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math.z-score-outlier Calculator
Calculates z-scores for a set of observations and identifies statistical outliers using the 3-sigma rule. Data points more than 3 standard deviations from the mean are considered outliers in most applications — z-score is the standard screening method.
Inputs
Value
Reference formula or conversion factor shown for context.
Mean
Arithmetic average. Sensitive to outliers — if your data has extreme values, the median may be more representative.
Std Dev
Reference formula or conversion factor shown for context.
Results
z-score
Number of standard deviations a value is from the mean. |z| below 2: within normal range. |z| above 2: in the outer 5% of the distribution. |z| above 3: in the outer 0.3%.
P(X > value)
The computed numeric or monetary value.
P(X ≤ value)
The computed numeric or monetary value.
outlier?
Reference formula or conversion factor shown for context.
value
The computed numeric or monetary value.
z = (x-μ)/σ
Reference formula or conversion factor shown for context.