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Lecture 4

Lecture 4 - OCtober 3

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University of Toronto St. George
Damian Dupuy

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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