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A LevelMaths: Probability & Statistics 1CIERevision Notes1. Data Presentation & Interpretation1.3 Working with Data1.3.2 Skewness

Skewness (CIE A Level Maths: Probability & Statistics 1)

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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 Tip

  • 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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    Amber

    Author: Amber

    Expertise: Maths

    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.