Understanding Z-Scores | A Standardized Measure for Statistical Comparison

Standardized value

A standardized value, also known as a z-score, is a measure used in statistics to compare individual data points to a larger population

A standardized value, also known as a z-score, is a measure used in statistics to compare individual data points to a larger population. It represents the number of standard deviations an observation is from the mean of the population.

To calculate the standardized value, we subtract the mean of the population from the individual data point and then divide it by the standard deviation of the population. The formula for calculating the z-score is:

z = (x – µ) / σ

where:
z is the standardized value (z-score)
x is the individual data point
µ is the mean of the population
σ is the standard deviation of the population

A positive z-score means that the individual data point is above the mean, while a negative z-score indicates that the data point is below the mean. The magnitude of the z-score tells us how far away the data point is from the mean, with larger values representing greater deviations.

Standardized values are useful for comparing observations from different populations or different data sets. They allow us to understand where a particular data point stands in relation to the rest of the data and provide a standardized basis for making comparisons and drawing conclusions.

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