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Showing posts with label mean. Show all posts
Showing posts with label mean. Show all posts

24 May, 2021

Simulation of the arithmetic mean and data normality

The world around us is full of uncertainties. In research, in engineering and sciences, uncertainties must be dealt with in a formalized way, using statistics.  We are required to follow procedures for dealing with inevitable variation in routine testing:  in laboratory, in production and construction, in relation to quality control and quality assurance issues.

Excel statistical functions help in solving many practical problems in that area, as well as in simulation and estimation of probabilities of certain outcomes. Here I just like to share with you couple of charts based on simulation I've carried out in Excel regarding the critical role of sampling frequency and the number of tested samples in evaluation of various processes and material properties.

The simulation example shown below is based on assumption of normal distribution of sampling and uses two basic statistical functions:

  • RAND() , which returns evenly distributed random numbers from 0 to 1 (not including 1), and
  • NORM.INV, which returns the inverse of the normal cumulative distribution for the specified arithmetic mean and standard deviation.

Here is the chart illustrating the effect of the number of tests (samples) on the value of Mean. The data have been obtained with the formula =NORM.INV(RAND(),2.60,0.009), where 2.60 is the expected arithmetic Mean and 0.009 is Standard Deviation of the population ('targets'). We can see that variability of the running Mean is very high up to about 15 tests. Its reliability increases with number of samples and reaches good stability starting at around 50 tests (samples). At the same time the spread of data widens up to about three standard deviations, as can be expected in any normal distribution.