Enter your numbers to get every common statistic at once. For six concrete cube results of 32.5, 30.8, 34.1, 31.2, 33.6 and 29.9 MPa, the mean is 32.02 MPa, the median 31.85, the range 4.2 and the sample standard deviation 1.66 MPa, a coefficient of variation of 5.2%.
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Results
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Mean (average)
32.0167
Median
31.85
Mode
none (no value repeats)
Count
6
Sum
192.1
Minimum and maximum
29.9 and 34.1
Range
4.2
Standard deviation (sample, n − 1)
1.6558
Standard deviation (population, n)
1.5115
Variance (sample)
2.7417
Quartiles Q1 and Q3
30.8 and 33.6
Interquartile range
2.8
Coefficient of variation
5.17 %
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Formula
Mean = Σx ÷ nMedian = middle value of the sorted listMode = the value that appears most oftenRange = maximum − minimumVariance = Σ(x − mean)² ÷ (n − 1) (sample) or ÷ n (population)Std dev = √varianceCV = std dev ÷ mean × 100%
Worked Example
Six cube results (MPa): 32.5, 30.8, 34.1, 31.2, 33.6, 29.9:
Add all the values and divide by how many there are. For 32.5, 30.8, 34.1, 31.2, 33.6 and 29.9: 192.1 ÷ 6 = 32.02.
What is standard deviation?
A measure of spread: roughly how far a typical value is from the mean. Take the square root of the variance. Low means the results are consistent; high means they vary a lot.
Should I use the sample or population standard deviation?
Use the sample one (divide by n − 1) when your numbers are some of a larger group, such as test cubes taken from a pour. Use the population one (divide by n) only when you have every value.
How is standard deviation used for concrete?
Mixes are designed for a target mean strength above the specified strength, using the standard deviation of test results. IS 10262 sets the target at the higher of fck + 1.65 × s and fck plus a fixed margin, so steadier results can allow a leaner mix.
What is the coefficient of variation?
The standard deviation as a percentage of the mean. It lets you compare spread between sets with different averages: 1.66 ÷ 32.02 = 5.2%.
What if there is no mode?
When no value appears more than once there is no mode. If two or more values tie for the most often, all of them are modes.
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