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1.2 notes - vaSTAT3000 Section 1.2: Describing...

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vaSTAT3000 Section 1.2: Describing Distributions with Numbers Measures of Center mean (average) median (middle) mode (most often) median – the midpoint of a distribution; the number such that half the observations are smaller and the other half are larger. -Resistant statistic. Reflects hats typical if data is skewed or outliers then you use MEDIAN. Calculating a Sample Median 1. Arrange the n data values from smallest to largest. 13
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2. If n is odd, the median is the middle number. If n is even, the median is the mean of the two middle numbers. Ex: A data set contains the observations 6, 1, 4, 3, 1 mode - the data value that occurs most often in the data set The statistic for categorical data . Typically meaningless in quantitative situations. mean –the sum of the data values divided by the number of data values contained in the data set. Use when you have symmetric data. Rather say mean than median 14
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Calculating a Sample Mean x = ____ 1 1 n i i x X n = = n ( sample size), Notation for a Data Set Recall// n denotes the number of data values in a sample, or n = sample size. Data values occurring in a sample are symbolically represented by x 1 , x 2 , x 3 , … , x n . Summation Notation The Greek letter Σ (capital sigma) is used to denote summation. Σ x i = x 1 + x 2 + + x n 15
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Σ x i 2 = x 1 2 + x 2 2 + + x n 2 ( Σ x i ) 2 = (x 1 + x 2 + + x n ) 2 Ex: A data set contains the observations 6, 1, 4, 3, 1 a. Σ x i = 6+1+4+3+1=15 xbar= 15/5= 3 sample mean b. ( Σ x i ) 2 = 15^2=225 c. Σ x i 2 = 6^2+1^2+3^2+1^2=63 d. Σ ( x x - ) = e. Σ ( x x - ) 2 = Deviations SSxx 16
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( x x - ) ( x x - ) 2 6 6-3=3 9 1 1-3=-2 4 4 4-3=1 1 3 3-3=0 0 1 1-3=-2 4 Sums Σ ( x x - ) =0 Σ ( x x - ) 2 =18 Example 1.10 Table 1.3 (on page 14 in the textbook) gives the number of full-time staff employed by Indianapolis architectural firms. Compute the mean, median, and mode of the staff counts. Staff Count 111 126 155 57 70 68 62 52 131 61 110 22 13 115 15 14 24 7 15 96 17 72 15 70 17 N=25 Mode= 15 Average= 1515/25= 60.6 Median= 61 ( n+1/2) Maybe symmetrical b/c mean and median are close to the same value. 17
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This note was uploaded on 06/05/2011 for the course STAT 3000 taught by Professor Staff during the Spring '08 term at UGA.

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1.2 notes - vaSTAT3000 Section 1.2: Describing...

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