Lecture-3-Summer2010 - LECTURE 3 Descriptive Statistics:...

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LECTURE 3 Descriptive Statistics: Numerical Methods (Part 1) This lecture covers material on measures of location and variability (or dispersion). Microsoft Excel is used for some applications. Read: Chapter 3, Sections 3.1 and 3.2. Note: If the numerical measures of location and dispersion are computed for a population, they are known as population parameters; if computed for a sample they are known as sample statistics. Measure Population Parameter Sample Statistic Number of elements N n Mean μ Variance σ 2 s 2 Standard Deviation σ s Measures of Location These measures define the central point or location of the data, or the central tendency of the data. They include the Mean, Trimmed Mean, Median, Mode, Percentiles, and Quartiles. Mean: The mean (also known as the average) value of a variable is obtained by adding all the data values and dividing by the number of data items. Note: The mean can be influenced by unusually large or unusually small values in the data. Therefore outliers in the data can cause the mean to unrepresentative of the general mass of data. Example: In a neighborhood of 10 homes, 9 homes are priced at $100,000 dollars while one home is priced at $1,000,000. The mean (or average) home price is $190,000 which is not an accurate representation of home prices in that area and can misguide a prospective home buyer. 1
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For the monthly payments sample data, the data values x i are: 1001, 1200, 390, 432, 542, 654, 3218, 4567, 103, 211, 2345, 1541, 3209, 2112, 3005, 1389 The sample size n = 16. The mean = Σx i /n Σx i = 1001+1200+ 390+ 432+ 542+ 654+ 3218+ 4567+ 103+ 211+ 2345+ 1541+ 3209+ 2112+ 3005+ 1389 = 25919 = 25919/16 = 1619.94 --------------------------------- Median: The value of the variable such that half the values in the data set are above it; and half the values are below it. It helps to arrange the data values in either ascending or descending order to compute the median. If n is odd, then the median is the value of the central or middle data item. If n is even, then the median is the average value of the two middle data items. Note: The median is not influenced by unusually large or unusually small values in the data. This is because it does not use actual numerical values, only their positions in an ordered set of data. Therefore it is completely insensitive to extremes. 2
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This note was uploaded on 09/21/2011 for the course OM 210 taught by Professor Singer during the Summer '08 term at George Mason.

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Lecture-3-Summer2010 - LECTURE 3 Descriptive Statistics:...

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