Z-Score Calculator

How to Calculate Z-Score

The z-score, also known as the standard score, is a measure of how many standard deviations a raw score is away from the population mean. It's a crucial concept in statistics that allows us to compare scores from different distributions.

Formula and Its Components

The formula for calculating z-score is:

\[Z = \frac{X - \mu}{\sigma}\]

Where:

• Z = Z-score
• X = Raw score
• μ (mu) = Population mean
• σ (sigma) = Population standard deviation

Calculation Steps

1. Determine the raw score (X).
2. Identify the population mean (μ).
3. Identify the population standard deviation (σ).
4. Subtract the mean from the raw score.
5. Divide the result by the standard deviation.

Example Calculation

Let's calculate the z-score for a raw score of 75 in a population with a mean of 70 and a standard deviation of 5.

1. Raw score (X) = 75
2. Population mean (μ) = 70
3. Population standard deviation (σ) = 5
4. Z = (75 - 70) / 5
5. Z = 5 / 5 = 1

The z-score is 1, which means the raw score is one standard deviation above the mean.

Visual Representation

This diagram illustrates the position of the raw score (red line) relative to the mean (dashed line) on a standard normal distribution curve. The z-score of 1 indicates that the raw score is one standard deviation above the mean.