Understanding the Z-Score Formula: How to Standardize and Compare Data Points

Z-score formula

The z-score formula is a mathematical equation that is used to standardize and compare data points in a normal distribution

The z-score formula is a mathematical equation that is used to standardize and compare data points in a normal distribution. It allows us to determine how far a particular data point is from the mean in terms of standard deviations.

The formula for calculating the z-score is:

z = (x – μ) / σ

Where:
– z is the z-score
– x is the data point in question
– μ is the mean of the data set
– σ is the standard deviation of the data set

To calculate the z-score, you need to subtract the mean (μ) from the data point (x), and then divide the result by the standard deviation (σ). This will give you the number of standard deviations a data point is away from the mean.

For example, let’s say we have a data set of exam scores with a mean of 75 and a standard deviation of 10. If a student’s score is 85, we can calculate the z-score as follows:

z = (85 – 75) / 10
z = 10 / 10
z = 1

A z-score of 1 indicates that the student’s score is 1 standard deviation above the mean.

Alternatively, if a student’s score is 70, the z-score would be calculated as:

z = (70 – 75) / 10
z = -5 / 10
z = -0.5

A z-score of -0.5 indicates that the student’s score is 0.5 standard deviations below the mean.

By using the z-score formula, we can compare different data points and determine their relative positions within a distribution. This can be helpful in analyzing and interpreting data, especially in fields such as statistics and data analysis.

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