Interquartile Range Calculator

convention     median of halves, odd centre excluded
data sorted    1  2  3  4  |  5  6  7  8
method         Q1 is the median of the lower 4, Q3 the median of the upper 4.

Q1 2.5    Q3 6.5
IQR            6.5 - 2.5  =  4
middle 50%     2.5 to 6.5, holding 4 of the 8 values

same data under R7 linear interpolation at (n - 1)p
IQR 3.5

Q1

2.5

Q3

6.5

IQR

4

Middle 50%

2.5 to 6.5

Copy

Box plot on an axis from 1 to 8. Whisker at 1, box from 2.5 to 6.5 with the median at 4.5, whisker at 8. No value is outside the fences.

Q3 minus Q1, the middle 50% of the data, drawn as the box.

Under median of halves, odd centre excluded, 8 values give Q1 2.5 and Q3 6.5, an interquartile range of 4.

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.