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"Provide the value for the underlying distribution of the data at the number of standard deviations given in column F."Thank you so much for your comment, Fred Marshall, you have understood the requirement 100 % correctly.
In that regard, it's interesting to note that there is NO data value that reaches +4 sigma but it might be said that the underlying distribution could reach that value.
After all, there are only 112 values given and the probability of a value occurring at 4 sigma is low.
J12==F12*STDEV.P(J$30:J$14Regarding these 2 different formulas, would you please tell what EXACT DIFFERENCE, does that makes. And which one is preferred over the other, if we are trying to find the middle values and the outlier values from a data sample, by using the concept of standard deviations.1)
etc.
A more precise view might be:
j12=F12*STDEV.P(J$30:J$141)+AVERAGE( J$30:J$141 )
I really do not know if the data is zero mean or not.Well you already have the data in Excel and AVERAGE will give the mean and it comes out around 0.2..
Regarding these 2 different formulas, would you please tell what EXACT DIFFERENCE, does that makes. And which one is preferred over the other, if we are trying to find the middle values and the outlier values from a data sample, by using the concept of standard deviations.The exact difference is a constant equal to AVERAGE(J$30:J$141). The idea is that there is an UNDERLYING normal distribution around some mean value. i.e. where does the peak of the normal curve reside? Since the average of the data is only around 0.2 then one might choose to ignore it OR one might choose to *decide* for a variety of real-world reasons that the process would be zero mean. So, expressed "in pictures", this added constant value shifts the normal distribution so the peak is located at the mean value of the DATA.
If we assume that the data is not symmetrically distributed around the mean, then does that means we cannot use Standard Deviations based concepts on this data,No but it may mean that a normal distribution isn't perhaps the best UNDERLYING MODEL for the DATA.
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