A LevelMathsCambridge (CIE)Probability & Statistics 1Revision NotesData Presentation & InterpretationWorking with DataSkewness

Skewness (Cambridge (CIE) A Level Maths): Revision Note

Exam code: 9709

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Cambridge (CIE) Maths: Probability & Statistics 1AQA Maths: Statistics

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

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

  • 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

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