Skewness of Data (College Board AP® Statistics)

Skewness of data

What is skewness?

• When a set of data is plotted on a graph, the shape of the distribution of the data can be seen

• The shape of the distribution can be

  • symmetrical

  • or non-symmetrical

    • There are many different shapes that non-symmetrical distributions can take

• Skewness describes the direction in which a non-symmetrical distribution of data 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

How do I find the skewness from a boxplot?

• If a set of data is shown on a boxplot then looking at the differences between the quartiles can help to decide how it is skewed

  • If the median is roughly in the middle of the first and third quartiles, then the distribution is approximately symmetric

    • Q3 -  Q2  Q2- Q1

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

    • Q3 -  Q2 > Q2- Q1

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

    • Q3 -  Q2 < Q2- Q1

How do I find the skewness from the median and the mean?

• It is possible to find the skewness if given the median and the mean of a data set

  • In a symmetric distribution

    • the median and the mean are roughly the same

    • median mean

  • In a positively skewed distribution 

    • median < mean

  • In a negatively skewed distribution 

    • mean < median