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I am new to Standard Deviation. I have taken a 2 small samples of Data and obtained the mean, and Standard Deviation.enter image description here

I have copied and pasted a picture of my spreadsheet.

As you can see i have worked out the SD and mean of each group.

I have subsequenyly worked out a combined average, and then worked out the differences from combined average from each of the seperate averages.

I then calculated the combined SD using the following Excel formula.

Blockquote

=SQRT((A10*((C13^2)+(C17^2)))+(E10*((G13^2)+(G17^2)))/(A10+E10))

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I cant get my head round how the SD of each sample is 0, yet the combined SD is 1.17. Can someone please explain this? Maybe i have calculated the combined SD incorrectly?

Mr Assistance
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1 Answers1

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I think you're calculating things correctly.

Each sampling taken separately has a standard deviation of $0$ because every item is the same price in the sample. There is no variation.

But when you combine the samples into one, now you have a variation, so the standard deviation is greater than $0$.

John
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  • Thanks for confirming the calculation is correct. I initially had different prices in my samples but then i set them all the same which led me to question things. Say i combined the Samples into 1. The Standard deviation of the one sample = 0.522. Why does this differ from combining the 2 individual Samples? – Mr Assistance Aug 07 '14 at 20:43
  • @MrAssistance The total variance is the sum of the variances inside the groups and the variances between the groups.

    Example:

    Group 1: $1,2,3 \ $

    Group 2: $4,6,8 \ $

    variance inside the group 1=$2/3 \$

    variance inside the group 2=$8/3 \$

    The average of this two variance: $\frac{8/3+2/3}{2}=10/6$

    $\overline{x_1}=2$

    $\overline{x_2}=6$

    $\overline x_{12}=4$

    The variance between the 2 groups is $\frac{(2-4)^2+(6-4)^2}{2}=4=24/6$

    The total variance should be $10/6+24/6=34/6$

    You can proof this, if you calculate the variance of 1,2,3,4,6,8

     – callculus42 Aug 07 '14 at 23:16
  • Hello thanks for reply calculus. I went to a website and input my numbers into an online calculator which calculates the combined SD. My original stab at the combined SD is not correct, as per the snapshot of the spreadssheet i took. It appears one of my brackets are not placed correctly. The correct answer is in fact 0.4979. The website i used was http://conm.atozmath.com/CONM/Ch2_CombinedSD.aspx. – Mr Assistance Aug 09 '14 at 11:47
  • The correct excel formulat should be =SQRT((K12((M15^2)+(M19^2))+O12((Q15^2)+(Q19^2)))/(K12+O12)) – Mr Assistance Aug 09 '14 at 11:55