---
title: "Skewed Distributions"
url: https://www.learningloftinstitute.com/glossary/skewed-distribution
source: Learning Loft Institute
language: en
updated: 2026-08-21
section: "Glossary › Skewed Distributions"
---
# Skewed Distributions
> **Answer.** A distribution is skewed when one tail is longer than the other. The skew is named after the tail: right, or positive, skew has a long tail towards the high values and pulls the mean above the median. Left, or negative, skew does the opposite, leaving the mean below the median.
## Key facts
| | |
| --- | --- |
| Definition | A skewed distribution is one whose graph is not symmetrical, having a longer tail stretching out on one side than on the other. |
| Where students meet it | Grade 9 or 10, when histograms and box plots have to be described in words, and in GCSE Statistics. |
| Also known as | Positively skewed distribution, Negatively skewed distribution, Asymmetric distribution |
## The name follows the tail, not the hump
This is where nearly everyone goes wrong first. A right-skewed distribution has most of its data on the left and a thin tail reaching right; it looks left-heavy, and calling it left-skewed feels natural. The convention names the direction the tail points, because the tail is what makes the distribution unusual.
The alternative names help, because they attach a sign instead of a direction. Positive skew means the tail runs towards the larger, more positive values; negative skew means it runs towards the smaller ones. If you can remember which end of a number line is positive, you can recover the whole convention without remembering anything else.
## What examiners actually ask
Questions rarely stop at naming the shape. They ask what the skew does to the averages, or hand you a mean and a median and ask you to deduce the shape — which is the same fact used backwards. Three cases cover it:
Read the middle case carefully. Mean ≈ median tells you the distribution is roughly symmetric; it does not tell you it is normal, or that it has one peak, or anything about how spread out it is. A class where half revised and half did not produces two separate humps, and the mean and median settle neatly between them, in a gap where almost nobody actually scored.
- Left, or negative, skew — long tail towards the low values: mean < median
- Roughly symmetric — the two tails match: mean ≈ median
- Right, or positive, skew — long tail towards the high values: mean > median
## Why the mean moves and the median does not
The mean is built from the size of every value, so a value far out in a tail contributes its full distance and drags the mean towards it. The median is built only from position: the extreme value counts as one item at the end of the queue, and moving it further out does not change which item is in the middle. That asymmetry is the whole mechanism, and it is worth being able to say it in a sentence, because that is what an explanation mark is for.
One honest caveat. The mean-and-median ordering is reliable for the single-peaked distributions that school and SAT questions use, and it is what mark schemes expect, but it is a rule of thumb rather than a theorem — statisticians can construct data sets where a right-skewed shape has its mean below its median. Nothing you meet before university will be one of them.
A box plot shows the same information without a mean anywhere. If the median line sits nearer the bottom of the box and the upper whisker is the longer one, the data is right-skewed; if the median sits high in the box with a long lower whisker, it is left-skewed. A symmetric distribution puts the median in the middle with whiskers of similar length.
## Questions
### Is right skew the same as positive skew?
Yes, they are two names for the same shape: a long tail towards the high values, with the mean sitting above the median. Left skew and negative skew are likewise the same thing. British textbooks tend to use positive and negative, American ones right and left, and exam papers use either, so both are worth knowing.
### Can I tell the skew from a mean and a median alone?
You can make a sound inference. A mean noticeably above the median suggests a right tail, and a mean below suggests a left one, which is exactly what exam questions expect you to say. Say "suggests" rather than "proves" — two numbers cannot describe a whole distribution, and a sketch or a box plot would settle it.
### Which average should I use for skewed data?
Usually the median, because the skew is what pulls the mean away from the bulk of the values. That is why typical incomes or house prices are reported as medians. The mean is still the right choice when the total matters — a school's total budget depends on the mean spend per pupil, not the median.
### Does a skewed distribution mean something is wrong with the data?
Not at all. Plenty of real quantities are naturally skewed, because they have a floor they cannot pass but no ceiling — waiting times, reaction times and rainfall all start at zero and can run long. Skew is a description of shape, not a fault to be corrected.
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