Z Calculation Formula
Full z calculation formula calculator: z equation statistics, z stat equation, standardized z value, z score explanation, normal curve z values, z score formula ap stats, and more.
Z Calculation Formula Calculator
z = (x − μ) / σZ calculation formula: z = (x − μ) / σ where x = observed value, μ = population mean, σ = standard deviation. This is the z stat equation and z equation statistics used in AP Statistics (z score formula ap stats).
Find the Z Value — Find z Value That Corresponds to Given Area
Find the z value that corresponds to the given area or probability. Inverse normal distribution — find the indicated z scores shown in the graph. Enter cumulative probability to find z.
Normal Curve Z Values — How to Read the Z Score Table
Standard normal curve z values table. How to read the z score table: find your z score, read the cumulative probability. Use z scores to compare the given values across different distributions. Z score formula: z = (x−μ)/σ.
| Z | P(<Z) | P(>Z) | Percentile | Interpretation |
|---|---|---|---|---|
| -3 | 0.13% | 99.87% | 0.1th | Extremely below average |
| -2.5 | 0.62% | 99.38% | 0.6th | Far below average |
| -2 | 2.28% | 97.72% | 2.3th | Well below average |
| -1.5 | 6.68% | 93.32% | 6.7th | Below average |
| -1 | 15.87% | 84.13% | 15.9th | Below average |
| -0.5 | 30.85% | 69.15% | 30.9th | Slightly below average |
| 0 | 50.00% | 50.00% | 50.0th | Average (mean) |
| 0.5 | 69.15% | 30.85% | 69.2th | Slightly above average |
| 1 | 84.13% | 15.87% | 84.1th | Above average |
| 1.5 | 93.32% | 6.68% | 93.3th | Well above average |
| 1.96 | 97.50% | 2.50% | 97.5th | 95th percentile |
| 2 | 97.72% | 2.28% | 97.7th | Top ~2.3% |
| 2.5 | 99.38% | 0.62% | 99.4th | Top ~0.6% |
| 2.576 | 99.50% | 0.50% | 99.5th | 99th percentile |
| 3 | 99.87% | 0.13% | 99.9th | Top ~0.1% |
FAQ — Z Calculation Formula & Z Score Explanation
Z score explanation — what is z scoring?
Z score explanation: A z score (or standardized z value) measures how many standard deviations an observation is from the mean. Z scoring formula: z = (x − μ) / σ. Z value definition statistics: it standardizes data for comparison across different scales. Use z scores to compare the given values from different distributions.
Z score formula AP stats — z equation statistics?
Z score formula ap stats: z = (x − μ) / σ. This is the z equation statistics and z stat equation used on the AP Statistics exam. The z calculation formula gives a standardized z value that can be looked up in the normal curve z values table to find area/probability.
Find z value that corresponds to given area — how to read the z score table?
To find the z value that corresponds to the given area: look up the probability in the standard normal table (z table), then read the row/column z value. How to read the z score table: rows = ones and tenths of z, columns = hundredths. Find the indicated z scores shown in the graph by matching shaded area to cumulative probability. Use our inverse normal calculator above.