# The right formula for Z score

I have come across the two equation for z score.

1. Z =  (x-u)/ std dev

2. Z = (x bar - u)/ std error of sample mean, std dev/ root n

what is the difference between this two and when to use? Many thx

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Use the former when you’re creating a confidence interval for a single observation.

Use the latter when you’re creating a confidence interval for the mean of a number of observations, or performing an hypothesis test about a mean.

Simplify the complicated side; don't complify the simplicated side.

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The former one is for one population observation or one sample observation. While the latter one is for many observation ( sampling observation ). Did I get it right?

You did.

Simplify the complicated side; don't complify the simplicated side.

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Thank you so much, cheers!

Jiratoso wrote:

I have come across the two equation for z score.

1. Z =  (x-u)/ std dev

2. Z = (x bar - u)/ std error of sample mean, std dev/ root n

what is the difference between this two and when to use? Many thx

The first is descriptive to tell if a certain value is an outlier or suspect outlier and can be used to make intervals that describe where a certain percent of the data values fall. The second is for inferences about the population mean and is usually called a z-statistic.