Concrete Strength Variation - Frequency Density & Compressive Strength Distribution Curve

The concrete compressive strength test result of cubes from a random sampling of a mix although exhibit variations, when they are plotted on a histogram are found to follow a bell-shaped curve, which is termed as the Normal or Gaussian Distribution Curve.

The results are said to follow a normal distribution as shown in the figure-1, given that they are equally placed above the mean value. The normal distribution curve can be used to ascertain the variation of concrete strength from the mean. The area beneath the curve shows the total number of test results.


The proportion of results less than the specified value is represented by the area under the curve to the left – hand side of the vertical line drawn through the specified value.


A normal distribution curve can be defined by two parameters, namely the mean strength and the standard deviation.


The figure-2 shows the frequency density versus compressive strength distribution curves of concrete mixes A and B. The curves are symmetrical about the mean value. The Mix B Indicates better quality control than that is obtained from the Mix A, even though both the mixes have the same average strength.

The measure of Variability of Concrete Strength

The terms and the parameters required for the measurement of the variability is mentioned one by one

Mean Strength

It is defined as the arithmetic mean of the set of actual test results. The average or the mean x for a set of ‘n’ observation x1, x2, ……xn is expressed as,


It is defined as the difference between the largest and the smallest value from the set of observations.

Standard Deviation

The root mean square (rms) deviation of the consignment from the mean x is termed as the standard deviation and is defined numerically as

Where S= Standard Deviation, x = arithmetic mean, xi = any value in the set of observations; n= total number of observations


The square of standard deviation is called as the variance, i.e. Variance,

The standard variation increases with the increase in the variability.

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