Skewness (Edexcel GCSE Statistics)

Skewness Basics

What is skewness?

• Skewness describes the way in which data in a distribution is 'leaning' 

  • A distribution that has its 'tail' on the right side has positive skew

    • Most of the data values are on the lower end

    • The distribution is stretched out in the positive direction

    • Values above the median have a greater spread than values below the median

  • A distribution that has its tail on the left side has negative skew

    • Most of the data values are on the higher end

    • The distribution is stretched out in the negative direction

    • Values below the median have a greater spread than values above the median

  • A distribution that is evenly spread out to the left and right is symmetrical

• Skewness can be spotted quite easily in histograms

• On a box plot looking at the median and quartiles can help you decide how a distribution is skewed

  • If the median is closer to the lower quartile then the distribution has positive skew

    • median - LQ < UQ - median

  • If the median is closer to the upper quartile then the distribution has negative skew

    • median - LQ > UQ - median

  • If the median is in the middle of the two quartiles then the distribution is symmetrical

• Looking at the values of the averages can help you decide how a distribution is skewed

  • mean > median > mode can indicate positive skew

  • mode > median > mean can indicate negative skew

  • In a perfectly symmetrical distribution the three averages are equal

Calculating Skew

• It is possible to calculate the skew of a data set using this formula

  • 

    • This formula is on the exam formula sheet, so you don't need to remember it

• If the skew is positive then the data has positive skew

  • The larger the value, the stronger the skew

    • A skew of 7 is stronger than a skew of 3

• If the skew is negative then the data has negative skew

  • The more negative the value, the stronger the skew

    • A skew of -7 is stronger than a skew of -3

• If the skew is equal to zero then the data is symmetrical