AQA A Level Maths: Statistics复习笔记2.3.3 Skewness

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

What is 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