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Count {{ countDisplay }} IQR {{ iqrDisplay }} {{ outlierDisplay }}
One dataset, up to 5,000 finite values. Confirm the parsed count before using the result.
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Tukey splits the sorted halves; inclusive and exclusive modes use interpolated percentile ranks.
Values equal to a fence remain inside; only values strictly beyond it are flagged.
Choose 0–6. The neutral default is 2.
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A long list of observations becomes easier to read when five landmarks show its span and center. After sorting the values, the minimum and maximum mark the ends, the median splits the ordered list in half, and the first and third quartiles describe the middle half of the data.

StatisticPosition in the ordered dataWhat it helps reveal
MinimumSmallest observationLower endpoint
Q1Lower quartileLower edge of the middle half
MedianMiddle observation or midpoint of the middle pairTypical center without averaging extremes
Q3Upper quartileUpper edge of the middle half
MaximumLargest observationUpper endpoint

The distance from Q1 to Q3 is the interquartile range (IQR). Because it ignores the outer quarters, it is less sensitive to extreme values than the full range. A box plot turns the same quantities into a shape: the box spans Q1 to Q3, the median crosses the box, and whiskers extend to the most distant observations that remain inside the selected fences.

Quartiles do not have one universal small-sample convention. Tukey hinges, inclusive percentiles, and exclusive percentiles can return different Q1 and Q3 values from the same list, which also changes the IQR and outlier fences. Record the method when results will be compared with a spreadsheet, textbook, report, or another dataset. A fence flag is a reason to investigate an observation, not proof that it is erroneous.

How to Use This Tool:

Use values that represent one comparable quantity and keep its measurement unit consistent.

  1. Paste the Number list. Commas, spaces, and surrounding text are accepted when numeric tokens can be found; thousands separators such as 1,200 are read as part of one number.
  2. Choose the Quartile method required by the course, spreadsheet, or reporting policy. Use the same method for every dataset being compared.
  3. Choose a 1.5 × IQR fence, a 3 × IQR outer fence, or no fence. Set Decimal places for display without changing the calculation's stored precision.
  4. Read the five landmarks first, then check the IQR, whiskers, and outlier list. Use the sorted observations to confirm any unexpected boundary or repeated value.

Interpreting Results:

Compare the median with the two halves of the box. A longer Q3-to-median distance suggests more spread on the high side; a longer median-to-Q1 distance suggests more spread on the low side. The minimum and maximum can make the full range look large even when the middle half is compact.

Values exactly on a fence remain inside it; only values strictly below the lower fence or strictly above the upper fence are flagged. Fences are disabled when fewer than four values are present, the IQR is zero, or No outlier fence is selected. Small or repeated datasets can therefore produce a valid five-number summary without a meaningful outlier screen.

Technical Details:

All finite numeric tokens are sorted in ascending order before the summary is calculated. The input is limited to 5,000 values. Display rounding from 0 to 6 decimal places happens after the quartiles, spread statistics, fences, and whiskers are found.

Formula Core:

The IQR, fences, and quartile-based skew measure use:

IQR=Q3−Q1 FL=Q1−k×IQR FU=Q3+k×IQR SB=Q3+Q1−2Q2IQR

k is 1.5 for the standard fence and 3 for the outer fence. Q2 is the median. Bowley skew SB is set to zero when IQR is zero; values at or above 0.25 are labeled high-side stretch, values at or below −0.25 low-side stretch, and values between those boundaries balanced middle. Fewer than five observations receive the small-sample label first.

Quartile Rules:

MethodQ1 and Q3 ruleSmall-sample behavior
Tukey hingesMedian of the lower and upper halves; the overall median is excluded from both halves when count is oddA single value is used for all five landmarks
Inclusive percentileZero-based rank (n − 1)p with linear interpolation at p = 0.25 and 0.75Endpoints remain available
Exclusive percentileOne-based position p(n + 1) with linear interpolationPositions beyond the data fall back to the nearest endpoint

The lower whisker is the smallest observation greater than or equal to the lower fence, and the upper whisker is the largest observation less than or equal to the upper fence. The minimum and maximum in the five-number summary remain the actual dataset endpoints even when they are flagged as outliers.

Worked Example:

For 12, 18, 19, 21, 24, 26, 31, 34, 38, 42, 47, and 55 with Tukey hinges, the five-number summary is 12, 20, 28.5, 40, 55. The IQR is 20, so a 1.5 × IQR rule places the fences at −10 and 70. Every observation remains inside the fences, and the whiskers stay at 12 and 55.

References: