Standardizing a formula involves converting data from different scales to a common scale using the Z-score. This allows for comparison across different datasets by transforming the data to have a mean of 0 and a standard deviation of 1.
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The Z-score formula is $Z = \frac{X - \mu}{\sigma}$ where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation.
Standardizing data helps in comparing values from different normal distributions.
After standardization, 68% of values lie within one standard deviation of the mean (i.e., between Z-scores -1 and 1).
A positive Z-score indicates that the value is above the mean, while a negative Z-score indicates it is below the mean.
Standardizing enables use of standard normal distribution tables to find probabilities and percentiles.
Review Questions
What does a Z-score represent in terms of standard deviations?
Why is it useful to standardize data when working with different datasets?
How do you calculate a Z-score for a given value?
Related terms
Z-Score: A statistical measurement that describes a value's relation to the mean of a group of values, calculated as $(X - \mu)/\sigma$.
Normal Distribution: A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
$\mu$ (Mu): $\mu$ represents the population mean in statistics.