Module 1 · Descriptive Statistics · Topic 6
Distribution Shape. The shape of a distribution describes how data values are spread around the center. Distributions can be symmetric, left-skewed (negatively skewed), or right-skewed (positively skewed).
Understanding Skewness. In a right-skewed distribution, the right tail is longer and the mean is pulled above the median. In a left-skewed distribution, the left tail is longer and the mean is pulled below the median. In a symmetric distribution, mean ≈ median.
Kurtosis. Kurtosis measures the “tailedness” of a distribution. Leptokurtic distributions (excess kurtosis > 0) have heavier tails. Platykurtic (excess kurtosis < 0) have lighter tails. Mesokurtic (excess kurtosis ≈ 0) matches the normal distribution.
xbar = sum(x_i) / n — The arithmetic average of a data set.s^2 = sum((x_i - xbar)^2) / (n - 1) — Average squared distance from the sample mean with Bessel correction.Income data is typically right-skewed: most people earn moderate incomes, but a few earn extremely high incomes, pulling the mean above the median. Exam scores where most students do well tend to be left-skewed.
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