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How to find standard deviation

  1. Aug 3, 2017 #1
    1. The problem statement, all variables and given/known data

    For the five data 0, 7, 8, 10, and 10 find the standard deviation.

    2. Relevant equations

    I know the formula:
    Z = (X-Mew)/Sigma
    Sigma = Standard Deviation
    Mew = Mean = 7
    X= score?
    Z= number of standard deviation=?

    3. The attempt at a solution
    I have found mean which is 7 but i dont know how to find Z & X. Some body please guide me.
  2. jcsd
  3. Aug 3, 2017 #2
    What is the definition of the standard deviation?
  4. Aug 3, 2017 #3


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    Homework Helper

    You are not being asked for Z, and all your X values are given. What you are missing is the sigma, or standard deviation.
    In case your google search for "how to calculate standard deviation" didn't return any results, here is a start.
    Standard deviation is defined as the square root of the variance, which is the average of the squared distances from the mean.
    In formulaic terms, you have:
    ## \sigma^2 = \frac{ \sum_{i = 1}^N (X_i-\mu)^2 }{N}##
    If these data refer to a sample and not the whole data set, then your denominator changes to (N-1). That's all.
  5. Aug 7, 2017 #4

    I was not aware of the formula provided in post#3. I thought there is only one formula. Through post#3 I am able to find out the difference between the two formulae. To use the one provided in post#3, all X values must be provided:

    Sigma^2 = ((0-7)^2 + (7-7)^2 + (8-7)^2 + (10-7)^2+ (10-7)^2)/5 = 68/5

    Therefore sigma= 3.7

    Thanks, God bless you.

  6. Aug 9, 2017 #5


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    Science Advisor
    Homework Helper
    Gold Member

    Yes you were. WBahn gave you link http://bfy.tw/DBqv
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