A normal probability curve has which type of skewness?

Concept

Skewness measures the left-right asymmetry of a probability distribution. It is represented by the standardized third central moment.

A symmetric distribution has matching shapes on both sides of its centre, so its third central moment and skewness are zero.

Application

The normal density is symmetric about its mean μ: points μ − a and μ + a have equal density for every distance a.

Therefore the positive and negative third-power deviations cancel in the third central moment, giving skewness 0.

Contrast

• Positive skewness has a longer right tail, unlike the balanced tails of a normal curve.

• Negative skewness has a longer left tail, unlike the balanced tails of a normal curve.

• Leptokurtic refers to kurtosis (tail weight and peakedness), not to the direction of skewness.

• Zero skewness is the skewness description produced by the symmetry of the normal curve.

Hence, a normal probability curve has zero skewness.