Outlier Calculator
Enter a data set to find its quartiles and identify any outliers using the standard interquartile range (IQR) method — a common technique for flagging unusual values.
How the Outlier (IQR Method) formula works
The 1.5×IQR rule:
IQR = Q3 − Q1 Lower bound = Q1 − 1.5 × IQR Upper bound = Q3 + 1.5 × IQR Any value outside [Lower bound, Upper bound] is an outlier
Step-by-step calculation
- Sort the data and find the first quartile (Q1, the median of the lower half) and third quartile (Q3, the median of the upper half).
- Subtract Q1 from Q3 to get the interquartile range (IQR).
- Calculate the lower and upper bounds by extending 1.5×IQR below Q1 and above Q3.
- Any data point outside those bounds is flagged as an outlier.
Worked example
Data set: 4, 8, 15, 16, 23, 42, 100. Q1 ≈ 8, Q3 ≈ 42, IQR = 34. Lower bound = 8 − 51 = −43. Upper bound = 42 + 51 = 93. Since 100 exceeds the upper bound, it's flagged as an outlier.
Frequently asked questions
Why 1.5× the IQR specifically?
1.5×IQR is a widely used convention (popularized by statistician John Tukey) that works well for many roughly symmetric distributions — it's a practical rule of thumb rather than a strict mathematical law, and some fields use stricter or looser multipliers.
Does having an outlier mean the data point is wrong?
Not necessarily — an outlier just means a value is statistically unusual relative to the rest of the data set. It could reflect a data entry error, or it could be a genuine, meaningful extreme value worth investigating further rather than discarding.