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© Nuffield Foundation 2012 © Rudolf Stricker Nuffield Free-Standing Mathematics Activity House price moving averages

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© Nuffield Foundation 2010 How have house prices in the UK changed since 2000? Do the house prices change more in some quarters of the year than in others? How could fluctuations due to seasonal factors be smoothed out?

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© Nuffield Foundation 2010 House price moving averages Moving averages can be used to smooth out fluctuations due to seasonal factors. Moving averages For data points p 1, p 2, … the simple moving average at interval m with n data points is: It is often quicker to calculate successive values using

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© Nuffield Foundation 2010 Weighted moving averages The problem of lag can be addressed by using weighting. where the denominator is the triangular number with sum. The linear weighted moving average is:

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Reflect on your work What is a moving average? Why are they used? Describe two methods of calculating a moving average. Describe how to find a weighted moving average. Why does a weighted moving average help to overcome the problem of lag? © Nuffield Foundation 2012

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How to calculate seasonal index Pick time period (number of years) Pick season period (month, quarter) Calculate average price for season Calculate average.

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