Z-score formula
The Z-score formula is used to calculate the standard score, also known as the Z-value or Z-score, of a given data point in a distribution
The Z-score formula is used to calculate the standard score, also known as the Z-value or Z-score, of a given data point in a distribution. It tells you how many standard deviations a data point is away from the mean of the distribution.
The formula for calculating the Z-score is:
Z = (X – μ) / σ
Where:
Z is the Z-score,
X is the data point you want to find the Z-score for,
μ is the mean of the distribution, and
σ is the standard deviation of the distribution.
To calculate the Z-score, you subtract the mean from the data point and then divide it by the standard deviation.
For example, let’s say you have a data point of 75 in a distribution with a mean of 60 and a standard deviation of 10. You can calculate the Z-score as follows:
Z = (75 – 60) / 10
Z = 15 / 10
Z = 1.5
So, the Z-score for the data point 75 in this distribution is 1.5. This means that the data point is 1.5 standard deviations above the mean.
Z-scores are a helpful tool in statistics as they allow you to compare data points from different distributions, determine outliers, and find the relative position of a data point within a distribution.
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