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Lecture 4

# Lecture 4 - OCtober 3

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University of Toronto St. George

Geography

GGR270H1

Damian Dupuy

Fall

Description

Lecture 4 – October 3
Measures of Dispersion VI
Coeffiecient of Variation
– Allows for comparison of variability spatial samples
– Tests which sample has the greatest variability
– climatic data, rainfal or other forms of precipation, and then look at where you get a
variability. OR Traffic flows over the course of the day, in different hwy
– Standard deviation or Variance are absolute measures so, they are influenced by the size
of the values in the dataset
– results that are influenced by outliers, there are to caviats you have to put just to
measure
– To allow a comparison of variation across two or more geograpic samples, can use a
relative measure of dispersion called Coefcient of Variation
Practical Significance of Standard Deviaton
– Tchebysheff's Theorem and Empirical rule
– Given a number k greater than or equal to 1 and a set of n measurements, at least [1-
Empirical rule (KEEPIT IN UR CHEAT SHEET)
– we are relating the std deviation with the empirical rule
– Std Deviation is always a ( – or + )
– You are standardizing a distance
– you will have a greater or lesser the mean
– 68% of the observation will always fall between -1 and +1 std deviation
– 95% of the observations will awlays fall between -2 and +2 std deviation
– 99.7 " " " " " " " -3 and +3 " "
– you use it for predicting the possiblity of particual value
– also probability at some point,
Z scores
– it standadizes any value on that curve, so that we can compare any value that we have to our
std deviation
– Stanrdized scores are refered to as Z scores
– Indicate how many standard deviations separate a particular value from the mean
– it can be 1 std deviation, or 1.2 or 1.02
– Z scores can be + or – depending of they are more or less than the mean
– Z score of the mean is 0 and the standard deviation is +1 or – 1
– eg. if it is 2 std deviation from the mean then the Z score is +2 or -2
– Z score of the mean is 0
Z scores II – you dont need the Z score table
– Table of Normal Values provides probability infromation on a standardized scale
– But we can also calculate Z scores – Formula involves comparing valus to the mean value, and dividing by the standard deviation
– Results is interpreted as the "number of standard deviations an observation lies above or
below the mean"
Z Score Formula
X-Xbar
z= S
where z is the standard score,
S= the standard deviation of a sample
X= each value in the data set
Xbar= mean of all values in the data set
Describign Bivariate Data
Graph
Simple Bivariate Graphs
Comparative Pie Charts Stacked Bar Chart
– you dont get a relationship
– a correlation gives you a relationships
– however it wont give you if x causes y, because you dont have enough information
Bivariate DATA1
– Correlation
– Allows us to observe statistically the relationship between two variables
– are we looking at + or - , how strong is the relationship
– you stop at when what causes it
– Looking at the strength and direction of the relationship between two variables
– Most common graphic technique is the Scatterplot
– The scatter of points Graph
– it constist of pairs of variables
– each person or observation will have a point to somethign to say, e.g what
occupation type they are or their income and schooling
– What is x and y ??? --> something is function of something, but not saying what
causes the follo

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