Nuffield Free-Standing Mathematics Activities Music Festival

How important is the weather for organising a music festival? Hot Sunny Wet Which month has the best chance of good weather for an outdoor festival? In this activity you will use data from past years to find out.

The mean temperature for a month is given by the formula: Mean monthly temperature data for the years 2001 – 2010 (Includes night-time as well as daytime temperatures.) Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 2001 3.2 4.2 4.9 7.3 12.0 13.7 16.5 16.4 13.0 7.1 3.4 2002 5.3 6.6 7.2 8.8 11.5 13.9 15.4 16.6 9.7 8.2 5.4 2003 3.7 9.3 11.6 15.5 17.0 17.7 14.0 8.9 7.9 4.7 2004 5.0 6.2 9.1 11.7 15.0 17.1 14.4 10.3 7.5 2005 5.7 4.0 6.8 8.6 11.0 16.3 15.8 14.8 12.7 6.0 4.3 2006 3.6 4.6 8.3 11.8 19.1 15.9 12.6 6.1 2007 6.9 10.9 14.7 15.1 15.3 10.7 4.8 2008 6.3 5.2 5.9 7.7 12.9 13.8 16.0 13.2 9.5 3.5 2009 2.9 6.7 14.5 11.2 3.0 2010 1.2 2.6 5.8 10.5 14.9 16.9 15.2 13.6 10.2 5.1 -0.5 The mean temperature for a month is given by the formula: sum of the temperatures mean number of years Think about Why is the mean a good representative value? When might the median be better? You can use a calculator or a spreadsheet to work this out.

To measure spread n x1 x2 x3 x4 x5 x6 x7 Think about why is squared before the values are added Standard deviation s n = n Think about how the standard deviation will increase as the spread increases Think about why the sum is divided by n This formula is quite difficult, but you do not need to remember it. Your calculator can work out the standard deviation for you.

Using a spreadsheet to find the mean and standard deviation use the formula or the statistical function = AVERAGE To find the standard deviation: use the statistical function = STDEVP

Comparing means and standard deviations: Think about Compare the results for July and August. What do they tell you about the temperature in July and August? July August Mean 16.36 C 16.24 C Standard deviation 1.10 C 0.73 C Try this Work out the mean and standard deviation for other months. Also use the rainfall and sunshine data. Write a short report. Decide which month you think is best for a music festival and say why.

Music Festival At the end of the activity Why is the mean a good representative value? What is measured by standard deviation? Can you predict next year’s weather reliably from previous data?