Short answer
A symmetric distribution has its mean and median at the same point; the histogram looks roughly equal on both sides. A positively skewed distribution has a long tail to the right — the mean is greater than the median. In a negatively skewed distribution the tail goes left and the mean is less than the median.
At a glance
- Key stage
- GCSE
- Subject
- Statistics
- Type
- Explainer
- For
- Students
- Read time
- 5 min
- Last updated
- 21 October 2026
Where this fits
- Key Stage 3Years 7–9
- GCSEYears 10–11This article
Method at a glance
- Location
- Spread
- Shape
What is the shape of a distribution?
A distribution's shape describes how data values are spread across the range. In a GCSE statistics question you might be asked to describe the shape from a histogram, frequency polygon, or box plot, or to explain what the shape tells you about the context.
| Shape | Alternative name | Tail direction |
|---|---|---|
| Symmetric | Normal / bell-shaped | Both sides roughly equal |
| Positively skewed | Right-skewed | Tail extends to the right |
| Negatively skewed | Left-skewed | Tail extends to the left |
The tail is the long, thin region of the distribution where frequencies are low.
What is a symmetric distribution?
In a symmetric distribution, the left and right halves mirror each other around the peak. The mean, median, and mode all coincide (or are very close together).
Example context: Heights of adult men from the same population tend to be approximately symmetric — most men are close to the average, with roughly equal numbers slightly above and slightly below.
On a box plot: a symmetric distribution has the median line near the middle of the box, with the whiskers roughly equal in length.
What is a positively skewed distribution?
A positively skewed distribution has most data values clustered at the lower end, with a long tail stretching to the right (towards higher values).
Key relationship: mode < median < mean
The mean is pulled to the right by the extreme high values; the median is less affected. This makes the median a more representative average when data is positively skewed.
Example context: Income data is often positively skewed — most people earn moderate salaries, but a small number of very high earners pull the mean above the median. House prices in a city often follow the same pattern.
On a histogram: the peak is towards the left, with the frequency trailing off gradually to the right.
What is a negatively skewed distribution?
A negatively skewed distribution has most data values clustered at the upper end, with a long tail to the left (towards lower values).
Key relationship: mean < median < mode
The mean is pulled left by the extreme low values.
Example context: Scores on a very easy test tend to be negatively skewed — most students score near the top, with a few outliers who scored much lower. Similarly, age at retirement tends to be negatively skewed: most people retire close to state pension age, but some retire very early.
On a box plot: a negatively skewed distribution has the median line closer to the upper quartile, with a longer lower whisker than upper whisker.
How do you describe a distribution in an exam answer?
A good description covers three things:
- Location: quote the mean or median.
- Spread: quote the range or interquartile range (IQR).
- Shape: state whether it is symmetric, positively skewed, or negatively skewed, and give a brief reason.
Example answer: "The distribution of waiting times is positively skewed. The median is 12 minutes and the IQR is 8 minutes. The long tail to the right suggests a small number of customers waited much longer than average."
| Element | What to write |
|---|---|
| Shape | "positively skewed" / "negatively skewed" / "approximately symmetric" |
| Evidence | "tail extends to the right" / "median is below the mean" |
| Context | Explain what this means for the real-world situation |
How does skewness affect the choice of average?
When data is skewed, the median is usually the more representative average because it is not affected by extreme values. The mean is dragged towards the tail and may give a misleading impression of the "typical" value.
Example: In a set of salaries with one very high earner, the median salary is more informative than the mean.
When data is approximately symmetric, the mean and median are close together and either can be used.
Frequently asked questions
Can I identify skewness from a box plot?
Yes. Compare the position of the median line within the box and compare the whisker lengths. If the median line is closer to the lower quartile and the upper whisker is longer, the distribution is positively skewed. If the median line is closer to the upper quartile and the lower whisker is longer, it is negatively skewed.
Does a perfectly symmetric distribution ever occur in real life?
Truly perfect symmetry is rare, but many natural measurements (heights, reaction times, measurement errors) are approximately symmetric. When GCSE questions say "symmetric," they mean "roughly symmetric" — do not worry about minor deviations.
What is the difference between skewness and spread?
Spread (range, IQR, standard deviation) tells you how wide the distribution is. Skewness tells you whether it is lopsided to one side. A distribution can be wide and symmetric, or narrow and heavily skewed — these are independent properties.
Is skewness a Higher tier only topic at GCSE?
Describing the shape of distributions using the terms "positively skewed" and "negatively skewed" is mostly examined at Higher tier. Foundation students may be asked to compare two distributions (e.g. from box plots) without needing to use the formal term "skewed," though knowing the vocabulary is helpful.
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Key terms
- symmetric distribution
- positively skewed
- negatively skewed
- tail
- On a box plot
- Key relationship
- On a histogram
- Location