Produced by MEI on behalf of OCR © OCR 2013 Introduction to Quantitative Methods Statistics Introduction to the Normal distribution This presentation is designed for students. It plays automatically and has an audio commentary; adjust your volume if necessary.

Produced by MEI on behalf of OCR © OCR 2013 The real world …and the model p = 0.5 Flips of the coin are independent You would expect to get between 6 and 14 heads 95% of the times you do the experiment.

Produced by MEI on behalf of OCR © OCR 2013 The real world …and the model Histogram to show growth in size of 472 crabs during moulting of shell Normal distribution with mean 14.7 mm and standard deviation 2.4 mm

Produced by MEI on behalf of OCR © OCR 2013 The real world …and the model Normal distribution with mean 12 mm and standard deviation 3.2 mm

Produced by MEI on behalf of OCR © OCR 2013 Probabilities from the Normal Distribution

Produced by MEI on behalf of OCR © OCR 2013 The real world …and the model Histogram to show growth in size of 472 crabs during moulting of shell Normal distribution with mean 14.7 mm and standard deviation 2.4 mm

Produced by MEI on behalf of OCR © OCR 2013 Shell size of 472 crabs before moulting Skewed distribution

Produced by MEI on behalf of OCR © OCR 2013 Two Normal distributions

Produced by MEI on behalf of OCR © OCR 2013 Standard deviation The standard deviation is a measure of spread.

Produced by MEI on behalf of OCR © OCR 2013 Properties of Normal distributions A Normal distribution is a symmetrical, bell- shaped curve. 68% (about two-thirds) of the data lie within 1 standard deviation of the mean … continued

Produced by MEI on behalf of OCR © OCR 2013 Is it a good fit? You can tell whether a Normal distribution is a good fit by looking at the curve drawn over the histogram, or by looking at a Normal probability plot. The closer the dots are to the straight line, the better the fit.

Produced by MEI on behalf of OCR © OCR 2013 Acknowledgements Dungeness crab data from University of California, Berkeley