Outlier Detection CalculatorFree online math calculator — instant results, no sign-up

Sort the data as x₁ ≤ … ≤ xₙ. For p ∈ {0.25, 0.75}, set h = 1 + (n − 1)p, j = floor(h), and g = h − j; calculate Q(p) = (1 − g)xⱼ + gxⱼ₊₁ when j < n, or Q(p) = xₙ when j = n. Then Q₁ = Q(0.25), Q₃ = Q(0.75), IQR = Q₃ − Q₁, L = Q₁ − 1.5 × IQR, and U = Q₃ + 1.5 × IQR. A value xᵢ is an outlier if xᵢ < L or xᵢ > U.

• nNumber of observations.
• xᵢObservation at position i in the sorted data, with positions starting at 1.
• pQuantile proportion: 0.25 for the first quartile or 0.75 for the third quartile.
• hInterpolated position of the requested quantile.
• jInteger part of h, obtained by rounding down.
• gFractional part of h, used as the interpolation weight.
• Q(p)Quantile calculated by linear interpolation between adjacent sorted observations.
• Q₁, Q₃First and third quartiles, representing the 25th and 75th percentiles.
• IQRInterquartile range, the difference between Q₃ and Q₁.
• L, ULower and upper outlier fences.

The calculator sorts the observations, finds the first and third quartiles using linear interpolation at positions 1 + (n − 1)p, and computes their difference. It extends 1.5 times that difference below Q₁ and above Q₃ to obtain the fences, then checks each observation against them. For 2, 4, 6, 8, 10, the quartile positions are 2 and 4, so Q₁ = 4, Q₃ = 8, and IQR = 4. The fences are 4 − 1.5 × 4 = -2 and 8 + 1.5 × 4 = 14; every observation lies within these fences.

These are the calculator's starting values and the results it actually produces for them.

1. 1Enter your observations in Values, separated by commas, or keep the default 2, 4, 6, 8, 10.
2. 2Check that every entry is numeric and that all observations use consistent units.
3. 3Run the calculation to obtain the interpolated-quartile outlier fences.
4. 4Read the Lower fence and Upper fence results; the default data produce -2 and 14.
5. 5Review the Outliers result; the default data show None because no value is below -2 or above 14.