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Math Help - Standard Deviation using 2 numbers?

  1. #1
    jdc
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    Standard Deviation using 2 numbers?

    Cheers all.
    I am a programmer charged with finding the standard deviation of a number. It has been many years since I did any statistics work. I could use some help. Google has me lost...

    We have an online questionnaire taken by students. For each question, we have two mean scores. The first is the mean (average) score of all student taking the questionaire. The second is the mean (average) score of a particular sub-set of these same students.

    Example numbers. 1st question: I get a mean for my first group of 5.09 and 3.83 for my sub-set group. How do I find the standard deviation of the 3.83 as it relates to 5.09?

    If possible, can anyone tell me the steps as I would have to do them on a simple calculator. In code, I cannot do math using symbols like Sigma and and mean... Example of how I tried this.

    I tried:
    1) find the mean. I have 5.09. I figured this is then mean I should use.
    2) subtract the mean from the first number. -1.26
    3) square the result = 1.5876
    4) add the results (only one number) so: 1.5876
    5) divide by n (1) = 1.5876
    6) square the root = 1.26.

    For some reason that doesn't seem right. Thoughts?

    Thanks for any insite.
    Jdc...
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  2. #2
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    The standard deviation of a collection of numbers is the square root of the variance which is, intuitively, a measure of how much the individual numbers differ from the average (mean) of the collection.

    Your steps describe the formula for calculating the standard deviation but the numbers you are using are not applicable to the formula. You need the individual scores to calculate deviation. The deviation of the subgroup could be much smaller than that of the whole group or much larger depending on the nature of the subgroup and the individual answers. For example consider the following distribution:

    {0,1,1,1,1,1,1,2,3,3,3,3,3,3,4}

    The mean is 2, the standard deviation of the whole group is 1.15 If we choose the subgroup {0,1,2,3,4} the mean is 2 but the standard deviation is 1.41. Choosing the subgroup {2} leads to a mean of 2 and stanard deviation of 0.

    Now with that being said if you are looking for the standard deviation of the 2 averages, your procedure is almost correct:

    1. Find the average of the 2 averages: (5.09 + 3.83)/2 = 4.46
    2. Find the difference between the average and each number and square it.
    (4.46-5.09)^2 = .3969
    (4.46-3.83)^2 = .3969
    3. add the numbers .3969+.3969 = 0.7938
    4. Divide by the number of values inthe collection (2) = 0.7938/2 = .3969
    5. square root the number: sqrt(.3969) = .63

    Notice that |4.46-5.09| = |4.46-3.83| = .63
    For two numbers the standard deviation is just the difference between either number and the average. Intuitively this makes sense.

    Is the standard deviation of the two averages what you are after?
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  3. #3
    jdc
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    Reply: Standard Deviation for two numbers.

    iknowone - Thanks,
    You obviously know your stats.

    To your last question: >> "Is the standard deviation of the two averages what you are after?"

    Reply: I'm not sure.

    As mentioned, it's been a long while since I've done any statistics and standard deviations math. 15 years of programming and this is my program using standard deviation.

    The department this is for gave me was a lot of raw data and a report layout to follow. I know the 3.83 is the mean of the subset group and the 5.09 is the mean of all students for the same question. If I'm stating this correctly, the 5.09 is the main average, since it applies to the overall population of students. From this I gather they want to know how 3.83 deviates from from the 5.09 average. I hope.

    I'll prompt the powers that be for a more precise definition of what they want and show them your figures.

    thanks for your help. It is much appreciated.
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