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Math 203_Lecture 2

Math 203_Lecture 2 - Principles of Statistics 1 Lecture 2...

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Principles of Statistics 1 Lecture 2: Math 203 Abbas Khalili Department of Mathematics and Statistics McGill University May 03, 2011 Principles of Statistics 1 Lecture 2: Math 203 – p. 1/4
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Numerical methods for summarizing quantitative data : First we introduce some notations: Principles of Statistics 1 Lecture 2: Math 203 – p. 2/4
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Numerical methods for summarizing quantitative data : First we introduce some notations: We often use X , Y , Z , ... to represent variables (characteristics) of interest. Principles of Statistics 1 Lecture 2: Math 203 – p. 2/4
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Numerical methods for summarizing quantitative data : First we introduce some notations: We often use X , Y , Z , ... to represent variables (characteristics) of interest. For example, let X be a variable of interest in our data. The observed values of X are represented by X 1 , X 2 , . . . , X n where n is the number of data points (observations) in the data; n is also called sample size. Principles of Statistics 1 Lecture 2: Math 203 – p. 2/4
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Example In the body temperature data we have: Principles of Statistics 1 Lecture 2: Math 203 – p. 3/4
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Example In the body temperature data we have: X : body temperature of a person Principles of Statistics 1 Lecture 2: Math 203 – p. 3/4
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Example In the body temperature data we have: X : body temperature of a person n = 130 : number of observations (sample size) Principles of Statistics 1 Lecture 2: Math 203 – p. 3/4
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Example In the body temperature data we have: X : body temperature of a person n = 130 : number of observations (sample size) And data are: X 1 = 35 . 7 , X 2 = 35 . 9 , . . . , X 130 = 38 . 2 Principles of Statistics 1 Lecture 2: Math 203 – p. 3/4
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Notations Summation n summationdisplay i =1 Principles of Statistics 1 Lecture 2: Math 203 – p. 4/4
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Notations Summation n summationdisplay i =1 And n summationdisplay i =1 X i = X 1 + X 2 + . . . + X n . Principles of Statistics 1 Lecture 2: Math 203 – p. 4/4
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Notations Summation n summationdisplay i =1 And n summationdisplay i =1 X i = X 1 + X 2 + . . . + X n . Example: Let X 1 = 1 , X 2 = - 4 , X 3 = 3 , X 4 = - 3 . Then, 4 summationdisplay i =1 X i = X 1 + X 2 + X 3 + X 4 = 1 + ( - 4) + 3 + ( - 3) = - 3 Principles of Statistics 1 Lecture 2: Math 203 – p. 4/4
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Numerical methods for quantitative data Measures of the central tendency of data: show the tendency of data to cluster, or center, around certain value. Mean, Median, Mode . Measures of variability of data: show the spread of data. range, variance, interquartile range Principles of Statistics 1 Lecture 2: Math 203 – p. 5/4
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Measures of central tendency Mean (Average): ¯ X = 1 n n i =1 X i . Principles of Statistics 1 Lecture 2: Math 203 – p. 6/4
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Measures of central tendency Mean (Average): ¯ X = 1 n n i =1 X i . Median: 50% of the data points are below the median and 50% are above the median. Principles of Statistics 1 Lecture 2: Math 203 – p. 6/4
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Measures of central tendency Mean (Average): ¯ X = 1 n n i =1 X i .
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