Standard Deviation

The standard deviation is a useful measure for determining how spread out the readings are from the arithmetic mean (Average Reading). Most controlled environments typically try to keep the environmental conditions at a stable and consistent humidity and/or temperature. The standard deviation can be used to help indicate how stable the environmental conditions were maintained. One standard deviation (sometimes expressed as "one sigma") away from the mean, positive or negative represents approximately 68 percent of all the readings. Two standard deviations, or two sigmas, away from the mean represents approximately 95 percent of the readings. Three standard deviations represent about 99 percent of the readings.

For example, if the arithmetic mean of the readings was 50.6°C and the standard deviation was 2.3°C, then approximately 68% of the readings were between 48.3°C and 52.9°C, 95% of all the readings were between 46.0°C and 55.2°C and 99% of the readings were between 43.7°C and 57.5°C. Further more, if all the readings were recorded over a span of 1 day (24 hours) then the temperature was between 48.3°C and 52.9°C for approximately 16 hours and 19 minutes during the recorded period of time.

Mathematically standard deviation can be expressed as illustrated.

LogTag^® Analyzer allows the calculation of sample or population based standard deviation. Which of those is used for the calculation can be set by clicking Options from the Edit Menu, then navigating to the Summary Statistic section and selecting sample based or population based.

Here you can also adjust the number of decimal places used to display the result, but please note this setting is shared amongst all statistics calculations.

For a more detailed explanation of the various ways to calculate standard deviation please consult the relevant literature related to statistical and probability calculations.