Z-Score Table, Chart and More (Standard Normal Table)
This score measures how many standard deviations a data point is from the mean of a distribution. It’s calculated by subtracting the mean from the value and dividing by the standard deviation. Positive z-scores indicate values above the mean, while negative z-scores represent values below it.
📊 Positive Z-Scores (0.00 to 3.99)
Cumulative Probability from Left
| z |
|---|
📊 Negative Z-Scores (-3.99 to -0.00)
Cumulative Probability from Left
| z |
|---|
FIND US AT:
A z-score table, also called a standard normal table, shows the cumulative probability associated with each z-score in a standard normal distribution (mean = 0, standard deviation = 1). The table helps you find the probability that a randomly selected value falls below a given z-score without complex calculations.
To use the table, locate the row corresponding to your z-score’s first decimal place, then find the column for the second decimal place. The intersection gives you the cumulative probability from the left tail. For example, a z-score of 1.96 corresponds to approximately 0.9750, meaning 97.50% of values fall below this point. Z-tables are essential tools in statistics for hypothesis testing, confidence intervals, and probability calculations.Retry
Z-Score Calculator
Test Value Calculator
Common Z-Score Values and Their Significance
Certain z-scores appear frequently in statistical analysis and are worth memorizing. A z-score of ±1.00 captures approximately 68% of all values in a normal distribution, while ±2.00 encompasses about 95%. The commonly cited z-score of ±1.96 corresponds to the 95% confidence level used in many research studies, meaning only 5% of values fall outside this range. For stricter 99% confidence intervals, statisticians use z-scores of ±2.576. Understanding these benchmarks helps you quickly assess whether a data point is typical or unusual without consulting the table each time.
Interpreting Results in Context
A z-score alone tells you position within a distribution, but interpretation depends on your specific question.
- When you need the probability of a value falling above your z-score rather than below it, subtract the table value from 1.
- For the probability between two z-scores, find each cumulative probability and calculate the difference.
If you’re working with a two-tailed test, such as determining whether a value is significantly different from the mean in either direction, double the tail probability. For instance, with a z-score of 1.96, the two-tailed probability of being this extreme or more is approximately 0.05 (2 × 0.025), which is why this value marks the threshold for statistical significance at the 5% level.
Limitations and Assumptions
Z-score tables assume your data follows a normal distribution, which isn’t always the case. Before applying z-scores, verify that your data is approximately bell-shaped through histograms or normality tests. For small sample sizes or heavily skewed distributions, t-distributions or non-parametric methods may be more appropriate. Additionally, the standard table provides probabilities to only a few decimal places; specialized software can calculate more precise values when needed. Remember that z-scores measure relative position within a specific dataset, so a z-score of 2.0 in one context may represent very different absolute values than in another, depending on the original mean and standard deviation.