The zscore calculator is designed to determine the zvalue from the raw score, sample mean and size, and a data sample.
Compute Zscore Using:
The zscore, also known as the standard score, defines how far a specific data value is from the mean (average) of a dataset. It's measured in terms of standard deviations.
It helps to understand whether a data point is unusual or typical compared to the rest of the data.
Z = 0: The data point is exactly at the mean.
Z > 0: The data point is above the mean.
Z < 0: The data point is below the mean.
The zscore for a single data point is calculated using the following formula:
z = 

Where,
z = Standard score,
x = Row score or a data point,
μ = Population mean,
σ = Population standard deviation.
The following formula is used to calculate the zscore for a sample:
z = 

Where,
x̄ = Sample mean,
n = Sample size,
μ = Population mean,
σ = Population standard deviation.
Calculate the zscore for a row score of 23, population mean of 42, and standard deviation of 17.6.
Here,
x = 23
μ = 42
σ = 17.6
Apply the zscore formula.
z = 

z = 

z = 

z = 1.07955
Pvalue from the Z Table:
P(x < 23) = 0.14017
P(x > 23) = 1  P(x < 23) = 0.85983
P(23 < x < 42) = 0.5  P(x < 23) = 0.35983
Suppose the sample mean is 55, the sample size is 12, the population mean is 46, and the population standard deviation is 32. Compute the zvalue for a given normal distribution.
Here,
x̄ = 55
n = 12
μ = 46
σ = 32
Put values into the formula.
z = 

z = 

z = 

z = 

z = 0.97428