Question 1

What is a z-score?

Accepted Answer

A z-score (standard score) measures how many standard deviations a value is from the mean of its distribution. A z-score of 0 means the value equals the mean; +1.5 means 1.5 standard deviations above the mean.

Question 2

How do I calculate a z-score?

Accepted Answer

The formula is z = (x − μ) / σ, where x is the raw score, μ is the population mean and σ is the standard deviation. Subtract the mean, then divide by the standard deviation.

Question 3

What does the probability (p-value) mean?

Accepted Answer

It is the area under the standard normal curve for the chosen region. For example, P(Z < z) is the probability that a random value is below your score; the percentile is that probability expressed as a percentage.

Question 4

What is a good z-score?

Accepted Answer

There is no universal good or bad z-score. In testing, z-scores above 1.96 or below −1.96 are statistically significant at the 0.05 level. In education, a z-score above 1 places you in roughly the top 16%.