Outlier Calculator

Flag outliers with Tukey’s 1.5 × IQR rule: any value below Q1 − 1.5·IQR or above Q3 + 1.5·IQR. The calculator shows the quartiles, the fences and which values fall outside, on a dot plot and a box plot.

Outliers
45
IQR
4
Minimum
12
Q1
15
Median (Q2)
16.5
Q3
19
Maximum
45
Lower fence
9
Upper fence
25
Q1 15M 16.5Q3 19
Box plot. Whiskers reach the most extreme values inside the fences; red circles are outliers.
1015202530354045
▲ mean 19.2 · ◆ median 16.5

Step-by-step working

  1. Sort the data12, 14, 15, 15, 16, 17, 18, 19, 21, 45
  2. Find the median (Q2) of all 10 valuesQ2 = 16.5
  3. n is even, so split the data into two equal halveslower: 12, 14, 15, 15, 16 upper: 17, 18, 19, 21, 45
  4. Q1 is the median of the lower half; Q3 is the median of the upper halfQ1 = 15, Q3 = 19
  5. Interquartile range = Q3 − Q1IQR = 19 − 15 = 4
  6. Fences: 1.5 × IQR below Q1 and above Q3lower = 15 − 1.5 × 4 = 9 upper = 19 + 1.5 × 4 = 25
  7. Any value outside the fences is an outlier45

Note: Excel’s QUARTILE.INC (and some textbooks) interpolate instead, giving Q1 = 15 and Q3 = 18.75. Both are accepted methods; use the one your course teaches.

Formula lower fence = Q1 − 1.5 × IQR upper fence = Q3 + 1.5 × IQR

Ask the tutor about your result

An AI tutor reads your inputs and results above and explains them in plain English. The numbers come from the calculator; the explanation is AI-written, so check it against your notes.

Why the median ignores outliers

Eight quiz scores. Drag the slider to turn the last score into an outlier and watch which “average” gets pulled.

42444648505254
▲ mean 47.75 · ◆ median 47.5
Mean ▲
47.8
Median ◆
47.5
Gap
0.3

The mean uses every value’s size, so one extreme value drags it. The median only cares about order, so it stays put. That’s why house prices and incomes are reported as medians, and why a mean far from the median hints at skew or outliers.

How to find outliers step by step

  1. Find Q1 and Q3 (see the IQR calculator for the method).
  2. Compute IQR = Q3 − Q1.
  3. Multiply the IQR by 1.5.
  4. Subtract that from Q1 for the lower fence; add it to Q3 for the upper fence.
  5. Any value outside the fences is an outlier. Using 3 × IQR instead identifies “extreme” outliers.

What to do with an outlier

An outlier is a flag, not a verdict. First check for a typo or measurement error; fix or remove those, and say so. If the value is genuine, keep it and consider reporting resistant statistics (median and IQR) alongside the mean and SD. The z-score method (|z| > 3) is an alternative for roughly normal data, but outliers themselves inflate the SD, which can hide them.

Frequently asked questions

Why 1.5 × IQR?

John Tukey proposed it in Exploratory Data Analysis (1977) as a practical cut-off. For normally distributed data it flags about 0.7% of values, so real outliers stand out without flagging too many ordinary points.

Is a value exactly on the fence an outlier?

No. Only values strictly beyond the fences are outliers.