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Lecture 3

# Lecture 3 - September 26.odt

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School
University of Toronto St. George
Department
Geography
Course
GGR270H1
Professor
Damian Dupuy
Semester
Fall

Description
Lecture 3 – September 26 Measures of the Centre – Mean – Most commonly used measure of central tendency – Sum of all values or observations divided by the number of observation Sample Population (check page check paper) Mean Example – the order of the numbers in the sample, its their value that they hold that matters Temperature Data: 7.3, 10.7, 9.1, 8.4, 13.9, 9.4, 8.2 =ADD them all up /7 =67/7= 9.57 (mean) = 9.6 (rounded up) (always round up based on the data you given, like the numbers above) Measures of the Centre 2 – Median – Value occupying the 'middle possition' in an ordered set of observations – with the median the value doesnt necessarly matter, its the value that occupies the middle possition. – Order the observations, lowest to highest, and find the middle position Formula: 0.5 (n+1) (this gives you the position) Median Example – Uneven Observation – Temperature Data: 7.3, 10.7, 9.1, 8.4, 13.9, 9.4, 8.2 Order: 7.3, 8.2, 8.4, 9.1, 9.4, 10.7, 13.9 Using formulth....... 0.5(7+1) = 4 position in the ordered set Therefore = 9.1 Median Example – Even Observations Temperature data: 7.3, 10.7, 9.1, 8.4, 13.9, 9.4, Order: 7.3, 8.2, 9.1, 9.4, 10.7, 13.9 Using Formula ..... 0.5 (6+1)=3.5 position in the ordered set So, add 3 and 4 and divide by 0.5 = 1/2 (9.1+9.4) = 1/2 (18.5)=9.25 Median Temperature is 9.25 Measure of the Centre 3 Mode – Value that occurs with the highest frequency – Allows you to locate the peak of a relative frequency histogram – Mode is 3 household members (based on the table presented) Choosing an Appropriate Measure – Mean is usually best measure as it is sensitive to change in a single observation – it is able to take the changes that can or might occur in the observation – it is also or can be the most represntative – however, it is not always a good measure, distribution by-mobil – it is not actually telling you that high peak – But not a good measure when... – Distribution is bi-modal (2 modes) – Skewed distributions Instead you can Use median It is good to use for normal graph Measures of the Centre 4 Normal – Mean, Median and Mode will be found in the middle Bimodal – Two modes – Mean and Median in the Middle Positively Skewed – Mode will always be to the LEFT – MEAN will always be to the RIGHT – because it is taking on-board the value of the outlier – Median will be somewhere in the middle Negatively Skewed – Mode will be on RIGHT – Mean will be on LEFT – Median will always b
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