# Are there any outliers in my data?

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.

- Page: https://www.acalculator.org/statistics/outlier-calculator
- JSON spec: https://www.acalculator.org/statistics/outlier-calculator.json
- Version: 6bc79a4be36c

## Default answer

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.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| data | Your numbers | The numbers, separated by commas, spaces, semicolons, or new lines. |
| method | Quartile method | How Q1 and Q3 are found. NIST uses position (N + 1)p. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| verdict | Outliers | How many outliers there are, mild and extreme. |
| mild | Mild outliers | Values beyond an inner fence but not an outer fence. |
| extreme | Extreme outliers | Values beyond an outer fence. |
| q1 | Q1 | The first quartile (25th percentile). |
| q3 | Q3 | The third quartile (75th percentile). |
| iqr | IQR | The interquartile range, Q3 − Q1. |
| lowerInner | Lower inner fence | Q1 − 1.5 × IQR. |
| upperInner | Upper inner fence | Q3 + 1.5 × IQR. |
| lowerOuter | Lower outer fence | Q1 − 3 × IQR. |
| upperOuter | Upper outer fence | Q3 + 3 × IQR. |
| kept | Without outliers | The values inside the inner fences, smallest first. |
| min | Smallest value | The smallest number. |
| median | Median | The middle value. |
| max | Largest value | The largest number. |

## 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.

## Assumptions

- 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.

## Worked examples

1. data = 1 or 2, method = nist gives q1 = 3.25, q3 = 9.75, iqr = 6.5, upperInner = 19.5, upperOuter = 29.25, mild = 25, extreme = 60, verdict = 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. data = 10 or 20, method = nist gives q1 = 27.5, q3 = 82.5, lowerInner = -55, upperInner = 165, upperOuter = 247.5, extreme = 1000, mild = 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. data = 10 or 20, method = halves gives q1 = 30, q3 = 80, iqr = 50, upperInner = 155, upperOuter = 230, verdict = 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. data = 1 or 2, method = inclusive gives q1 = 3.75, q3 = 9.25, upperInner = 17.5, upperOuter = 25.75, mild = 25, extreme = 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).

## FAQ

### 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.

## Sources

- NIST/SEMATECH e-Handbook of Statistical Methods, §7.1.6 What are outliers in the data? (lower and upper quartiles Q1 and Q3, the 25th and 75th percentiles; IQ = Q3 − Q1; lower inner fence Q1 − 1.5 IQ, upper inner fence Q3 + 1.5 IQ, lower outer fence Q1 − 3 IQ, upper outer fence Q3 + 3 IQ; a point 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 (set p(N + 1) = k + d; Y(p) = Y[k] + d(Y[k+1] − Y[k]) for 0 < k < N; Y[1] for k = 0 and Y[N] for k ≥ N). https://www.itl.nist.gov/div898/handbook/prc/section2/prc262.htm (retrieved 2026-10-02)