What is the 1.5 IQR rule for outliers?

A value is an outlier if it is below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR, where IQR is Q3 minus Q1.

How do I calculate the upper fence?

Upper fence = Q3 + 1.5 × IQR. With Q1 = 15 and Q3 = 20, the IQR is 5 and the upper fence is 27.5.

Why are my quartiles different from Excel?

There are several quartile methods. Excel QUARTILE.INC interpolates between values, while some calculators take the value at a fixed position in the sorted list. Clear outliers are usually flagged by all methods.

Should I delete outliers?

Not automatically. Check for data errors first, keep real extreme values, and report results with and without the outlier if it changes your conclusion.

How to Find Outliers Using the IQR Method (1.5 × IQR Rule)

The short answer

A value is an outlier under the IQR method if it is below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR, where IQR = Q3 − Q1. Paste your numbers into the Statistics Calculator to get Q1, Q3 and the IQR instantly, then work out the two "fences" and check which values fall outside them.

Step by step

Sort the data from smallest to largest. The calculator does this for you.

Find Q1 and Q3. Q1 (the first quartile) is the value about a quarter of the way through the sorted list; Q3 is about three quarters of the way through.

Work out the IQR: Q3 − Q1. This is the spread of the middle half of the data.

Find the lower fence: Q1 − 1.5 × IQR.

Find the upper fence: Q3 + 1.5 × IQR.

Flag outliers: any value below the lower fence or above the upper fence.

Some people also use a second pair of fences at 3 × IQR. Values beyond those are sometimes called extreme outliers.

Worked example: delivery times

Here are 12 delivery times in minutes:

12, 14, 15, 15, 16, 17, 18, 18, 19, 20, 21, 45

Paste them into the Statistics Calculator. Among the results you will see:

Result	Value
Count (n)	12
Mean (Average)	19.1667
Median	17.5
Q1 (25th percentile)	15
Q3 (75th percentile)	20
IQR	5

Now the fences:

Lower fence = 15 − 1.5 × 5 = 15 − 7.5 = 7.5
Upper fence = 20 + 1.5 × 5 = 20 + 7.5 = 27.5

No value is below 7.5. One value, 45, is above 27.5, so it is an outlier. It is even beyond the 3 × IQR fence (20 + 15 = 35), so it would count as an extreme outlier too.

You can see its effect on the averages. With 45 included the mean is 19.17 minutes; without it the mean drops to 16.82, while the median barely moves (17.5 to 17). That is the usual pattern: outliers pull the mean, the median resists them. For more on that choice, see Mean vs Median vs Mode.

Why your quartiles may differ from Excel or a textbook

There is more than one accepted way to calculate quartiles, and tools do not all use the same one.

The Statistics Calculator takes Q1 and Q3 straight from the sorted list, at positions n × 0.25 and n × 0.75 counted from zero and rounded down. For 12 values that is the 4th value (15) and the 10th value (20).
Excel's QUARTILE.INC interpolates between values and gives Q1 = 15 and Q3 = 19.25 for the same data, so its IQR is 4.25 and its fences are 8.625 and 25.625.
Many textbooks take the median of each half of the data. For this data that gives 15 and 19.5.

In this example every method flags 45 and nothing else, which is typical: the methods usually agree on clear outliers and only differ for values sitting right on the edge of a fence. If you are doing coursework or a report, use the method your teacher or style guide specifies and say which one you used. If a value is borderline under one method, mention that rather than quietly dropping it.

What to do with an outlier

Finding an outlier is the start of a question, not the answer. Before removing anything:

Check for errors. A 45-minute delivery could be a typo for 15, a timer left running, or a real delay. Data entry mistakes are the easiest outliers to fix.
Ask whether it belongs. If one order went to a different city, it may not belong in this dataset at all.
Keep real extremes. If the delay really happened, it is information. Customers felt it. Removing it would make the service look better than it was.
Report both versions when in doubt: the summary with and without the outlier, and why.
Prefer robust statistics. The median and IQR are not dragged around by a single extreme value, so they often describe skewed data better than the mean and standard deviation.

When the 1.5 × IQR rule is not a good fit

Very small samples. With 5 or 6 values, quartiles jump around and the fences are unreliable.
Strongly skewed data, such as incomes or house prices. A long right tail is normal there, so the rule flags many legitimate high values. Consider working on a log scale or simply describing the tail.
Data with natural limits. Exam marks out of 100 cannot go above 100, so an upper fence of 112 is meaningless; the rule may never flag anything at the top.
When you need a probability statement. The IQR rule is a quick screening method. It does not tell you how unlikely a value is.

Common mistakes

Using 1.5 × Q3 instead of 1.5 × IQR. The multiplier applies to the IQR, the gap between the quartiles.
Adding to Q1 or subtracting from Q3. The lower fence is Q1 minus the margin and the upper fence is Q3 plus the margin.
Forgetting to sort. Quartiles only make sense on sorted data. Do it by hand carefully, or let the calculator do it.
Treating the fence value itself as an outlier. A value exactly equal to a fence is inside the fences.
Mixing up standard deviation rules. "More than 2 or 3 standard deviations from the mean" is a different method. The calculator's standard deviation is the population version; read Population vs Sample Standard Deviation if you need the sample one.

Quick checklist

Paste the data into the Statistics Calculator.
Note Q1, Q3 and IQR.
Lower fence = Q1 − 1.5 × IQR. Upper fence = Q3 + 1.5 × IQR.
List values outside the fences, investigate each one, and record what you decided.