z-score

Z-score of a number is its distance from the mean in the multiples of standard deviation.

Applications: Z-score can be used to determine if an observation has strayed too far from its mean. The bigger the absolute value of z-score, the farther is the value from its mean. For example in the table below,  -5 and 7 are farthest from mean, since their z-score are biggest in the pack of the observation. 0 and 1 are closest since their z-score is smallest.
This characteristic of z-score is often used in technical analysis to generate trading signals. When the indicator under consideration is too far above the mean, for a mean-reverting price series a sell signal can be generated. Similarly, when the indicator falls too far below the mean, a buy signal can be generated.
Computation of z-score is as follows:
 

1. Calculate mean or average of the data.
2. Calculate standard deviation of the data.
3. For every observation, calculate the z-score as:                                                                                                                                                                           (observation –mean)/standard deviation

 


 

Observations
-5	-4	-4.5	-3	0	1	2	7
Mean	Stdev
-0.81	4.12
Obs.	-5	-4	-4.5	-3	0	1	2	7
Z-score	-1.02	-0.77	-0.89	-0.53	0.20	0.44	0.68	1.90