Outlier Calculator

convention     median of halves, odd centre excluded
data sorted    1  2  3  4  |  5  6  7  100
method         Q1 is the median of the lower 4, Q3 the median of the upper 4.

Q1 2.5    Q3 6.5    IQR 4
lower fence    2.5 - 1.5 x 4  =  -3.5
upper fence    6.5 + 1.5 x 4  =  12.5

outside        100 (above)
               1 of 8 values, listed here and kept in every figure above

same data under R7 linear interpolation at (n - 1)p
Q1 2.75    Q3 6.25    IQR 3.5

IQR

4

Lower fence

-3.5

Upper fence

12.5

Outside the fences

1 of 8

Copy

Box plot on an axis from 1 to 100. Whisker at 1, box from 2.5 to 6.5 with the median at 4.5, whisker at 7. 1 value is outside the fences and drawn as a point: 100.

The 1.5 x IQR fences and every observation outside them, listed and kept in the data.

Under median of halves, odd centre excluded, the fences are -3.5 and 12.5, and 1 of the 8 values sits outside them: 100 (above). It stays in the data.

Commas, spaces, tabs, semicolons and new lines all separate values, so a column copied from a spreadsheet pastes straight in, and up to 10,000 values are read at a time. Figures on screen are rounded to six decimal places; the arithmetic itself keeps full double precision. Nothing you type leaves this browser.

Worked examples

• 1 to 8, median of halveseven count, halves are clean
  Q1 2.5, median 4.5, Q3 6.5, IQR 4
  Use
• Same data under R7linear interpolation
  Q1 2.75, median 4.5, Q3 6.25, IQR 3.5
  Use
• 1, 2, 3, 4, 5, 6, 7, 100the fences decide
  Fences -3.5 and 12.5: 100 listed outside, kept in the data
  Use

Where the conventions disagree

The same 8 values under all four conventions. They agree on the median, always. Where they differ, it is on Q1 and Q3.