1. © Nuffield Foundation 2011 Nuffield Free-Standing Mathematics Activity Outdoor Gig

2. © Nuffield Foundation 2011 How important is the weather for organising an outdoor gig? Which month has the best chance of good weather for an outdoor gig? In this activity you will use data from past years to find out. Wet Sunny Hot

3. © Nuffield Foundation 2011 Total monthly hours of sunshine for the years 2001 – 2010 YearJanFebMarAprMayJunJulAugSepOctNovDec 2001 74.586.790.2134.6226.2192.7190.0177.8113.8103.665.875.4 2002 41.275.3112.4189.4180.2163.5163.9158.3154.693.455.334.3 2003 70.595.3165.2191.3189.9209.4172.5207.6166.0130.367.452.1 2004 49.588.3108.2133.3204.6198.2166.0173.8155.795.947.952.1 2005 56.472.079.5146.9216.6190.8178.4210.6150.681.190.857.0 2006 51.068.397.4160.4173.1229.7287.6151.4157.595.693.145.8 2007 60.570.4153.9216.5167.1149.8179.7198.1149.3109.471.251.2 2008 47.8118.2120.0153.9193.0199.3184.9112.8114.6122.556.666.4 2009 56.955.6153.2170.3212.7202.0177.1173.5142.890.265.762.2 2010 60.960.1125.8201.8204.8238.8152.1148.8138.8120.371.553.8 Think about Why is it difficult to see which is the sunniest month? Which months are obviously not the sunniest?

4. © Nuffield Foundation 2011 YearJul 2001 190.0 2002 163.9 2003 172.5 2004 166.0 2005 178.4 2006 287.6 2007 179.7 2008 184.9 2009 177.1 2010 152.1 Think about Why is the mean a good representative value? When might the median be better? To find the mean number of hours of sunshine for July Add all the data for July: Total = 190.0 + 163.9 + 172.5 + 166.0 + 178.4 + 287.6 + 179.7 + 184.9 + 177.1 + 152.1 = 1852.2 Divide by the number of years Mean = 1852.2  10 = 185.22 Mean = 185.2 hours of sunshine (to 1 dp) Try this Find the mean number of hours of sunshine for May, June and August.

5. © Nuffield Foundation 2011 YearJul 2001 190.0 2002 163.9 2003 172.5 2004 166.0 2005 178.4 2006 287.6 2007 179.7 2008 184.9 2009 177.1 2010 152.1 Think about Is July a reliably sunny month? Range = largest value – smallest value = 287.6 – 152.2 Range for July = 135.5 hours of sunshine You can use the range to compare the reliability with other months. 287.6 152.1 Try this Find the range for May, June and August.

6. Comparing mean and range values MayJuneJulyAugust Mean196.8197.4185.2171.3 Range 59.1 89.0135.5 97.8 Think about Compare the results. What do they tell you about the amount of sunshine? Work out the mean and range for rainfall and temperature. Write a short report. Decide which month you think is best for an outdoor gig, and say why. Try this Total monthly hours of sunshine (2001 – 2010)

7. Outdoor Gig At the end of the activity How do you work out the mean? How do you work out the range? Can you predict next year’s weather reliably from previous data? Why is the mean a good representative value? If you use data for 20 years, is there an easy way to divide by 20 without using a calculator? What is measured by the range? If you use data for 50 years, is there an easy way to divide by 50 without using a calculator?