1. © Nuffield Foundation 2011 Nuffield Free-Standing Mathematics Activity Music Festival

2. © Nuffield Foundation 2011 How important is the weather for organising a music festival? 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. Wet Sunny Hot

3. © Nuffield Foundation 2011 Mean monthly temperature data for the years 2001 – 2010 (Includes night-time as well as daytime temperatures.) YearJanFebMarAprMayJunJulAugSepOctNovDec 20013.24.24.97.312.013.716.516.413.0 7.13.4 20025.36.67.28.811.513.915.416.613.99.78.25.4 20034.23.77.29.311.615.517.017.714.08.97.94.7 20044.95.06.29.111.715.015.417.114.410.37.55.3 20055.74.06.88.611.015.016.315.814.812.76.04.3 20064.03.64.68.311.815.519.115.916.312.67.96.1 20076.65.76.910.911.614.715.115.313.710.77.24.8 20086.35.25.97.712.913.816.0 13.29.56.83.5 20092.94.06.79.511.714.515.916.414.011.28.33.0 20101.22.65.88.610.514.916.915.213.610.25.1-0.5 The mean temperature for a month is given by the formula: mean number of years sum of the temperatures You can use a calculator or a spreadsheet to work this out. Think about Why is the mean a good representative value? When might the median be better?

4. To find the mean temperature for July = 16.36  C Use your calculator in COMP mode: Use your calculator in Stats Mode to check this result. Think about What are the advantages and disadvantages of each method?

5. Standard deviation   n = To measure spread n x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 x7x7 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. Think about why is squared before the values are added Think about how the standard deviation will increase as the spread increases

6. Standard deviation of July temperatures 16.5, 15.4, 17, 15.4, 16.3, 19.1, 15.1, 16, 15.9, 16.9 Mean = 16.36  C Standard deviation,  n = 1.095… = 1.10  C (to 2 dp) Use your calculator in Stats Mode to check this result. Try this Work out the mean and standard deviation for August.

7. Comparing mean and standard deviations: JulyAugust Mean 16.36  C16.24  C Standard deviation 1.10  C0.73  C Think about Compare the results for July and August. What do they tell you about the temperature in July and August? 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. Try this

8. 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?