How do you find the standard deviation of 1,3,5,6,8?

Question

How do you find them, and why do you do it in this method? I'm sorry it's so troublesome but I want to understand how to do it too..

Answer 1

Standard deviation is a measurement of how close a bunch of numbers cluster around their average value. To statistically minimize the affect of a single outlying "bad" value, mathematicians developed the following equation.

First, you calculate the average of the numbers, and subtract this average from each individual number to get its deviation. Square each of these deviations and add them all together. Divide by one less than the total number of numbers, and take the square root to get the Standard Deviation. In this case, you should get 2.702.

If you want to calculate the standard deviation of an entire population, you divide by the total number instead of N-1 (makes little difference if N is very large)... but this is likely more info than you need!

Answer 2

First you get the mean:
Mean = (1+3+5+6+8)/5 = 4.6
Then you find squares of individual deviations[(xi-xmean)^2]:
(1-4.6)^2 = 12.96
(3-4.6)^2 = 2.56
(5-4.6)^2 = 0.16
(6-4.6)^2 = 1.96
(8-4.6)^2 = 11.56

Then we find mean of these:
(12.96+2.56+0.16+1.96+11.56)/5
=5.84

This is called sigma square.
Finally, the standard deviation is:

sqrt(5.84)
Std. Deviation=2.41660919

Hope this helps and the method doesn't apper cumbersome.

Answer 3

there is a formula for these calculations.
first, add all numbers and divide them by 5 number of characters you have) you will get 4.6; then, from each of your "characters (1,3,5,6,8) subtract 4.6 (ignore negative numbers, everything in ABSOLUTE value) and square each result, add all results; now, divide your sum of squares (I got 47.8) by 4 (number of "characters" minus 1). the result is under square root (my final answer is 11.95 under the square root).
THATS IT

Answer 4

Mu=(1+3+5+6+8)/5=23/5
SD=Sigma (X-Mu)(X-Mu)/5=[(1-23/5)^2]/5+[(3-23/5)^2]/5+[(5-23/5)^2]/5+[(6-23/5)^2]/5+[(8-23/5)^2]/5=..........

Answer 5

This web site has it
http://www.mnstate.edu/wasson/ed602calcsddevs.htm
its easier than explaining it.