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Z Score Formula Online - Tutorpace

# 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