in some exam past papers I have been doing I have come across the statistics equationz=(sample mean - mean)/standard deviationas well as the equationz = (sample mean - mean)/(standard deviation/sqrt n).could anyone please explain when to use which equation and what the difference is? thanks so much!

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Mariam Hickman · Accepted Answer

It is the difference between the   z score for a datum from an entire population and a sampling.The   z score for a datum   x is   z  =  (  x  −  μ  )      /    σ where   μ is the population mean and   σ is the population standard deviation.If the datum   x is not from the entire population but rather from a sampling from that population then the standard deviation is divided by the square root of the sample size   n.

Trystan Castaneda · Accepted Answer

The   z-score calculation is designed to answer the question: &quot;How far from typical is this result?&quot;When dealing with a single datum, the single-value formula   z  =            x      −      μ        σ   gives us the answer. But when dealing with a whole pile of individual measurements, we expect the Law of Large Numbers, and its more formal cousin the Central Limit Theorem, to take over: more attempts means the mean of our results is going to look more like the population mean. To model this, we divide the usual standard deviation by       n  :   z  =                              x          ¯                    −      μ              σ              /                    n            .

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