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STAT 101 (27)
Chapter 2

Chapter 2.odt

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Department
Statistics
Course
STAT 101
Professor
Qian( Michelle) Zhou
Semester
Fall

Description
Chapter 2 Measuring Centre: The Mean • mean = add all values of observation and divide it by the number of observations ◦ x-bar ◦ is not resistant to influence of extreme measures – not a resistant measure • Sigma (E) = add em all up Measuring Centre: The Median • median (M) – midpoint of distributions ◦ first arrange set in order of S to L ◦ if number of observation is odd, the M is in the middle of the set; if even, take the two centre observation and find the average of it ◦ always locate median in the order of list by counting (n+1)/2 ▪ this doesn't give the median it's just the location of the median in an ordered list th • ex) n+1/2 = 16/2 = 8; median is the 8 observation in the ordered list Comparing the Mean and the Median • median is resistant • if distribution is exactly symmetric, mean and median are the same • in skewed distribution, mean is usually farther out in the long tail than median Measuring Spread: The Quartiles • Quartiles mark out the middle half ◦ they are resistant ▪ ex) would Q1 would still be 10 if the outlier was 600 than 60 ◦ gotta arrange observation in increasing order, locate the median in the ordered list ▪ median is aka the Second quartile • First quartile – lies 1/4 of the way up the list, is left from the median • third quartile – lies 3/4 of the way up list; to the right of the median ex) one way to locate the 1 quartile of 5 10 10 10 10 12 15 20 20 25 30 30 40 40 60 i) first find median – which is 20 ii) to find location of the Q1 --> n + 1/2 (in this case, n is the number from the beginning to the middle) --> 7+1/2 = 4 iii) the first quartile is 10 The Five-Number Summary and Boxplots • Five-number summary – distribution consisting of the minimum, Q1, median, Q3 and maximum • Boxplot – graph of a five-number summary ◦ centre box spans the Q1, M and Q3 (the middle line is M) ◦ lines extend from min (@bottom) and max (@top) ◦ if data is right skewed, Q3 would be farther away from M than Q1 is Spotting Suspected Outliers • Interquartile range (IQR) – distance b/w Q3 and Q1 ◦ Q3 – Q1 = IQR ◦ more resistant measure of spread ◦ however, IQR is not useful in describing skewed distributions b/c the two sides of askewed distribution have different spreads, so one number can't summarize them ◦ only used to find suspected outliers
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