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Standard deviation (s.d.) is the distance a certain value is from the sample or population mean. For example, let's say a there's a study for the age of pet owners using a sample size of 50 pet owners, and the mean age is 45 years old. Meanwhile, the standard deviation is 15 years. That means a 60 year old pet owner is one standard deviation from the sample's average age, a 75 year old owner is two standard deviations from the average, while a 30 year old owner is one standard deviation below the average. Such a measurement allows us to figure out how spread out data values are in any given sample or population in a study. Large standard deviations indicate that the data values are more varied and cover a wider range, as opposed to smaller ones which indicate data that is bunched together within a smaller range of values.

To find the standard deviation of a sample, first find the mean of all the data values. Let's say our simple consists of the numbers 8, 4, 2, 10, 6.

Added up together, we get 30, and divided by the number of values,5, we get an answer of 6.

Next subtract 6 from each value of the sample. 8-6= 2, 4-6= -2, 2-6= -4, 10-6= 4, 6-6=0.

Now that you've subtracted, square each difference. 2=4, -2=4, -4=16, 4=16, 0= 0.

Now add each product together, then divide by the number of values minus 1: 4+4+16+16+0=40/(5-1)= 40/4=10.

With 10 as the variance, finding the standard deviation is as simple as finding the square root of 10: =3.16 (rounded to the hundredth place).

Thus, our sample has standard deviation of 3.16, from the mean of 30.

Finding the standard deviation of a population is almost the same as a sample, except that one divides the sum of the squared values by the full number of data values a (no subtracting by 1).