STAT 210 1st EditionLecture 9Outline of Last Lecture I. Measures of CenterII. Distributions Outline of Current LectureIII. Measures of Central LocationIV. RangeCurrent LectureV. Mean (average)VI. Population mean is denoted by greek lettersVII. If all values of a characteristic are the same, it’s a constant (no spread in the data)VIII. If they’re not the same, it’s a variable (we measure amount of spread)IX. Range = maximum value – minimum valuea. Heavily impacted by outliersX. Standard Deviation = measure of variability about he mean a. Denoted by = population standard deviationXI. Sample standard deviation a. S = ∑(xi−xbar)2n−1b. Calculate sample mean x barc. Compute n deviations from the mean x –x bar ∑(x−xbar)= 0d. Square each deviation (x – xbar)^2 e. Add the squared deviations ∑(x−xbar)2f. Divide by n-1 where n = sample size ∑(x −xbar)2n−1XII. Variance = measure of spread around the mean that is related to the standard deviationa. s^2 = ∑(x −xbar)2n−1 = variance XIII. Interquartile Range (IQR) = compute measure of spread around the median (resistant to outliers) a. Lower quartile (observations with 25% of the data less than it and 75% of the data greater than it) Q1b. Upper quartile (observations with 75% of the data is less than it and 25% of the data is greater than it) Q3i. Arrange data from smallest to largestii. Calculate median location (n+1)/2iii. Find upper and lower quartilesc. if n is an odd number the median will be the middle ordered observationd. if n is even the median is the average of the middle 2 ordered
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