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Standard Deviation Calculations

The standard deviation is calculated for rollups and for event and report generation purposes.

Rollups:

• For hourly rollups, the standard deviation is calculated for the polled values.
• For daily rollups, the standard deviation is calculated for hourly averages.
• For weekly rollups and beyond, the standard deviation is calculated for the daily averages.

Events:

• The standard deviation provides a statistical indicator of how much variability exists in the population data that factored into the baseline average calculations.

Reporting:

• For hourly reporting, the standard deviation is calculated for the polled values.
• For daily reporting, the standard deviation is calculated for hourly averages.
• For weekly reporting and beyond, the standard deviation is calculated for the daily averages.

Example: Calculate the Standard Deviation of Population.

The following example shows how the standard deviation of the population is calculated, given 12 points of data.

The population refers to a set of potential values, including not only cases that are observed but those cases that are potentially observable.

The formula for calculating this standard deviation is:

population deviation = Square root of (Sum ( X - population mean)/number of data points)

X

Is the data point value in the population.

Follow these steps:

1. Collect 12 points of data.

   1 2 3 4 5 6 7 8 9 10 11 12

   30 10 20 70 60 30 80 10 90 20 70 50

2. Calculate the population mean.

   The population mean = sum of data point values in population/number of data points.

   The population mean for this example is 45.

3. Calculate the difference of each data point from the mean.

   The differences for this example are:

   -15 -35 -25 25 15 -15 35 -35 45 -25 25 5

4. Calculate the square of the difference for each data point.

   The squares for this example are:

   225 1225 625 625 225 225 1225 1225 2025 625 625 25

5. Calculate the sum of the squares:

   The sum of the squares for this example is 8900.

6. Calculate the sum of the squares, divided by the number of data points in the population.

   The sum for this example is 741.6666667.

7. Calculate the square root of the sum of squares of data point value from the population mean.

   The square root for this example is 27.23355773.

   The standard deviation for this example is 27.23355773.