1. Produced by MEI on behalf of OCR © OCR 2013 Introduction to Quantitative Methods Roughly speaking Dealing with errors

2. Produced by MEI on behalf of OCR © OCR 2013 Estimating a table width Without using any measuring instrument, estimate how wide you think a classroom table is. Give three numbers. Your best estimate A length which you are sure is shorter than the table A length which you are sure is longer than the table

3. Produced by MEI on behalf of OCR © OCR 2013 Estimating a table width Now use a 30cm ruler to estimate how wide you think the table is. Again, give three numbers. Your best estimate A lower bound for the width An upper bound for the width Now try again, using a 1m ruler.

4. Produced by MEI on behalf of OCR © OCR 2013 Measuring or estimating Give some examples of things which are measured. How accurately can they be measured? How important is it that they are measured accurately?

5. Produced by MEI on behalf of OCR © OCR 2013 Measuring or estimating

6. Produced by MEI on behalf of OCR © OCR 2013 Measuring or estimating http://www2.nationalgrid.com/uk/Industry-information/electricity-transmission-operational-data/ Shows the frequency of the electricity supply over a 1 hour period

7. Produced by MEI on behalf of OCR © OCR 2013 Measuring or estimating How is rainfall measured? Met office videos on Youtube https://www.youtube.com/watch?v=JVOxLrMaWA8 https://www.youtube.com/watch?v=_qcfsJud3oU

8. Produced by MEI on behalf of OCR © OCR 2013 The width of a room is 5.2 m to the nearest 10 cm 5.2 m ± 0.05 m 5.2 m ± 1% 5.2 m to 2 sig figs 5.2 m to 1d.p. Lower and upper bounds 5.25.15.3 lower bound is 5.15 m upper bound is 5.25 m

9. Produced by MEI on behalf of OCR © OCR 2013 Error bounds Fill in the gaps. Click on a cloud to reveal the answer.

10. Produced by MEI on behalf of OCR © OCR 2013 Counting and estimating What is the difference between counting and measuring? Can you think of examples when counting might not be exact? 1 2 3 4 5…

11. Produced by MEI on behalf of OCR © OCR 2013 How many tigers in India? Here are the data from one region (three states) in India, from the two most recent surveys. The best estimate is given, together with lower and upper bounds. What conclusions can you draw?

12. Produced by MEI on behalf of OCR © OCR 2013 Royal occasion One section of a crowd barrier is 2 m long. In practice each section covers a road-length of 190 cm ± 10 cm. From a map I estimate the length of the Mall to be 930 m, to the nearest 10 m. How many sections of barrier do I need to provide to cover one side of the Mall?

13. Produced by MEI on behalf of OCR © OCR 2013 Royal occasion

14. Produced by MEI on behalf of OCR © OCR 2013 Acknowledgements Picture of crisps by Niklas Bildhauer http://commons.wikimedia.org/wiki/File:Salt-and-Vinegar.JPG licensed under the Creative Commons Attribution-Share Alike 2.5 Generic, 2.0 Generic and 1.0 Generic license.Creative Commons2.5 Generic2.0 Generic1.0 Generic Picture of ‘Big Ben’ clock tower by David Iliff License: CC-BY-SA 3.0 http://en.wikipedia.org/wiki/File:Clock_Tower_-_Palace_of_Westminster,_London_-_May_2007.jpg licensed under the Creative Commons Attribution-Share Alike 3.0 Unported licenseCreative CommonsAttribution-Share Alike 3.0 Unported Variation in frequency of mains supply from publically available data from the National Grid http://www2.nationalgrid.com/uk/Industry-information/electricity-transmission-operational-data Picture of rain by Juni from Kyoto Japan, http://commons.wikimedia.org/wiki/File:Here_comes_rain_again.jpg licensed under the Creative Commons Attribution 2.0 Generic licenseCreative CommonsAttribution 2.0 Generic Picture of Bengal tiger by Brian Gratwicke, http://commons.wikimedia.org/wiki/File:Bengal_Tiger_India.jpghttp://commons.wikimedia.org/wiki/File:Bengal_Tiger_India.jpg licensed under the Creative Commons Attribution 2.0 Generic licenseCreative CommonsAttribution 2.0 Generic Data on tigers from Y.V.Jhala, Q.Qureshi, R.Gopal, and P.R.Sinha (Eds.) (2011). Status of the Tigers, Co-predators, and Prey in India, 2010. National Tiger Conservation Authority, Govt. of India, New Delhi, and Wildlife Institute of India, Dehradun. TR 2011/003 pp-302 http://www.projecttiger.nic.in/WriteReadData/PublicationFile/Tiger_Status_oct_2010.pdf Picture of the Mall by Efarestv http://commons.wikimedia.org/wiki/File:The_Mall.JPGhttp://commons.wikimedia.org/wiki/File:The_Mall.JPG licensed under the Creative Commons Attribution-Share Alike 3.0 Unported licenseCreative CommonsAttribution-Share Alike 3.0 Unported