Interpreting the z-score

The z-score can tell us how many standard deviations aways a value is from the mean. In order to calculate the z-score you need the population mean and the standard deviation.

To get the z-score the the mean is subtracted from your value and then divided by the standard deviation.

The z value you get is how many standard deviations away from the mean your value is.

In order to see the percentage of values below yours then the z-score can be put into this chart

“https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf”

If we wanted to find a z-score of -.21 then we find -.2 on the left column then .01 on the top row and we get .41683. This means that 41% of the data is below this point.