How to use it
- Paste the Data values, one per line or separated by spaces.
- Choose the Quartile method: Tukey's hinges, or linear interpolation as Excel's QUARTILE.INC does.
- Read the Interquartile range (IQR), Q1, Median and Q3, then the Outliers.
- Check the Box plot and How it is worked out.
Quartiles by two methods
The quartiles cut the sorted data into four parts of about equal size. Tukey's hinges split the data at the median and take the median of each half; when the count is odd, the median belongs to both halves. The linear method places each quartile at position (n − 1) × p + 1 of the sorted data and interpolates between the two neighbouring values, which is what Excel's QUARTILE.INC does.
The two methods agree for many data sets and differ for small ones. Neither is more correct; a report should name the method it used.
Tukey: Q1 = median of the lower half, Q3 = median of the upper half
linear: position = (n − 1) × p + 1, interpolated
IQR = Q3 − Q1Fences, whiskers and outliers
In a box plot the box runs from Q1 to Q3 and the median is drawn inside it. Tukey's rule marks as outliers the values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. The whiskers stop at the most extreme values inside those fences, and outliers are drawn as separate points. The rule is a convention for spotting unusual values, not a test that they are errors.
What the calculator does not cover
- Quartiles of grouped data, such as a frequency table with class intervals.
- Other percentiles and the mean and standard deviation: see the statistics calculator.
- A graphic box plot. The plot here is drawn in text, so it can be copied, but it has no colours or axes.
Worked example: 12 values with one high outlier
For the values 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 20 and 39, Tukey's hinges give Q1 = 12.5, median 14.5 and Q3 = 17.5, so the IQR is 5. The fences are 5 and 25, so 39 is an outlier. The linear method gives Q1 = 12.75 and Q3 = 17.25, an IQR of 4.5 and fences of 6 and 24, and 39 is again the only outlier.
| Measure | Tukey's hinges | Linear |
|---|---|---|
| Q1 | 12.5 | 12.75 |
| Median | 14.5 | 14.5 |
| Q3 | 17.5 | 17.25 |
| IQR | 5 | 4.5 |
| Upper fence | 25 | 24 |
Frequently asked questions
What is the interquartile range?
It is Q3 minus Q1, the range that holds the middle half of the data. Because it ignores the lowest and highest quarters, it is not affected by a few extreme values.
Why do different calculators give different quartiles?
They use different rules for the position of the quartiles, especially for small data sets. Tukey's hinges and the linear method are two common rules, and the results differ when the count is small.
Is an outlier always a mistake?
No. The 1.5 × IQR rule flags values that are unusual for the data, which may be correct and interesting. Check the source before you remove any value.
Should the median be included in both halves?
For Tukey's hinges with an odd count, yes: the median is part of both halves. Some calculators, such as the TI-83, leave the median out of both halves, which gives other quartiles; this tool follows the hinge rule.
How many values do I need?
At least two, but quartiles from a handful of values are rough. Five or more values give a box plot that means more.
Does the calculator send my data anywhere?
No. The calculation runs in your browser, and nothing you type is sent to our servers.
Sources
- NIST/SEMATECH e-Handbook of Statistical Methods: Box plot
- Wikipedia: Quartile, Method 2 (Tukey's hinges)
- Hyndman and Fan (1996), Sample quantiles in statistical packages, The American Statistician 50(4)
Figures and text last checked on Tuesday, November 10, 2026.