Calculate Q1, Q3, and IQR with the inclusive QUARTILE.INC method and linear interpolation.
The Interquartile Range Calculator reports Q1, Q3, and their difference, IQR = Q3 − Q1. It uses the inclusive quartile method associated with Excel QUARTILE.INC and linear interpolation. The output is the span between the first and third quartiles under that named convention, not a full five-number summary or an automatic outlier decision.
Quartile conventions differ. Some methods select a median of each half, while others interpolate at different rank positions. The same input can therefore produce slightly different quartiles under another convention. This page makes its method explicit so that results can be compared only when the method is compatible.
Enter finite values separated by commas or whitespace. The page sorts accepted values and ignores empty separators; invalid or non-finite tokens are listed. At least two accepted values are required. Q1 and Q3 remain on the original measurement scale, and IQR has the same unit as the inputs.
After sorting the n accepted values, the inclusive quartile position for probability p is 1 + (n − 1)p using one-based positions. For p = 0.25, this gives Q1; for p = 0.75, it gives Q3.
When a position falls between sorted observations, the value is obtained by linear interpolation between the two surrounding values. The interquartile range is then IQR = Q3 − Q1. Because the quartiles are ordered, the IQR is non-negative except for possible numeric-range limitations.
This is the QUARTILE.INC convention, not a universal definition shared by every statistical package. A method that uses a different rank rule can return different Q1, Q3, and IQR values, even though the input list is identical.
Q1 is the inclusive first quartile and Q3 is the inclusive third quartile under the page’s interpolation rule. IQR subtracts Q1 from Q3. Keep the method label with these values when presenting them because another quartile convention may use different positions.
For the default values 4, 8, 15, 16, 23, 42, the inclusive positions are 2.25 and 4.75. Interpolation gives Q1 = 9.75 and Q3 = 21.25, so IQR = 21.25 − 9.75 = 11.5. Each result is in the same unit as the input values.
The IQR summarizes the central quartile span; it does not label individual values as outliers on this page. A separate rule may compare observations with fences based on Q1 and Q3, but no such flags or outlier rows are displayed here.
A position such as 2.25 lies one quarter of the way from the second sorted value to the third. The calculator interpolates between those endpoints rather than rounding the position to one observation. The same principle applies at position 4.75, three quarters of the way between the fourth and fifth values. This explicit rank arithmetic explains why a quartile can be a decimal even when every input is a whole number.
Adding a fixed amount to every observation shifts both quartiles by that amount and leaves their difference unchanged. Converting all observations by a positive unit factor scales Q1, Q3, and IQR by that factor. Keep the unit transformation and interpolation method consistent when comparing results from separate lists.
The reported quartiles and IQR summarize only the accepted finite values using the inclusive linear-interpolation method. They do not establish a population interval, a confidence level, or an outlier classification.
For reproducible reporting, retain the dataset definition and the QUARTILE.INC convention. If another method is required by a protocol or software standard, use that method consistently instead.