Skewness (Cambridge International A-Level Mathematics)

Skewness

What is skewness?

• The distribution of a data set is either symmetrical or it has skewness.

• Skewness describes the way in which data in a non – symmetrical distribution is leaning

• A distribution that has its tail on the right side has positive skew

• A distribution that has its tail on the left side has negative skew

• If the distribution is shown on a box plot looking at the difference between the quartiles can help decide how it is skewed

  • If the median is closer to the lower quartile then the distribution has positive skew

    • Q₃ - Q₂ > Q₂- Q₁

  • If the median is closer to the upper quartile then the distribution has negative skew

    • Q₃ - Q₂ < Q₂ - Q₁

• Looking at the values of the statistics can help you decide whether distribution is positively skewed or negatively skewed

  • In a positively skewed distribution

    • Mode < median < mean

  • In a negatively skewed distribution

    • Mean < median < mode

Exam Hint

• You only need to be able to recognise the different types of skewness
• It can help to comment on skewness when asked to compare distributions