Identify outliers in a dataset using both the Tukey IQR fence method and z-score method, with Q1, Q3, IQR, fences, mean, and standard deviation.
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1
IQR outliers
0
Z-score outliers (|z| > 3)
9
Total values
IQR outliers (outside fences)
| Q1 (25th percentile) | 4 |
| Q3 (75th percentile) | 7 |
| IQR (Q3 − Q1) | 3 |
| Lower fence (Q1 − 1.5 × IQR) | -0.5 |
| Upper fence (Q3 + 1.5 × IQR) | 11.5 |
| Mean | 15.56 |
| Standard deviation | 31.73 |
Also in Statistics
Descriptive Statistics
This calculator identifies outliers in a dataset using two standard methods: the Tukey IQR fence method and the z-score method. Enter your data to see which values fall outside the fences or exceed your chosen z-score threshold, along with Q1, Q3, IQR, and key summary statistics.
John Tukey's fence method defines outliers as values that fall more than 1.5 × IQR below Q1 or above Q3. Q1 and Q3 are the 25th and 75th percentiles respectively, and IQR = Q3 − Q1 is the interquartile range.
A "mild" outlier falls between 1.5 × IQR and 3 × IQR beyond the quartiles. An "extreme" outlier falls more than 3 × IQR beyond. This calculator uses the standard 1.5 × IQR threshold.
A z-score measures how many standard deviations a value is from the mean: z = (x − x̄) / s. Values with |z| > 3 are flagged by default. This method assumes approximate normality and uses the sample standard deviation.
The z-score method is sensitive to masking — an extreme outlier can pull the mean and inflate the SD, potentially making another outlier appear non-extreme. The IQR method is more robust to this effect.
For most exploratory data analysis, the IQR fence method is preferred: it is robust, non-parametric, and widely understood. Use the z-score method when your data are approximately normally distributed.
Neither method is definitive. Always investigate flagged values before removing them — they may be legitimate extreme observations or the most informative data points.
Frequently asked questions
Only if you have a valid reason — for example, a data entry error or a measurement from the wrong population. Removing valid extreme values biases your analysis. If outliers are legitimate, consider robust statistical methods that are less sensitive to them.
The IQR method is non-parametric and uses the quartile structure. The z-score method is parametric and uses the mean and SD. For non-normal data or datasets with many outliers, the two methods can yield different results. The IQR method is generally more reliable for non-normal distributions.
Quartile calculation requires at least 4 values to produce meaningful Q1 and Q3 estimates using linear interpolation.
Related
These related calculators come from the same leaf category, nearby sibling categories, or the same top-level topic.
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Calculate Q1, Q2, Q3, the interquartile range (IQR), Tukey fences, and identify outliers in a dataset.
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