Z Score Formula

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Definition: -A z score is the number of standard deviation that a value of x, is above or below the mean.
 

Note:-f the value of x is less than the mean, the z score is negative; if the value of x is more than the mean, the z score is positive, and if the value of x equals the mean, the associated z score is zero.
 

Z score formula:-

Z score formula for x= (x- µ)/σ
Z score formula for x? = (x? -µ)/( σ/√n)
Where,
µ= Population mean
σ= Population standard deviation
n= sample size.

 
Example: - Let x be a continuous random variable that has a normal distribution with a mean of 50 and a standard deviation of 10. Convert the following x values to z values.
1)    X= 55
2)    x=35
 

Solution:- For the given normal distribution, µ=50 and σ=10.
1)    The z score for x=55 is computed as follows:
Z= (x-µ)/σ
   = (55-50)/10
   = 5/10
   =1/2
   =0.50
Therefore z score for x=55 is 0.50
 

. For the given normal distribution, µ=50 and σ=10.
2)    The z score for x=35 is computed as follows:
Z= (x-µ)/σ
   = (35-50)/10
   = -15/10
   =-3/2
   =-1.50
Therefore z score for x=55 is -1.50



 

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