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Unformatted text preview: MATH 221 Statistics for Decision - Making Lecture Notes Week 3 Measures of Variation / Probability Student Name Measures of Variation After a group of data values has been gathered, we could possibly ask ourselves the question: &quot; To what extent is the data dispersed? &quot; That is, how far spread is the data? Is the difference between the highest data value and the lowest data value a large variation? We could also ask: &quot; On the average, how does each data value compare with some mean value? &quot; These questions indicate the need for so - called measures of dispersion ( variation ) that attempt to provide the answers. Measures of dispersion focus on comparing the given data values to each other or some central number. Compare this focus to that of central tendency measures, which instead attempt to find: &quot; What number(s) best describe the entire set of data values? &quot; The Range The most elementary measure of dispersion is the range. The range is the difference between the largest value of a given set of values and the smallest value within this same set. The range therefore compares the highest number to the lowest number. Range = Highest Value - Lowest Value Example 1 A random sample of fifteen charge card accounts gave the following information about the payment due on each card. Find the range of these amounts. $ 43.78 $ 162.50 $ 204.30 $ 40.32 $ 172.50 $ 32.40 $ 105.73 $ 189.23 $ 164.18 $ 40.38 $ 159.12 $ 87.46 $ 165.23 $ 48.80 $ 110.86 Solution Here, the largest value in the given group of values is $ 204.30 and the smallest value is $ 32.40 . The range therefore is equal to the difference $ 204.30 - $ 32.40 or $ 171.90 . Finding the Range Using MS Excel Using MS Excel, the range can be determined using the built - in MAX and MIN functions. Consider the spreadsheet shown below. A B C 1 Employee Name Salary 2 Bobby Benson $ 25,750.00 Copyright 2010 by P.E.P. 1 MATH 221 Statistics for Decision - Making Lecture Notes Week 3 Measures of Variation / Probability Student Name 3 Cathy Cummings $ 26,922.00 4 Denise Daniels $ 83,942.00 5 Eddie Edwards $ 45,220.00 6 Fred Fields $ 98,125.00 7 Gina George $ 53,125.00 8 Henry Hansen $ 18,500.00 9 Justin James $ 41,480.00 10 11 Salary Range 12 To determine the range of salaries in cell B11 , you would enter the following formula into that cell. = MAX ( B2 : B9 ) - MIN ( B2 : B9 ) This particular formula would find the range of the salaries located within the group of...
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