standard deviation

Question

how to find standard deviation

Answer 1

find the variance then take the square root of the variance

variance = the sum of squared deviations from the mean, divided by degrees of freedom, which is n = the number of scores, observations or numbers, if the data is the population. But if it's just a sample from the population, divide by n-1.

find the mean, which is just the arithmetic average. sum all the data, then divide by the number of data

then take each data and subtract the mean. Then square the result. Do this for each data. Sum the squared deviations from the mean

that gives you the variance

then take the square root of the variance to get the standard deviation

take a specific simple example. You have 3 observations 1, 3 and 5

the mean = (1+3+5)/3 = 9/3 = 3

calculate deviations from the mean

1-3 = -2

3-3 =0

5-3 = 2

square the deviations from the mean

(-2)^2 = 4

0^2 = 0

2^2 = 4

sum the squared deviations from the mean

4+0+4 = 8

divide 8 by 3, the numeber of the observations if that is the entire population, 1, 3 and 5

8/3 = the variance

take the square root to calculate the standard deviation

sqr(8/3) = (2/3)sqr2 = about (2/3)(1.414) = about 0.943 = standard deviation

Unless this is just a sample from the larger populatiion

then

divide by n-1 = 3-1 = 2

8/2 = 4

square root of 4 = 2 = the standard deviation