ISA Interchange

Welcome to the official blog of the International Society of Automation (ISA).

All Posts

Estimated Standard Deviation

Because an exact number for standard deviation could only be obtained by taking an infinite number of measurements, the below formula calculates the estimated standard deviation.

Let’s take a set of measurements from a temperature transmitter with a range of 0-100 deg, Celsius.

IDEAL VALUES     AS FOUND VALUES
0 1
10 12
20 21
30 28
40 42
50 51
60 62
70 68
80 85
90 91
100 102

The first step for calculating for estimated standard deviation will be to find our average deviation or mean.

For our example the deviations are:

1,2,1,2,2,1,2,2,5,1,2

The average deviation would be 1.909 degrees Celsius.

The next step is to determine how far off each measurement is from the average deviation.

.9,.1,.9,.1,.1,.9,.1,.1,3.1,.9,.1

Then we take the square of each of these and sum.

.81+.01+.81+.01+.01+.81+.01+.01+9.61+.81+.01=12.91

Then we divide by the number of measurements minus 1, which is 10, to arrive at 1.29

The square root of 1.29 is 1.136 and is our estimated standard deviation.

The Estimated standard deviation, based upon the 11 checks made, is 1.136 degrees Celsius for the transmitter.

Estimated Standard Deviation is expressed in same units as data.

References:

A Beginner’s Guide to Uncertainty of Measurement by Stephanie Bell.

Standard Deviation Calculator

 

Mark Weisner
Mark Weisner
Mark Weisner is a technical specialist at ISA.

Related Posts

What Is Functional Safety?

Functional safety focuses on the detection of a potentially dangerous condition and depends on automatic ...
Jennifer Infantino Halsey Apr 7, 2020 5:15:00 AM

Companies Ramp Up Production of N95 Masks in Response to COVID-19

COVID-19 has exponentially increased the need for N95 disposable masks in hospitals and medical facilitie...
Kara Phelps Apr 3, 2020 5:15:00 AM

Newsweek Vantage Report on Cyber Risks to Critical Infrastructure: ISA's the Expert Partner

Newsweek Vantage recently published an independent report on cyber risks to critical infrastructure—and t...
Kara Phelps Mar 24, 2020 3:11:27 PM