SigmaCalc

Skewness Calculator

Is your data lopsided, and which way?

Dataset (comma / space / new-line separated)

Skewness

0.824

right-skewed (long tail to the right)

What you entered

Dataset: 10 values

1
Mean
Σx ÷ 10= 12.7
2
Second moment: average of (x−mean)²
Σ(x−mean)² ÷ n= 17.81
3
Third moment: average of (x−mean)³
Σ(x−mean)³ ÷ n= 61.956
4
Standard deviation (population)
√17.81= 4.2202
5
Skewness: third moment ÷ std dev³
61.956 ÷ 4.2202³= 0.8243
6
Interpretation
skewness = 0.8243= right-skewed (long tail to the right)

Result

Skewness: 0.824

Skewness of 0.824 — this dataset is right-skewed (long tail to the right).

Skewness and distribution shape

Skewness measures asymmetry. Zero is symmetric, positive means a long tail to the right, negative a long tail to the left.

Dataset	Mean	Median	Skewness	Shape
2, 4, 4, 4, 5, 5, 7, 9	5.00	4.50	0.656	Right-skewed
10, 12, 23, 23, 16, 23, 21, 16	18.00	18.50	-0.364	Left-skewed
1, 2, 3, 4, 5	3.00	3.00	0.000	Symmetric
5, 10, 15, 20, 25, 30	17.50	17.50	0.000	Symmetric
70, 75, 80, 85, 90, 95, 100	85.00	85.00	0.000	Symmetric
3, 7, 7, 19, 24, 30, 32, 45	20.88	21.50	0.249	Right-skewed

The mean and median columns are the intuition behind the number: where the mean sits above the median, the distribution is dragged right and skewness is positive; where it sits below, skewness is negative. Rows three to five are exactly symmetric and return precisely zero. Sign matters more than magnitude for most purposes - roughly, values beyond plus or minus 1 indicate substantial skew, and beyond 2 a strongly skewed distribution. Skewed data breaks the assumptions behind many standard tests, which is why it is worth checking before running a t-test or reporting a mean.

What skewness actually measures

Skewness quantifies asymmetry: a value near zero means the distribution is roughly symmetric, a positive value means a longer tail stretches to the right (a few unusually high values), and a negative value means the opposite — a longer tail to the left.

Why it matters beyond the shape

Skewed data pulls the mean away from the median — income, home prices, and wait times are all classic right-skewed distributions where a handful of large values inflate the average well above what's 'typical', which is exactly why skewness is worth checking before trusting a mean.

Frequently asked questions

What do positive and negative skewness mean?

Positive skew (right-skewed): a long tail to the right, mean > median. Examples: income, home prices, insurance claims. Negative skew (left-skewed): a long tail to the left, mean < median. Examples: exam scores on an easy test, retirement age.

How is skewness different from kurtosis?

Skewness measures asymmetry (which direction the tail stretches). Kurtosis measures tail heaviness (how likely extreme outliers are). A distribution can be symmetric but have heavy tails (high kurtosis), or be skewed with normal tails. They capture different aspects of shape.

If my data is highly skewed, what should I do?

Report the median instead of the mean, use IQR instead of standard deviation, and consider a log transformation before applying methods that assume normality. Many real-world datasets (income, wait times, file sizes) are naturally right-skewed.