30 May 2014

Skewness

Let’s talk S1, as this year’s exam is fast approaching.

I don’t like the way my S1 textbook deals with skewness. It basically just sets out methods for identifying skewness without really explaining what it is. In this post I discuss an alternative approach.

I normally use this starter question in my first S1 lesson of the year:

The point being that when there are outliers in a data set, the mean becomes rather useless (unless of course you wish to deceive people!).
Whilst teaching S1 I often find myself referring back to my Bibonacci starter (‘remember that CEO? He ruined the mean!’). So I decided to make a worksheet out of it - see below - which I used for the first time this year when teaching skewness (if you like this then please leave me a review on TES!). My pupils enjoyed the activity and it generated interesting discussions.
There is a similar activity here - from the website Illustrative Mathematics.

The key teaching point is that when data is skewed, the median is more meaningful than the mean. We have various methods for identifying skewness in a data set (summarised in these slides – sorry, original source unknown) - we normally consider the shape of a frequency diagram or box plot. Sometimes skewness is apparent just from looking at the raw data (this sideways stem-and-leaf diagram is interesting).

Pupils need to remember that positive skew means we have a few 'sparse' data points (possibly outliers) at the top end of the data set – and like in the Bibonacci example, this will pull the mean up. This will help them conceptually understand the various methods described in the textbook.

Finally, here's a neat trick that I learnt from my colleague Lizzie... Imagine a cute puppy sitting on the left of the graph. A positive skew is going to see the puppy (positive = yay, a puppy!) and a negative skew is going away from the puppy (negative = get away from this puppy!). It's a silly but simple and memorable way of ensuring that students don't get the graphs mixed up.