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Descriptive statistics and normality test

Paste your data (spaces, commas or new lines). Get the summary statistics, a histogram, outliers and an Anderson-Darling normality test.

Formulas

Mean x̄ = Σx / n Standard deviation s = √(Σ(x − x̄)² / (n − 1)) Quartiles linear interpolation (Excel QUARTILE.INC); IQR = Q3 − Q1 Skewness n / ((n − 1)(n − 2)) × Σ((x − x̄)/s)³ Anderson-Darling A² = −n − (1/n) Σ (2i − 1)[ln F(zᵢ) + ln(1 − F(z₍ₙ₊₁₋ᵢ₎))] adjusted A* = A²(1 + 0.75/n + 2.25/n²); p-value from D'Agostino and Stephens

Read more: Normal distribution · Capability for non-normal data · Graphical analysis · Basic statistics

FAQ

How do I read the Anderson-Darling p-value?

The null hypothesis is that the data come from a normal distribution. A p-value below 0.05 is evidence that they do not. A high p-value does not prove normality; with small samples the test has little power.

Why does normality matter?

Capability indices, ppm estimates, individuals charts and many tests assume roughly normal data. Skewed data can make a Cpk or a ppm estimate badly wrong in the tails.

What do skewness and kurtosis tell me?

Skewness near 0 means symmetric; positive means a long right tail. Excess kurtosis near 0 matches the normal; positive means heavier tails and more extreme values than a normal distribution.

How are outliers flagged?

Values more than 1.5 × IQR below the first quartile or above the third quartile (Tukey's fences), the same rule a box plot uses. Investigate them before deleting anything: an outlier is often the most informative point.

Which quartile method is used?

Linear interpolation between order statistics, the same as Excel's QUARTILE.INC. Other software may use a slightly different method, so Q1 and Q3 can differ a little for small samples.

Descriptive statistics underpin every quality exam

This shows up on the exams as a calculation question. Practice it with new numbers every time, and every wrong answer explained.

Free CQE quiz (5 questions)
Free Green Belt diagnostic (20 questions)
Free Black Belt diagnostic (25 questions)

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