Applies the 68-95-99.7 rule for data distribution within standard deviations of the mean for a normal distribution.
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Enter Mean (Average), Standard Deviation, and X-Value in the units shown.
Read Z-Score, Lower Bound (3 Standard Deviations), 99.7% Range (Within 3 Standard Deviations), Lower Bound (2 Standard Deviations), 95% Range (Within 2 Standard Deviations), Lower Bound (1 Standard Deviation), and 68% Range (Within 1 Standard Deviation) in the results panel. Results update as you change the inputs.
Choose a preset to load an example, then adjust the values for your situation.
See the inputs and their calculated results.
Mean (Average): 50; Standard Deviation: 10; X-Value: 60
Z-Score: 1; Lower Bound (3 Standard Deviations): 20; 99.7% Range (Within 3 Standard Deviations): 80; Lower Bound (2 Standard Deviations): 30; 95% Range (Within 2 Standard Deviations): 70; Lower Bound (1 Standard Deviation): 40; 68% Range (Within 1 Standard Deviation): 60
Mean (Average): 100; Standard Deviation: 15; X-Value: 130
Z-Score: 2; Lower Bound (3 Standard Deviations): 55; 99.7% Range (Within 3 Standard Deviations): 145; Lower Bound (2 Standard Deviations): 70; 95% Range (Within 2 Standard Deviations): 130; Lower Bound (1 Standard Deviation): 85; 68% Range (Within 1 Standard Deviation): 115
Mean (Average): 25; Standard Deviation: 5; X-Value: 30
Z-Score: 1; Lower Bound (3 Standard Deviations): 10; 99.7% Range (Within 3 Standard Deviations): 40; Lower Bound (2 Standard Deviations): 15; 95% Range (Within 2 Standard Deviations): 35; Lower Bound (1 Standard Deviation): 20; 68% Range (Within 1 Standard Deviation): 30
Use calculators for algebra, geometry, trigonometry, probability, statistics, averages, z-scores, tests, and graphing tasks.
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Performs a t-test (one-sample, two-sample, or paired) to compare means and determine statistical significance.
Finds the Z-score corresponding to a given cumulative probability (percentile) on a normal distribution.
Calculates the Chi-Square statistic and p-value for goodness-of-fit or test of independence. It requires observed and expected frequencies or values.
Identifies potential outliers in a dataset using the IQR * 1.5 rule (calculating fences).