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What is an Outlier?

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Used in a sentence

University Course Reader · STEM

One outlier in the December figures pulled the yearly average up by nearly 40%.

The reader highlighted one term — in an article or a paper PDF. Clicked made the statistics term “outlier” easy to understand:

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Overview

An outlier is a data point that sits far from the rest: much higher or lower than the pattern the other values make. It matters because one extreme value can drag an average a long way from where most of the data sits. A decision built on that average is really built on the outlier. The number alone does not say what to do with it. It may be a mistake, a one-off, or the start of a new pattern, and only checking the story behind it tells you which.
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Overview

An outlier is the one number that refuses to sit with the others: eleven months of about 100 and then a 900. It matters because averages are gullible. One huge value and the mean climbs to a level no month ever hit, and anyone planning off that mean is planning off the freak. The outlier isn't good or bad, it's just far away. Whether you fix it, ignore it, or take it seriously depends on why it's out there, and the number can't tell you. Go and look. 😎

A quick take — often all you need.

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Detail

An outlier is a value that lies unusually far from the others in a set of data. Its distance is what defines it, often set as more than two or three standard deviations from the middle. What to do about it is a separate question, and the answer comes in three kinds. The outlier may be an error: a decimal in the wrong place, a broken sensor, a figure typed twice. Errors get corrected or removed. It may be genuine but caused by something that will not repeat: a one-time event that inflated one reading. Genuine one-offs get kept in the record and left out of any forecast, because they say nothing about the ordinary run of things. Or it may be genuine and the first sign of a change, in which case it is the most important value in the set. Nothing in the number itself distinguishes these. Two datasets can hold the same outlier for opposite reasons, so the only honest response is to go and find out what happened. What makes this urgent is that averages are sensitive to extremes. A single very large value pulls the mean towards it, which is why a room with one billionaire has a meaningless average income and why medians exist.
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Detail

An outlier is a data point way off from the pack, far enough that it clearly doesn't belong with the rest. The usual test is a distance of two or three standard deviations, give or take, which is a way of scoring how weird a value is. Spotting one is easy. Knowing what to do with one is the whole skill, because there are three completely different reasons a number can be out there. Someone fat-fingered it: fix or bin it. It really happened, but for a reason that won't happen again: keep it in the records and out of the forecast. Or it really happened and it's the first sign of something new: now it's the most important number you've got. Nothing about the value tells you which. Two spreadsheets can show the identical spike for opposite reasons, so the move is to go and look. And it matters because averages fall for outliers every time. One monster value and the mean has wandered off to somewhere no real data point lives. That is why people reach for the median when there's a billionaire in the room. 😎

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Analogy

A factory sells around 100 units a month for eleven months, then 900 in one month. The average is now 167, a level no actual month resembled, and someone asks whether to expand the plant. Before answering, find out what the 900 was. If one customer's order was keyed as 900 instead of 90, fix the number and forget it. If the order was real but a competitor's plant was shut that month and their customers bought from you once, keep the record and leave it out of the plan. No expansion. But if that customer has moved all their business to you for good, the 900 is the new normal and the plant does need to grow. Same outlier, three different actions, and the number alone could not choose between them.
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Analogy

Every video you post gets about 2,000 views. Then one gets 10 million. Should you drop out of college and buy the camera rig? Not yet: go and find out what the 10 million was. If it was a counter glitch, one bot refreshing all night, it's nothing, so ignore it. If a huge account shared it by mistake and deleted the share an hour later, it's real, it happened, and it won't happen again, so enjoy it and change nothing. But if it went viral because of something you did on purpose, and 200,000 people subscribed and are now watching the next one, that outlier is your new starting point. Now the camera rig is worth a look. 😎
Deepest level reached.

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AI explanations may contain errors · Not professional advice

Formal definition — The same term, explained the usual way

An outlier is an observation that lies an abnormal distance from other values in a dataset, commonly identified as lying more than a set number of standard deviations from the mean or beyond 1.5 times the interquartile range from the quartiles. Outliers may arise from measurement or recording error, from genuine but rare events, or from a change in the underlying process, and their treatment depends on which: erroneous values are corrected or excluded, while genuine values are retained and their influence on summary statistics, particularly the mean, is examined, often by reporting robust measures such as the median.

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