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Lecture 3

# Lecture 3 - September 26.odt

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University of Toronto St. George

Geography

GGR270H1

Damian Dupuy

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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