Measures of Center Notes Spring

# Measures of Center Notes Spring - 2 of 11 1.1 Introduction...

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Unformatted text preview: 2 of 11 1.1 Introduction 1.1 Introduction Measures of center Robert Pershing Wadlow (February 22, 1918 - July 15, 1940) is the tallest person in medical history for whom there is irrefutable evidence. He is often known as the “Alton Giant” because of his Alton, Illinois hometown. Wadlow reached an unprecedented 8 feet 11.09 inches (2.72 m) in height and weighed 440 pounds (199 kg) at his death. His great size and his continued growth in adulthood was due to hypertrophy of his pituitary gland which results in an abnormally high level of human growth hormone. He showed no indication of an end to his growth even at the time of his death. Robert Wadlow compared to his father, Harold Franklin Wadlow. Make a new variable heights.skewed where Wadlow (97 inches) is added to our class. R: load ( ”ClassData . RData”) R: height = class . data\$ height R: height . skewed = c ( height , 97) R: par (mfrow = c (1 , 2) ) R: hist ( height ) R: hist ( height . skewed ) Anthony Tanbakuchi MAT167 Measures of Center 3 of 11 Histogram of height height Frequency 65 70 75 1 2 3 4 5 Histogram of height.skewed height.skewed Frequency 60 70 80 90 100 2 4 6 8 Skewed distribution. Definition 1.1 has left and right tails that are not symmetrical. positive longer right tail. negative longer left tail. negative (left) skewed, symmetrical, positive (right) skewed NOTATION Summation operator ∑ operator A compact notation for summation: total = n X i =1 x i (1) = x 1 + x 2 + ··· + x n (2) Summation: sum(x) Where x is a vector. R Command Mathematical Notation population sample data set x = { x 1 ,x 2 ,...,x N } x = { x 1 ,x 2 ,...,x n } size N n sum of data set ∑ N i =1 x i ∑ n i =1 x i freq dist ( k classes) f i = { f 1 ,f 2 ,...,f k } prop freq dist n = ∑ k i =1 f i Anthony Tanbakuchi MAT167 4 of 11 1.2 Three key measures of center R Notation population sample data set x=c(x1, x2, ...) x=c(x1, x2, ...) size N=length(x) n=length(x) sum of data set sum(x) sum(x) freq dist ( k classes) f=c(f1, f2, ...) prop freq dist n=sum(f) Measures of center and effect of outliers How are each of the measures of center effected by outliers? 1.2 Three key measures of center MEAN Mean: μ , ¯ x . Definition 1.2 The arithmetic mean is the sum of the data set divided by the number of values....
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## This note was uploaded on 02/10/2012 for the course MAT 1670 taught by Professor Tanbakuchi during the Spring '11 term at University of Florida.

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Measures of Center Notes Spring - 2 of 11 1.1 Introduction...

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