# combined standard deviation

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

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))

Blockquote

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?

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 $0$.
• @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 – callculus Aug 7 '14 at 23:16