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Unformatted text preview: Chapter 3 Descriptive Statistics 3.1 Describing Central Tendency Mean. Mean is a measure of central location computed by summing the data values and dividing by the number of observations. Sample Mean: Population Mean: Where: n = number of elements (observations) in a sample Where: N = number of elements (observations) in a population. For example: Given the data values: 46, 54, 42, 46, and 32. Get the Sample Mean. n = 5. Then, Sample mean is a point estimator of the population mean. In Excel: =AVERAGE(RANGE) Median . Median is a measure of central location provided by the value in the middle when the data are arranged in ascending order. First, Arrange the data in ascending order a) for an odd number of observations, the median is the middle value b) for an even number of observations, the median is the average of the two middle values Example a): 46, 54, 42, 46, and 32. Arrange in ascending order: 32, 42, 46, 46, 54 n = 5 (odd), then: Median = 46 Example b): 46, 54, 42, 46, 32, and 16. Arrange in ascending order: 16, 32, 42, 46, 46, 54 n = 5 (even), then: Median = (42+46)/2 = 44. Median is preferred when data contains outliers (extreme small or large values) In Excel: =MEDIAN(RANGE) Mode Mode is a measure of location, defined as the value that occurs with greatest frequency. Example: Given the data values: 46, 54, 42, 46, 32, and 16. Get the Mode. Arrange in ascending order: 16, 32, 42, 46, 46, 54 Class Frequency 16 1 32 1 42 1 46 2 54 1 The Mode, or the class with highest frequency, is 46. In Excel: =MODE(RANGE) 3.2 Measures of Variation Range = largest value smallest value Interquartile Range = Q3 Q1. Example: From our previous example: Interquartile Range = 72.5 45 = 27.5. Variance Variance is a measure of variability based on the squared deviations of the data values about the mean. Population Variance Sample Variance Where Where is the population mean N is the number of elements (observations) in the population is the sample mean n is the number of elements (observations) in the sample Example: Two suppliers Dawson and Clark deliver their products using the following delivery times: Order No. Dawson Clark 1 9 8 2 10 7 3 9 10 4 11 10 5 9 13 6 10 12 7 11 10 8 9 9 9 9 15 10 10 10 Determine their corresponding variances. What do these numbers suggest? Order No. Days Mean 1 9 9.70.7 0.49 2 10 9.7 0.3 0.09 3 9 9.70.7 0.49 4 11 9.7 1.3 1.69 5 9 9.70.7 0.49 6 10 9.7 0.3 0.09 7 11 9.7 1.3 1.69 8 9 9.70.7 0.49 9 9 9.70.7 0.49 10 10 9.7 0.3 0.09 Total 97 6.1 n 10 9.7 Days Frequency 7 8 9 5 10 3 11 2 12 13 14 15 Total 10 Dawson x ) ( x x i 2 ) ( x x i Order No. Days Mean 1 8 10.42.4 5.76 2 7 10.43.4 11.56 3 10 10.40.4 0.16 4 10 10.40.4 0.16 5 13 10.4 2.6 6.76 6 12 10.4 1.6 2.56 7 10 10.40.4 0.16 8 9 10.41.4 1.96 9 15 10.4 4.6 21.16 10 10 10.40.4 0.16 Total...
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 Spring '08
 DODONOVA

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