Nuffield Free-Standing
Mathematics Activity
House price
moving averages
© Rudolf Stricker
© Nuffield Foundation 2012
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?
© Nuffield Foundation 2010
How could fluctuations due to seasonal factors be smoothed out?
House price moving averages
Moving averages can be used to smooth out
fluctuations due to seasonal factors.
Moving averages
For data points p1, p2, … the simple moving
average at interval m with n data points is:
xm 
p m  p m1  p m2  ..... p m(n1)
n
It is often quicker to calculate successive values using
xm  1  xm 
© Nuffield Foundation 2010
p m( n1)
n

p m1
n
Weighted moving averages
.
The problem of lag can be addressed by
using weighting.
The linear weighted moving average is:
x
m

npm  n  1 p m1  n  2 p m2  .....  p m(n1)
n  n  1  n  2  ...  2  1
where the denominator is the
triangular number with sum
© Nuffield Foundation 2010
n n  1
2
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