Download fa NOTES 2021 10 25 Z-scores

n
X
Mean
Range:
i 1
i
n
X high  X low
n
Variance
2 
(X
i 1
i
 X )2
n
n
Standard Deviation:

(X
i 1
i
 X )2
n
https://www.calculator.net/z-score-calculator.html
A Z-score is a measurement of how many standard deviations above or below the mean an individual
piece of data is.
Z
x

z-score=(data value – mean)/std deviation
By knowing any 3 of these values, you can solve for the 4th value.
Once you know the z score, if you know the data is distributed normally, you can look up to find the
percental of data that is BELOW that value.
The easiest way to do this is by using a z-score calculator like this one.
Z
x

Percentage of data less than that Z-score (percentile)