Written by Dackohn; last reviewed November 2026.
Skewness measures asymmetry: positive means a long right tail, negative a long left tail. Excess kurtosis measures tail weight compared with a normal distribution, which scores 0. As a rough guide, |skewness| below 0.5 is fairly symmetric and above 1 is strongly skewed.
Skewness
In a right-skewed (positively skewed) distribution, most values are low with a few very high ones, as with incomes, house prices and reaction times. The mean is pulled above the median. A left-skewed distribution has the opposite shape, such as scores on an easy exam, where most people do well and a few do badly.
| |Skewness| | Usual description |
|---|---|
| Below 0.5 | Roughly symmetric |
| 0.5 to 1 | Moderately skewed |
| Above 1 | Strongly skewed |
Kurtosis
Kurtosis describes how much of the variance comes from rare extreme values. A normal distribution has kurtosis 3, so software usually reports excess kurtosis (kurtosis − 3), which is 0 for a normal distribution.
- Positive excess kurtosis: heavy tails and more extreme values than a normal distribution.
- Negative excess kurtosis: light tails. A uniform distribution has −1.2.
Textbooks often describe kurtosis as “peakedness”. That is misleading: it is mainly about the tails, and distributions can have a sharp peak with low kurtosis or a flat top with high kurtosis.
Worked example
Twenty reaction times, from 388 to 702 ms, have mean 460.75 and median 433.5. The mean exceeds the median, which hints at right skew. The numbers confirm it: skewness is 1.75 and excess kurtosis is 3.05, both driven by two slow responses of 620 and 702 ms. Taking logarithms reduces the skewness only to 1.40, so here a rank-based test may be the better choice.
Are they large enough to matter?
You can divide each by its standard error to get a z-value. In the example, the standard errors are 0.51 and 0.99, giving z = 3.42 and 3.07, beyond ±1.96. But this check depends heavily on sample size: with thousands of values, even trivial skew becomes significant. With large samples, judge by the size of the skewness and by looking at a plot.
What to do with skewed data
- Plot it. A histogram and a Q-Q plot show more than any single number.
- Report the median and IQR alongside or instead of the mean and SD.
- Transform positive values with a log or square root, which often helps with right skew.
- Consider sample size. With large samples, t-tests and ANOVA tolerate moderate skew. With small ones, use a rank-based test.
A warning about small samples
Both statistics are unstable in small samples, because a single value can change them a lot. Below about 20 observations, treat them as rough guides only. Note too that software differs: Excel and SPSS report adjusted values, which can differ noticeably from unadjusted ones when n is small.
Try it yourself
Skewness and Kurtosis Calculator →Get both statistics with standard errors and a plain-English reading. Normality Test →Shapiro–Wilk with a histogram and a Q-Q plot.Frequently asked questions
What is a normal range for skewness and kurtosis?
Skewness between -0.5 and 0.5 and excess kurtosis between about -1 and 1 are usually considered close to normal, though these are conventions and depend on the purpose.
Is kurtosis about the peak or the tails?
Mostly the tails. High kurtosis means more extreme values, regardless of how the peak looks.
Does Excel calculate excess kurtosis?
Yes. Excel's KURT function returns adjusted excess kurtosis, so a normal distribution gives a value near 0.
Related reading: Mean, median and mode · How to detect outliers · Parametric vs nonparametric tests
Sources & further reading: NIST/SEMATECH e-Handbook of Statistical Methods · OpenStax Introductory Statistics. How we compute & validate: methodology. Written & reviewed by Dackohn; last reviewed August 2026.