acalculator

Are there any outliers in my data?

Paste a list of numbers. The outlier calculator finds Q1, Q3 and the interquartile range, draws the inner fences at 1.5 IQR and the outer fences at 3 IQR beyond the quartiles, and lists the mild and extreme outliers, with your data without them.

Your numbers

Read as: 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 25; 60
Outliers
2 outliers: 1 mild, 1 extreme

Outlier check: 2 outliers: 1 mild, 1 extreme.

Mild outliers
25
Extreme outliers
60
Q1
3.25
Q3
9.75
IQR
6.5
Lower inner fence
-6.5
Upper inner fence
19.5
Lower outer fence
-16.25
Upper outer fence
29.25
Without outliers
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Smallest value
1
Median
6.5
Largest value
60

Outliers: 2 outliers: 1 mild, 1 extreme. Outlier check: 2 outliers: 1 mild, 1 extreme.

Box plot of your numbers

How to calculate

Finds outliers in a list of numbers with the IQR fences: values beyond Q1 − 1.5 IQR or Q3 + 1.5 IQR are mild outliers, and beyond 3 IQR extreme outliers, as the NIST/SEMATECH e-Handbook defines them.

Example with the default inputs (Your numbers [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 25, 60], Quartile method NIST, (N + 1)p (Excel QUARTILE.EXC)): Outlier check: 2 outliers: 1 mild, 1 extreme.

Method: IQR = Q3 − Q1; inner fences Q1 − 1.5 IQR and Q3 + 1.5 IQR; outer fences Q1 − 3 IQR and Q3 + 3 IQR. Beyond an inner fence is a mild outlier, beyond an outer fence an extreme outlier.

  • A value exactly on a fence is not an outlier.
  • Quartiles follow the chosen method; NIST’s is the default.
  • The numbers are compared as the exact decimals typed.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Your numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 25, 60, Quartile method NIST, (N + 1)p (Excel QUARTILE.EXC) gives Q1 3.25, Q3 9.75, IQR 6.5, Upper inner fence 19.5, Upper outer fence 29.25, Mild outliers 25, Extreme outliers 60, Outliers 2 outliers: 1 mild, 1 extreme.Source: NIST/SEMATECH e-Handbook of Statistical Methods, §7.1.6 What are outliers in the data? (inner fences Q1 − 1.5 IQ and Q3 + 1.5 IQ, outer fences Q1 − 3 IQ and Q3 + 3 IQ; beyond an inner fence is a mild outlier, beyond an outer fence an extreme outlier), https://www.itl.nist.gov/div898/handbook/prc/section1/prc16.htm (retrieved 2026-10-02); NIST/SEMATECH e-Handbook of Statistical Methods, §7.2.6.2 Percentiles (p(N + 1) = k + d; Y(p) = Y[k] + d(Y[k+1] − Y[k]); the minimum for k = 0 and the maximum for k ≥ N), https://www.itl.nist.gov/div898/handbook/prc/section2/prc262.htm (retrieved 2026-10-02)
  2. Your numbers 10, 20, 30, 40, 50, 60, 70, 80, 90, 1,000, Quartile method NIST, (N + 1)p (Excel QUARTILE.EXC) gives Q1 27.5, Q3 82.5, Lower inner fence -55, Upper inner fence 165, Upper outer fence 247.5, Extreme outliers 1000, Mild outliers None.Source: NIST/SEMATECH e-Handbook of Statistical Methods, §7.1.6 What are outliers in the data? (inner fences Q1 − 1.5 IQ and Q3 + 1.5 IQ, outer fences Q1 − 3 IQ and Q3 + 3 IQ; beyond an inner fence is a mild outlier, beyond an outer fence an extreme outlier), https://www.itl.nist.gov/div898/handbook/prc/section1/prc16.htm (retrieved 2026-10-02); NIST/SEMATECH e-Handbook of Statistical Methods, §7.2.6.2 Percentiles (p(N + 1) = k + d; Y(p) = Y[k] + d(Y[k+1] − Y[k]); the minimum for k = 0 and the maximum for k ≥ N), https://www.itl.nist.gov/div898/handbook/prc/section2/prc262.htm (retrieved 2026-10-02)
  3. Your numbers 10, 20, 30, 40, 50, 60, 70, 80, 90, 1,000, Quartile method Median of halves (TI-83) gives Q1 30, Q3 80, IQR 50, Upper inner fence 155, Upper outer fence 230, Outliers 1 outlier: 0 mild, 1 extreme.Source: NIST/SEMATECH e-Handbook of Statistical Methods, §7.1.6 What are outliers in the data? (inner fences Q1 − 1.5 IQ and Q3 + 1.5 IQ, outer fences Q1 − 3 IQ and Q3 + 3 IQ; beyond an inner fence is a mild outlier, beyond an outer fence an extreme outlier), https://www.itl.nist.gov/div898/handbook/prc/section1/prc16.htm (retrieved 2026-10-02)
  4. Your numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 25, 60, Quartile method Inclusive, 1 + (N − 1)p (Excel QUARTILE.INC) gives Q1 3.75, Q3 9.25, Upper inner fence 17.5, Upper outer fence 25.75, Mild outliers 25, Extreme outliers 60.Source: NIST/SEMATECH e-Handbook of Statistical Methods, §7.2.6.2 Percentiles (p(N + 1) = k + d; Y(p) = Y[k] + d(Y[k+1] − Y[k]); the minimum for k = 0 and the maximum for k ≥ N), https://www.itl.nist.gov/div898/handbook/prc/section2/prc262.htm (retrieved 2026-10-02)

How it works

Sort the N numbers: Y[1] ≤ Y[2] ≤ … ≤ Y[N].

