Standard Deviation

The standard deviation measures the average amount the data deviates from the average or mean of the data set.

Where:

S = Standard Deviation

Ý = Sum of

= each data point in a data set

mean = the average of the data points

N = the number of data points.

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The data table below represents turbidity data which is being analyzed for standard deviation. In this case, X represents the mean.

Dividing 99.88 by ( 7-1) , we get a value of 16.65. We then take the square root of 16.08 which gives us a standard deviation of 4.08. We retain the .08 as the original turbidity data shown in the table above was accurate to 2 decimal places (as in 4.75, 3.45, etc).

Reporting data results with standard deviation:

The mean turbidity data may be reported as 8.09 +/- 4.08.

The lower the standard deviation, the greater the precision. In this case, the precision is not very good, as there is about a 50% variance in the data sets!

[How to Use Standard Deviation to Compare Data Sets]

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