About the Outlier Calculator
This outlier calculator finds unusually high or low values in a list of numbers using Tukey’s fence method, the same rule used to draw the whiskers on a box plot. It sorts your data, finds the first quartile (Q1), third quartile (Q3) and the interquartile range (IQR = Q3 − Q1), then flags any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR.
Use it for statistics homework, for cleaning survey or sensor data before averaging it, or for spotting data-entry errors such as an extra zero. The results list every outlier, the fences, how many values were flagged, and the mean with and without the outliers so you can see how much they pull the average.
You can switch to a multiplier of 3 to find only "extreme" outliers, and choose the quartile method: the median-of-halves method taught in most textbooks and used by TI calculators, or the inclusive percentile method used by Excel’s QUARTILE.INC. The two can give slightly different fences on small data sets.
How to use the outlier calculator
- 1Paste or type your numbers, separated by commas, spaces or new lines.
- 2Keep the 1.5 × IQR multiplier, or choose 3 × IQR for extreme outliers only.
- 3Pick the quartile method your course or software uses.
- 4Read the list of outliers, the fences and the quartiles.
- 5Compare the mean with and without outliers to judge their impact.
Formula and method
The data are sorted and split into quarters. Q1 is the median of the lower half and Q3 the median of the upper half (with the overall median left out when the count is odd); the inclusive method instead interpolates the 25th and 75th percentiles. The interquartile range, IQR = Q3 − Q1, is the spread of the middle 50% of the data and is not affected by extreme values.
Tukey’s rule marks any value more than 1.5 IQRs below Q1 or above Q3 as an outlier. Using 3 IQRs instead flags only extreme outliers ("far out" values). Because the fences depend only on quartiles, a few huge values cannot hide themselves by inflating the spread, unlike a rule based on the standard deviation.
- Q1
- First quartile (25th percentile)
- Q3
- Third quartile (75th percentile)
- IQR
- Interquartile range, Q3 − Q1
- k
- Fence multiplier (1.5 standard, 3 extreme)
Worked examples
Twelve test scores with two suspicious values
Sorted, the data are 2, 10, 11, 12, 13, 14 | 14, 15, 16, 17, 18, 45. Q1 is the median of the lower six (11.5) and Q3 of the upper six (16.5), so IQR = 5. The fences are 11.5 − 7.5 = 4 and 16.5 + 7.5 = 24, so 2 and 45 are outliers. Without them the mean is 14.
Ten delivery times (days) with one late parcel
The lower half is 3, 4, 4, 5, 5 (Q1 = 4) and the upper half 5, 6, 6, 7, 30 (Q3 = 6), giving IQR = 2 and fences of 1 and 9. Only the 30-day delivery lies outside, and removing it drops the mean from 7.5 to 5 days.
Extreme outliers only, Excel quartiles
With QUARTILE.INC the quartiles are 11.75 and 16.25 (IQR 4.5). A 3 × IQR fence runs from 11.75 − 13.5 = −1.75 to 16.25 + 13.5 = 29.75, so only 45 counts as an extreme outlier; the low score of 2 is inside.
Frequently asked questions
How do you find outliers using the IQR?+
Find Q1 and Q3, compute IQR = Q3 − Q1, then calculate the fences Q1 − 1.5 × IQR and Q3 + 1.5 × IQR. Any data point below the lower fence or above the upper fence is an outlier.
Why 1.5 times the IQR?+
John Tukey proposed 1.5 × IQR as a practical cut-off for box plots. For normally distributed data it flags only about 0.7% of points, so values beyond it are genuinely unusual. A 3 × IQR fence marks extreme outliers.
Should I remove outliers from my data?+
Only with a reason. Remove values that are clearly errors (typos, faulty sensors). Genuine extreme observations carry real information; report results with and without them, or use robust statistics such as the median.
Why do different calculators give different quartiles?+
There are several accepted quartile definitions. The median-of-halves method (TI-84, most textbooks) and Excel’s inclusive interpolation can give different Q1 and Q3 on small data sets, which shifts the fences slightly.
Can I use the standard deviation to find outliers instead?+
Yes — a common alternative flags values more than 2 or 3 standard deviations from the mean (z-score method). It works well for roughly normal data, but outliers inflate the standard deviation, so the IQR method is more robust.