Lesson2 - Lesson II Author Atul Roy Measures of Center and...

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Lesson II Author Atul Roy Measures of Center and Spread Now that we have learn ed a few ways of displaying and organi z ing a data, the following examples will help you review the methods of summarizing a data set with a few numbers. Example 1. When looking at a transcript the GPA (the grade point average) is a single number that catches the attention of the most of the people. Recall the method of calculation of GPA. Suppose that the following table shows the grades of a student during a semester. Course Credits Grade Grade Points Accounting 3 A 4 Comp I 3 D 1 Precalculus 3 B 3 Programming 3 B 3 Psychology 3 B 3 Since all the courses are equally weighted, the GPA is 4 + 1 + 3 + 3 + 3 5 = 2. 8 This measure of center is called Mean. To calculate the mean of a set of numerical data, add all the observations and divide the sum by the total number of observations. That is if the data is x 1 , x 2 ,.... , x n , the mean is x 1 + x 2 + .... + x n n denoted by x if the data is a sample. Typically, mean of a population is denoted by µ Note that a) The mean takes into account each observation in the data but 1
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b) The mean is affected by extreme observations as is visible in the above example. Example 2. Another measure to express the central value is called Median. The median is the middle entry when the data is arranged i n numerical order. For example for the data Course Credits Grade Grade Points Accounting 3 A 4 Comp I 3 D 1 Precalculus 3 B 3 Programming 3 B 3 Psychology 3 B 3 If we arrange the grade points in order, 13334 Median is 3. If the number of observations in a data is even, then the mean of the middle two entries when the data is in order, for example, if the data set is 4, 7, 11, 15, 19, 21,29, 43 the median is 15 + 19 2 = 17 The home prices are often reported in terms of the median, for example 2
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New Existing All Single- Family Townhouse Detached Types Aspen Hill NA $2,267,000 Bennett $315,000 Bethesda $565,000 Clarksburg $410,000 Cloverly $325,000 Damascus $250,000 Darnestown $469,500 Dickerson Fairland $277,000 Gaithersburg City Vicinity Germantown $348,500 Goshen $327,500 Kemp Mill $265,000 Kensington/ Wheaton Lower Seneca Martinsburg & Vicinity North Bethesda $415,450 Olney $355,000 Patuxent $379,950 Poolesville $275,000 Potomac $710,000 Rock Creek $365,000 Rockville Silver Spring $346,500 Takoma Park* $255,000 Travilah $451,000 White Oak $288,000 County $340,000 Median Housing Sales Price by Planning Area, 2002 Montgomery County, MD Planning Area $334,500 $290,000 http://www.mc-mncppc.org/research/data_library/real_estate_development/housing/hc14l.shtm $244,000 Therefore the use of mean and median depends on the context. Please look at many examples in the text. Some Examples of the Use of Mean and Median : If a business wanting to start a service company in a residential area may want to look at the median income (for paying ability) of the residents because the mean may be pulled higher by a few high income people.
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Lesson2 - Lesson II Author Atul Roy Measures of Center and...

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