# WHAT IS STANDARD DEVIATION AND HOW TO CALCULATE IT WITH AN EXAMPLE CALCULATION

## What is Standard Deviation?

When repeated measurements give different results, we want to know how widely spread the readings are. The spread of values tells us something about the uncertainty of a measurement. By knowing how large this spread is, we can begin to judge the quality of the measurement or set of measurements.

The usual way to quantify spread is standard deviation. The standard deviation of a set of numbers tells us about how different the individual readings typically are from the average of the set.

Mathematically standard deviation is stated as, the root mean square deviation of all the result. This is denoted by σ. Standard deviation will be less if the quality control at site is better and most of the test results will be clustered mere the mean value. If quality control is poor, the test results will have much different from mean value and therefore, standard deviation will be higher.

## Example of Calculation of Standard Deviation For a Set of 20 Concrete Cube Test Results

 Sample Number Crushing Strength (x)MPa Average Strengthμ=∑x/n Deviation(x-μ) Square of Deviation(x-μ)2 1 43 40.2 +2.8 7.84 2 48 +7.8 60.84 3 40 -0.2 0.04 4 38 -2.2 4.84 5 36 -4.2 16.64 6 39 -1.2 1.44 7 42 +1.8 3.24 8 45 +4.8 23.04 9 37 -3.2 10.24 10 35 -5.2 27.04 11 39 -1.2 1.44 12 41 +0.8 0.64 13 49 +8.8 77.44 14 46 +5.8 33.64 15 36 -4.2 16.64 16 38 -2.2 4.84 17 32 -8.2 67.24 18 39 -1.2 1.44 19 41 +0.8 0.64 20 40 -0.2 0.04 Total=804 Total=359.20

Average Strength, μ = 804/20 = 40.2 MPa

Standard deviation = √[359.2/ (n-1)] = √(359.2/19) = 4.34 MPa

Where, n = Total number of samples

Coefficient of Variation = (Standard deviation/Average strength)*100

= (4.34/40.2)*100

= 10.80

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