Box and Whisker Diagrams Skewed Box and Whisker Diagrams

Symmetrical Some sets of data are almost symmetrical. For a symmetrical data set, the box and whisker diagram is also symmetrical and the mean and median are close together.

Skewness A data set that is not symmetrical is said to be skewed. e.g. This data set is skewed to the right. Data sets with the tail to the right are positively skewed. Data sets with the tail to the left are negatively skewed.

The right side of the data is longer – so this is skewed to the right. Skewness To determine if data is skewed, you look at the distance from the median to the two outer points, (whiskers). The right side of the data is longer – so this is skewed to the right. If the distance from the median to the lower extreme, (left), is longer, the data is skewed to the left. If the distance from the median to the upper extreme, (right), is longer, the data is skewed to the right.

NOTES:

Exercise Skewed left Skewed right The box and whisker diagrams show the heights of a sample of year 8 boys and girls. Girls Boys Source: CensusAtSchool Skewed left Skewed right Are the above box plots symmetrical, skewed right, or skewed left?

Practice Symmetrical Skewed left Skewed left Skewed right