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## Nuffield Free-Standing Mathematics Activity Music Festival

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**How important is the weather for organising a music**festival? Hot Wet Sunny 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.**Mean monthly temperature data for the years 2001 – 2010**(Includes night-time as well as daytime temperatures.) The mean temperature for a month is given by the formula: sum of the temperatures Think about Why is the mean a good representative value? When might the median be better? mean You can use a calculator or a spreadsheet to work this out. number of years**To find the mean temperature for July**Use your calculator in COMP mode: = 16.36C Think about What are the advantages and disadvantages of each method? Use your calculator in Stats Mode to check this result.**x7**x1 x2 x5 x6 x3 x4 n To measure spread Think about why is squared before the values are added Standard deviation sn = 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.**Mean = 16.36 C**Standard deviation of July temperatures 16.5, 15.4, 17, 15.4, 16.3, 19.1, 15.1, 16, 15.9, 16.9 Standard deviation, sn= 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.**Comparing mean and standard deviations:**Think about Compare the results for July and August. What do they tell you about the temperature in July and August? 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?