Values, weights - Numpy ndarrays with the same shape.Īssumes that weights contains only integers (e.g. Return the weighted average and weighted sample standard deviation. Or modifying the answer by as follows: def weighted_sample_avg_std(values, weights): Var = (lhs_numerator - rhs_numerator) / denominator Applied StatisticsĪnd Probability for Engineers, Enhanced eText. Where X is the quantity each person in group i has,Īnd n is the number of people in group i. Just in case you're interested in the relation between the standard error and the standard deviation: The standard error is (for ddof = 0) calculated as the weighted standard deviation divided by the square root of the sum of the weights minus 1 ( corresponding source for statsmodels version 0.9 on GitHub): standard_error = standard_deviation / sqrt(sum(weights) - 1)Ī follow-up to "sample" or "unbiased" standard deviation in the " frequency weights" sense since "weighted sample standard deviation python" Google search leads to this post: def frequency_sample_std_dev(X, n): std_mean the standard error of weighted mean: > weighted_stats.std_mean var the weighted variance: > weighted_stats.var std the weighted standard deviation: > weighted_stats.std You initialize the class (note that you have to pass in the correction factor, the delta degrees of freedom at this point): weighted_stats = DescrStatsW(array, weights=weights, ddof=0) But from the standard deviation calculation, the concrete member can be approved, and non-destructive tests are not prescribed.There is a class in statsmodels that makes it easy to calculate weighted statistics: .Īssuming this dataset and weights: import numpy as npįrom import DescrStatsW The highest value if the above two is considered, which isįrom table-3, we have the average/mean value of the compressive strength which is 65.12N/mm 2, which is higher than the standard deviation 64.90N/mm 2 Conclusionįrom Table-3, it can be noticed that the test results of five cubes are below 60 N/ mm 2, which means the cubes have failed. f ck + 0.825 x derived standard deviation.Table 4: Calculation of Standard DeviationĪs per the IS-456, for concrete of grade above M-20, Table 3: Test Result of Concrete Cubes SL No The standard deviation for the 33 number of cubes tests is calculated below. Greater than or equal to - f ck -4 N/mm 2Įxample Calculation of Standard Deviation for M60 grade Concrete with 33 cubes.Ī concrete slab of 400Cum was poured for which 33 cubes were cast for 28 days compressive test. Greater than or equal to - f ck -3 N/mm 2 Mean of Group of 4 Non-Overlapping Consecutive test results in N/mm 2į ck + 0.825 x derived standard deviation Table 2: Characteristic Compressive Strength Compliance Requirement Specified Grade The permissible deviation in the mean of compressive strength of the concrete is as per the below table prescribed by IS-456 Table No-11.
When the number of test results available are more than 30, the standard deviation of the test results is derived by the following method -įig 1: Variation Curve for Standard Deviation Note - The above values are dependent on site-control- having proper storage of cement, weigh batching of all materials, controlled addition of water, regular checking of all elements such as aggregate grading and moisture content, and regular checking of workability and strength. However, as soon as the minimum number of test results are available, the derived standard deviation shall be calculated and used. Table 1: Assumed Standard Deviation Sl.NoĬharacteristic compressive strength (N/mm 2) In the case, where sufficient test results for a particular grade of concrete are not available, the value of standard deviation is assumed as per the IS-456 Table 8 (Clauses 3.2.1.2) as shown below: The minimum number of cube test samples required to derive the standard deviation is 30. The calculation of standard deviation for compressive strength of concrete can done in 2 ways: 1. Example Calculation of Standard Deviation for M60 grade Concrete with 33 cubes.Ĭalculation of Standard Deviation for Concrete.Now, we can compare the portfolio standard deviation of 10.48 to that of the two funds, 11.4 & 8.94. Calculation of Standard Deviation for Concrete With a weighted portfolio standard deviation of 10.48, you can expect your return to be 10 points higher or lower than the average when you hold these two investments.