THIS IS LEGAL TO ASK!), once i change the location of my field trip how significant the difference (expressed through z score) of my last trip is with respect with the previous ones i took!

4. Yeah, you'll probably want to look into what squareandrare was talking about. Since each element in the vector represents something different you do NOT want to just take an average. That average doesn't make any sense.

If it's 78 degrees in Ames today and my friend Steve at 13 hot dogs today does (78+13)/2 represent anything meaningful? No.

But looking into the multivariate options that squareandrare suggested will allow you look at your next trip in comparison to the previous ones overall while allowing it to make sense.

5. Originally Posted by Dason
If it's 78 degrees in Ames today and my friend Steve ate 13 hot dogs today does (78+13)/2 represent anything meaningful? No.
lmao! It represents a funny joke

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