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

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

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

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

© Nuffield Foundation 2011

Nuffield Free-Standing Mathematics Activity

Music Festival

Page 2: © Nuffield Foundation 2011 Nuffield Free-Standing Mathematics Activity Music Festival.

© 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

SunnyHot

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© Nuffield Foundation 2011

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 Dec2001 3.2 4.2 4.9 7.3 12.0 13.7 16.5 16.4 13.0 13.0 7.1 3.42002 5.3 6.6 7.2 8.8 11.5 13.9 15.4 16.6 13.9 9.7 8.2 5.42003 4.2 3.7 7.2 9.3 11.6 15.5 17.0 17.7 14.0 8.9 7.9 4.72004 4.9 5.0 6.2 9.1 11.7 15.0 15.4 17.1 14.4 10.3 7.5 5.32005 5.7 4.0 6.8 8.6 11.0 15.0 16.3 15.8 14.8 12.7 6.0 4.32006 4.0 3.6 4.6 8.3 11.8 15.5 19.1 15.9 16.3 12.6 7.9 6.12007 6.6 5.7 6.9 10.9 11.6 14.7 15.1 15.3 13.7 10.7 7.2 4.82008 6.3 5.2 5.9 7.7 12.9 13.8 16.0 16.0 13.2 9.5 6.8 3.52009 2.9 4.0 6.7 9.5 11.7 14.5 15.9 16.4 14.0 11.2 8.3 3.02010 1.2 2.6 5.8 8.6 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:

nxx mean

number of years

sum of the temperatures

You can use a calculator or a spreadsheet to work this out.

Think aboutWhy is the mean a good representative value? When might the median be better?

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To find the mean temperature for July

= 16.36C

10916915 16 15.1 19.1 16.3 15.4 1715.416.5 ..

10163.6

nxx

Use your calculator in COMP mode:

Use your calculator in Stats Mode to check this result.

Think aboutWhat are the advantages and disadvantages of each method?

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Standard deviation n =

To measure spread

2

xx

xx

n

x1 x2 x3 x4 x5 x6 x7x

Think aboutwhy 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 aboutwhy is squared before the values are added

xx

Think abouthow the standard deviation will increase as the spread increases

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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 x

Standard deviation, n = 1.095…

= 1.10 C (to 2 dp)

Use your calculator in Stats Mode to check this result.

Try thisWork out the mean and standard deviation for August.

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Comparing mean and standard deviations:

July August

Mean 16.36 C 16.24 C

Standard deviation 1.10 C 0.73 C

Think aboutCompare 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

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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?