Асимметрия, эксцесс и нормальность

Beyond the average, every column has a shape. Knowing whether it is symmetric, lopsided, or heavy-tailed changes how you analyze it. 📊

Skewness measures how lopsided a distribution is. A perfectly symmetric bell has zero skew, while a long tail on one side pushes it positive or negative.

A positive skew has a long tail stretching right. Income is the classic case: most people cluster low while a few large values pull the mean upward.

A negative skew has its long tail on the left. Exam scores near a ceiling often look this way, with a few low results trailing far behind the pack.

Skew separates the mean from the median. In right-skewed data the mean sits above the median, which is why median is the safer center for skewed columns.

Kurtosis describes the tails. High kurtosis means heavy tails with more extreme values, while low kurtosis means thin tails and fewer surprises.

High kurtosis warns you to expect outliers. The distribution produces extreme values more often than a gentle bell curve ever would.

The famous bell curve is the normal distribution. It is symmetric, has skew near zero, and many statistical methods quietly assume your data looks like it.

You can check normality by eye with a histogram or a Q-Q plot, where points hugging the diagonal line suggest a roughly normal shape.

Some tests and models assume normality. When data breaks that assumption, your p-values and confidence intervals can quietly become unreliable.

A heavy right skew often relaxes after a log transform. Reshaping the column toward normal can make later modeling steps behave far more nicely.

A column has a long tail to the right and a positive skew value. Which statement is true?

Skew shows lopsidedness and kurtosis shows tail heaviness. The normal curve is the symmetric baseline, and a log transform can tame stubborn skew. ✅