Skewness Calculator

Skewness tells you whether a data set is lopsided; excess kurtosis tells you whether its tails are heavier or lighter than a normal distribution’s. Paste your data to get both, computed with the same sample formulas Excel’s SKEW and KURT use, plus a plain-English verdict.

11 values read.

Skewness
1.9056
Shape
Strongly right-skewed
Excess kurtosis
3.8495
Tails
Heavier than normal
Mean vs median
5.3636 vs 4
Count
11
±1 SD2468101214
▲ mean 5.3636 · ◆ median 4 · shaded band = mean ± 1 SD (1.9498 to 8.7775)

Step-by-step working

  1. Add the values and divide by the count to get the meanx̄ = (2 + 3 + 3 + 4 + 4 + 4 + 5 + 5 + …) ÷ 11 = 59 ÷ 11 = 5.363636
  2. Find the sample standard deviation ss = 3.413875
  3. Standardise each value, cube the z-scores and add themΣz³ = 15.591223
  4. Adjust for sample size (the formula Excel’s SKEW uses)G1 = n ÷ ((n − 1)(n − 2)) × Σz³ = 11 ÷ (10 × 9) × … = 1.905594
  5. Excess kurtosis uses fourth powers (Excel’s KURT): 0 for a normal distributionΣz⁴ = 43.724593 → excess kurtosis = 3.849509

Formula skewness G1 = n ÷ ((n − 1)(n − 2)) × Σ((x − x̄) ÷ s)³

Ask the tutor about your result

An AI tutor reads your inputs and results above and explains them in plain English. The numbers come from the calculator; the explanation is AI-written, so check it against your notes.

Reading the skewness value

  • About 0: roughly symmetric; mean and median are close.
  • Positive (right-skewed): a long tail of large values pulls the mean above the median, as with incomes or reaction times.
  • Negative (left-skewed): a tail of small values, as with scores on an easy test.

A common rule of thumb (Bulmer, Principles of Statistics) treats |skewness| below 0.5 as fairly symmetric, 0.5 to 1 as moderately skewed and above 1 as highly skewed. With small samples the estimate is noisy, so treat the verdict as a guide.

Reading excess kurtosis

Kurtosis compares the weight in the tails with a normal distribution. Excess kurtosis subtracts 3 so that a normal distribution scores 0. Positive values mean more extreme values than a normal curve would produce (heavy tails); negative values mean fewer (light tails, a flatter shape like the uniform distribution, whose excess kurtosis is −1.2). It is a statement about tails and outliers, not about how “peaked” the middle looks.

Frequently asked questions

Does this match Excel and Google Sheets?

Yes. Skewness uses the adjusted Fisher–Pearson formula behind SKEW(), and excess kurtosis the formula behind KURT(). Some software (and population formulas) give slightly different values for small samples.

How many values do I need?

At least 3 for skewness and 4 for kurtosis, and the values must not all be equal. For a stable estimate you want dozens.

Is the data normal if skewness is 0?

Not necessarily. Zero skewness only means symmetric. Check kurtosis and a plot as well; a formal test such as Shapiro–Wilk is better for normality.