Quartiles, by the method you choose:

  • NIST (default): the position of the p-th quantile is h = (N + 1)p. Write h = k + d with k whole and 0 ≤ d < 1. Then Y(p) = Y[k] + d (Y[k+1] − Y[k]); Y(p) = Y[1] when k < 1 and Y[N] when k ≥ N. Q1 uses p = 0.25, Q3 p = 0.75.
  • Inclusive: the same rule with h = 1 + (N − 1)p.
  • Median of halves: Q1 is the median of the lower half and Q3 of the upper half; with N odd, the middle value is in neither half.

Fences and outliers:

  • IQR = Q3 − Q1
  • inner fences: Q1 − 1.5 × IQR and Q3 + 1.5 × IQR
  • outer fences: Q1 − 3 × IQR and Q3 + 3 × IQR
  • a value below the lower outer fence or above the upper outer fence is an extreme outlier
  • any other value below the lower inner fence or above the upper inner fence is a mild outlier
  • a value on a fence is not an outlier

The median is the middle value (the mean of the two middle values when N is even).

Rules

  • 4 to 10,000 numbers. Every number is read as the exact decimal typed, and the quartiles, fences and comparisons are exact fractions.
  • A fence too large to show as a number (beyond about 1.8 × 10³⁰⁸) is left out; the outliers are still found exactly.

Output format. The headline reads "No outliers", "1 outlier: 0 mild, 1 extreme" or "2 outliers: 1 mild, 1 extreme". The outlier lists and the list without outliers give the values smallest first, separated by ", ", each with up to 15 significant digits and a true minus sign (−3), or "None". Quartiles and fences show up to 10 significant digits.

Worked examples by hand

1 to 10, 25 and 60 (N = 12), NIST. Q1 at 13 × 0.25 = 3.25: Y[3] + 0.25 × (Y[4] − Y[3]) = 3.25. Q3 at 9.75: 9 + 0.75 × 1 = 9.75. IQR = 6.5. Inner fences −6.5 and 19.5; outer fences −16.25 and 29.25. 25 is beyond 19.5 only: mild. 60 is beyond 29.25: extreme.

Same data, inclusive. Positions 1 + 11 × 0.25 = 3.75 and 9.25: Q1 = 3.75, Q3 = 9.25, IQR 5.5. Fences 17.5 and 25.75: 25 is mild, 60 extreme.

10, 20, … 90 and 1000 (N = 10), NIST. Positions 2.75 and 8.25: Q1 = 20 + 0.75 × 10 = 27.5, Q3 = 80 + 0.25 × 10 = 82.5, IQR = 55. Inner fences −55 and 165; outer fences −137.5 and 247.5. 1000 is an extreme outlier.

Same data, median of halves. Halves 10 to 50 and 60 to 1000: Q1 = 30, Q3 = 80, IQR 50; fences 155 and 230: 1000 is extreme.

Other questions people ask

How do I find outliers with the IQR?

Find the first and third quartiles and the interquartile range IQR = Q3 − Q1. Any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is an outlier. For 1 to 10, 25 and 60 (NIST quartiles 3.25 and 9.75), the upper fence is 9.75 + 1.5 × 6.5 = 19.5, so 25 and 60 are outliers.

What is the difference between a mild and an extreme outlier?

A mild outlier lies beyond an inner fence (1.5 IQR from the quartiles) but not beyond an outer fence (3 IQR). An extreme outlier lies beyond an outer fence. In the example, the outer fence is 9.75 + 3 × 6.5 = 29.25, so 25 is mild and 60 is extreme.

Is a value exactly on a fence an outlier?

No. NIST calls a point an outlier when it is beyond a fence, so a value equal to the fence stays in. This page compares the exact decimals you typed, so a value on the fence is never pushed over it by rounding.

Why do other calculators find different outliers?

Quartiles have several definitions, so the fences move a little. NIST uses position (N + 1)p, Excel's QUARTILE.INC uses 1 + (N − 1)p, and the TI-83 takes the medians of the two halves. Pick the method your class or software uses.

Should I delete outliers from my data?

Not just because they are outliers. Check each one: a typing error or a broken measurement can be fixed or removed, but a real extreme value is part of the data. Report what you removed and why.

How many numbers do I need?

At least 4. With very few values the quartiles say little about the spread, so the fences are rough.