AQA A Level Maths: Statistics复习笔记2.3.3 Skewness

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

2-3-3-skewness-diagram-1

  • 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

2-3-3-skewness-diagram-2

  • 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

2-3-3-skewness-diagram-3

Exam Tip

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

 

 

 

 

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