Math and Arithmetic
Statistics
How To

# How to calculate the standard deviation?

012 ###### 2014-06-01 10:43:11

Suppose you have n observations {x1, x2, ... , xn} for a variable, X.

Calculate m = (x1 + x2 + , ... , + xn)/n, the mean value.

Calculate s2 = (x12 + x22 + , ... , + xn2)/n

Then Variance = s2 - m2 = [mean of the squares] - [square of the mean]

and the standard deviation = sqrt(Variance)

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## Related Questions we calculate standard deviation to find the avg of the difference of all values from mean., Square the standard deviation and you will have the variance. You need more than one number to calculate a standard deviation, so 9 does not have a standard deviation.  Standard deviation is how much a group deviates from the whole. In order to calculate standard deviation, you must know the mean. In the same way that you calculate mean and median that are greater than the standard deviation! You cannot because the standard deviation is not related to the median. A z-score cannot help calculate standard deviation. In fact the very point of z-scores is to remove any contribution from the mean or standard deviation. The standard deviation is a measure of how spread out the numbers are. Three points is needed to calculate a statistically valid meaningful standard deviation.  =stdev(...) will return the N-1 weighted sample standard deviation. =stdevp(...) will return the N weighted population standard deviation. You cannot calculate standard deviation for objects such as concrete cubes - you can only calculate standard deviation for some measure - such as side length, surface area, volume, mass, alkalinity or some other measure. The mean and standard deviation do not, by themselves, provide enough information to calculate probability. You also need to know the distribution of the variable in question. Here's how you do it in Excel: use the function =STDEV(&lt;range with data&gt;). That function calculates standard deviation for a sample. You calculate standard deviation the same way as always. You find the mean, and then you sum the squares of the deviations of the samples from the means, divide by N-1, and then take the square root. This has nothing to do with whether you have a normal distribution or not. This is how you calculate sample standard deviation, where the mean is determined along with the standard deviation, and the N-1 factor represents the loss of a degree of freedom in doing so. If you knew the mean a priori, you could calculate standard deviation of the sample, and only use N, instead of N-1. Write a program to calculate the standard deviation of an array of values. S.D. = Use nesting function concept Standard deviation is a way to describe how the data is distributed around the Arithmatic Mean. It is not a simple formula to calculate, as shown in the links.  See the related links on how to calculate standard deviation. If there are more than a dozen data points, it is tedious to calculate by hand. Use excel or an online calculator. To get 2 standard deviations, multiply the calculated std deviation by 2. A single observation, such as 50486055535157526145 cannot have a standard deviation cube test compressive result. The standard deviation is the standard deviation! Its calculation requires no assumption.  Standard error of the sample mean is calculated dividing the the sample estimate of population standard deviation ("sample standard deviation") by the square root of sample size. The standard deviation is the square root of the variance. So, if variance = 03 = 3 the std dev = sqrt(3) = 1.732 Standard deviation (SD) is neither biased nor unbiased. Estimates for SD can be biased but that depends on the formula used to calculate the estimate.

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