Skewness (Edexcel International A Level Maths): Revision Note

Dan Finlay

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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

Examiner Tips and Tricks

  • It can help to comment on skewness when asked to compare distributions.

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Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.