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Descriptive Statistics Calculator

Full descriptive statistics: central tendency, dispersion, quartiles, skewness, and kurtosis.

Descriptive statistics formulas

Meanx̄ = Σxn
MedianMiddle value of the sorted data (average of the two middle values if n is even)
Sample variance / SDs2 = Σ(x − x̄)2n − 1, s = √s2
Coefficient of variationCV = sx̄ × 100%
Skewnessg1 = m3m23/2, mk = Σ(x − x̄)kn
Excess kurtosism4m22 − 3

Worked examples

  1. Data: 3, 7, 7, 8, 10.

    1. Mean = 35 ÷ 5 = 7, median = 7, mode = 7, range = 10 − 3 = 7
    2. Deviations: −4, 0, 0, 1, 3 → squares sum to 26
    3. s = √26 / 4 ≈ 2.550, CV = 2.550 ÷ 7 ≈ 36.4%
    4. m2 = 26/5 = 5.2, m3 = (−64 + 1 + 27)/5 = −7.2 → g1 ≈ −0.607
    5. m4 = (256 + 1 + 81)/5 = 67.6 → 67.6 ÷ 5.22 − 3 = −0.5

    Answer: Slightly left-skewed (−0.61), flatter than normal (−0.5)

Tips & common mistakes

  • Negative skew = a longer tail on the left (a few unusually low values).
  • Use the median instead of the mean when data is skewed (incomes, house prices).