How do you find the mean deviation and standard deviation of a set of data?

Question

hartnn · Answer

Mean is just the average 
Mean = (sum of all data points)/ (total number of data points)

anonymous · Answer

yeah but for the mean deviation what do you do?

hartnn · Answer

ok, there is formula, let me post it.

hartnn · Answer

$\large SD = \sqrt{\dfrac{x_1^2+x_2^2+...+x_n^2}{n}}$
where, n = total number of data points and x's are the actual data points

hartnn · Answer

you might want to know about variance also.

hartnn · Answer

$\large V=SD^2 = {\dfrac{x_1^2+x_2^2+...+x_n^2}{n}}$

hartnn · Answer

wait, just a correction

anonymous · Answer

the equation i have been using is i find the mean, and then subtract the original numbers from that mean, and then find the mean of those numbers (for standard deviation)

hartnn · Answer

$\large SD = \sqrt{\dfrac{(x_1-m)^2+(x_2-m)^2+...+(x_n-m)^2}{n}}$
yeah, my bad.

hartnn · Answer

where, m is the mean

anonymous · Answer

ill try that. what about for MD.

hartnn · Answer

$V=\large SD^2 = {\dfrac{(x_1-m)^2+(x_2-m)^2+...+(x_n-m)^2}{n}}$
V= Variance.
MD = mean deviation is the Standard Deviation shows how much variation or dispersion exists from the average

anonymous · Answer

so the difference is you dont use a square root?

hartnn · Answer

thats the variance.
the formula with square root is of standard deviation, the formula without square root is variance.
the formula of Mean deviation is what i will write

hartnn · Answer

$\large MD= \dfrac{|x_1-m|+|x_2-m|+...|x_n-m|}{n}$

hartnn · Answer

where m is the mean

anonymous · Answer

thats what i had for it, thanks so much harnn!

hartnn · Answer

welcome ^_^