If the shape of the graph is not like this, and is bunched up on wither the left or right side, we say the data is “Skewed”. There is a great one page summary about Skew on the following web page: However, we need to view the S&L Plot sideways to see whether the Skew is to the left or the right. Measurement of Skew can also be applied to Stem and Leaf Plots. The following video uses Microsoft Excel to show examples of Skewed Histograms, and how their shape affects the Mean Average Value. The Mean, Median, and Mode will all be close together in the middle. This particular maths class is fairly normal, and the sudents have produced both low and high scores. The “Kangaroo Rule” fits onto a symmetrical graph as shown below. If our Histogram is a pyramid type balanced shape, with both sides of the Median pretty much the same shape, then we say it is “Symmetrical”. The Mode is to the right of the middle Median, because the tall bars are all on the right hand side of the graph.ĭue to the long tail of low scores stretching to the left, the Mean will be dragged to the left of the Median. This means that the skew is to the Left, which is the negative direction. Placing a Kangaroo onto the graph shows that the tail goes to the left. This particular class of students has performed very well on the Algebra Test, and we have many high scores with tall bars on the right. The following example demonstrates and shows “Negative Skew”, where a Histogram stretches out to the left. The Mode is to the left of the middle Median, because the tall bars are all on the left hand side of the graph.ĭue to the long tail of high values stretching to the right, the Mean will be dragged to the right of the Median. Having an uneven skew shape in the Graph also affects the Mean,Median, and Mode. We call this the “Skew and Kangaroo Rule”. We can think of the shape of the Graph as resembling an Australian Kangaroo, and the direction of the Roo’s tail tells us the direction of the skew. This particular class of students has not performed well on the Algebra Test, and so we have many low scores with tall bars on the left. The following example demonstrates and shows “Positive Skew”, where a Histogram stretches out to the right. This often means that we should use the Median as our average in these situations, and not use the distorted Mean value. Skewed Graphs with their uneven shape affect the Mean Average Value. Skewed Data results for situations where there are either a lot of measured items that are very small, or a lot of items that are very large. If the shape of the graph is not like this, and is bunched up on either the left or right side, we say the data is “Skewed”. If the tallest area (Mode) is in the middle of the Graph, with even reducing on each side of this, the Graph is called Symmetrical. The shape of a Histogram, Bar Chart, or Stem and Leaf plot tells us the type of data distribution we have. This statistics lesson is all about Symmetry Skew and the Kangaroo ! Image Copyright 2013 by Passy’s World of Mathematics

Interpreting stem and leaf plots