What is an outlier?

An outlier is a data point that sits unusually far away from the rest of your values. It might be a measurement mistake, a data entry typo, or a rare-but-real event. The key word is unusually: outliers aren’t defined by vibes — they’re defined by rules. Different rules flag different points, because “unusual” depends on assumptions.

This calculator gives you three popular, practical rules: IQR fences (quartile-based), Z-score (mean/std-based), and Modified Z-score (median/MAD-based). If you’re not sure which one to use, start with IQR. It’s simple, widely taught, and it works well even when your data isn’t perfectly bell-shaped.

• IQR (Tukey fences): Best default for most lists. Doesn’t assume normality. Great for skewed data.
• Z-score: Best when your data is roughly normal and you want a “standard deviations away” explanation.
• Modified Z: Best when you suspect extreme tails or messy data; it’s robust to big spikes.

• Try the Grades sample and screenshot the outlier. People love “someone got a 3%??” moments.
• Use the QA logs sample and screenshot the latency spike. Engineers instantly relate.
• Share the result card to group chats with “Should we drop this point?” — guaranteed discussion.

Frequently Asked Questions

• Is an outlier always “bad data”?

  No. Outliers can be errors, but they can also be the most important observations. Example: a fraud transaction, a rare disease marker, a viral post, or a system outage. Use outlier flags to investigate — not to auto-delete.

• Why do different methods flag different outliers?

  Because each method assumes a different idea of “typical.” Z-scores use the mean and standard deviation, which are sensitive to extreme values. IQR and Modified Z use quartiles or the median, which are more robust.

• What if my dataset has fewer than 4 numbers?

  With tiny datasets, “outlier” rules become unstable because quartiles and standard deviation aren’t meaningful yet. This tool will still compute basic stats, but you should treat flags as low-confidence until you have more data.

• Should I use k = 1.5 or k = 3 for IQR?

  k = 1.5 is the classic rule (flags “mild” outliers). k = 3 flags only very extreme points. If you’re doing data cleaning, start at 1.5 and review what gets flagged. If you’re doing “find the wild anomalies,” use 3.

How the Outlier Calculator works (step-by-step)

Behind the scenes, every method follows the same pattern: we parse your numbers, compute a few summary statistics, apply a rule to set boundaries (or scores), and then label any values that cross the threshold. The differences are mainly which statistics we trust and how we measure “distance.”

You can paste values separated by commas, spaces, tabs, or new lines. The calculator extracts valid numeric tokens, including negatives and decimals. Non-numeric text is ignored (so pasting from a sheet with notes won’t break things).

Most robust statistics (quartiles, median) use sorted values. After parsing, the calculator sorts your list from smallest to largest.

n is the number of values. The mean is the average: mean = (x₁ + x₂ + … + xₙ) / n. The median is the middle value (or the average of the two middle values) after sorting.

The IQR (interquartile range) measures the spread of the middle 50% of values. First we find: Q1 = 25th percentile and Q3 = 75th percentile. Then: IQR = Q3 − Q1. Using a multiplier k (usually 1.5), we compute bounds:

• Lower fence = Q1 − k·IQR
• Upper fence = Q3 + k·IQR

Any value below the lower fence or above the upper fence is flagged as an outlier. This is popular because it works even when your data is skewed — it doesn’t assume a bell curve.

Z-score asks: “How many standard deviations away from the mean is this value?” First compute the sample standard deviation: s = sqrt( Σ(xᵢ − mean)² / (n − 1) ). Then for each value: z = (x − mean) / s. We flag outliers when |z| ≥ threshold (often 3).

Z-score is intuitive (“3 sigmas away”) but can be misleading when the distribution is highly skewed or when a single extreme value inflates the standard deviation.

Modified Z-score replaces mean/std with the median and a robust spread estimate called MAD (median absolute deviation). First compute: MAD = median( |xᵢ − median| ). Then: M = 0.6745 · (x − median) / MAD. We flag outliers when |M| ≥ 3.5 (common rule of thumb).

The 0.6745 constant aligns MAD with standard deviation under normality, but the big win is robustness: the median and MAD barely move when a few extreme points appear.

Outlier examples (with interpretation)

Data: 12, 13, 14, 15, 16, 18, 22, 90
Most values cluster between 12 and 22, but 90 is far away. IQR fences will usually flag 90 as an outlier immediately.

Data: 31, 33, 35, 36, 38, 41, 45, 52, 180
Skew is normal for money, views, downloads, etc. IQR and Modified Z tend to behave better than classic Z-score here.

Data: 88, 91, 92, 90, 86, 89, 93, 3
The “3” screams typo (maybe 93?) — but it could also represent a student who didn’t submit. The calculator flags it; you decide the story.

Data: 120, 118, 121, 119, 122, 117, 800, 123
The 800ms request might be a one-off incident or a reproducible bug. Use the flagged point to investigate traces, not to hide the issue.

If two methods disagree, that’s not a failure — it’s a clue. It usually means your data is skewed, multi-modal, or small. Try IQR + Modified Z, then inspect the raw list.