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3-2 example6

# 3-2 example6 - Student Grady Simonton Course Math119...

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Unformatted text preview: Student: Grady Simonton Course: Math119: Elementary Statistics - Spring 2.010 - CRN: 49239 Instructor: Shawn Parvini - 16 weeks Date: 2/18/10 Book: Triola: Elementary Statistics, 11e Time: 11:19 ANI Find the (a) mean, (b) median, (0) mode, and (d) midrange for the given sample data. Listed below are the amounts of personal income (in dollars) for ﬁve states. \$32,996 \$23,492 \$32,191 \$26,183 \$25,098 (a) The mean of a set of values is the measure of center found by adding the values and dividing the total by the number of values. Mean _ x (— sum of all sample values 11 (— number of sample values In order to calculate the mean, ﬁrst sum all the values. 2.. 32,996 +23,492 +32,191 +26,183 +25,09s 139,960 To ﬁnd the mean, divide the sum, \$139,960, by the number of observations. In this problem there are S observations. 139,960 5 27,992 Mean Thus, the mean per capita income is \$27,992. (b) The median of a data set is the measure of center that is the middle value when the original data values are arranged in order of increasing magnitude. First arrange the data in increasing order of magnitude. \$23,492, \$25,098, \$26,183, \$32,191, \$32,996 If the number of values is odd, the median is the number located in the exact middle of the list. If the number of values is even, the median is found by computing the mean of the two middle numbers. Since there are 5 observations, the number of values in the data set is odd. Thus, the median is the middle observation. The per capita Per Capita Income ' l' ' h . incomes are 1sted on the rig t \$23,492 \$25,098 \$26,183 Median= 26,183 \$32,191 \$32,996 Thus, the median per capita income is \$26,183. (c) The mode of a data set is the value that occurs most often. Page 1 Student: Grady Simonton Course: Math119: Elementary Statistics - Spring 2010 - CRN: 49239 Instructor: Shawn Parvini - 16 weeks Date: 2/18/10 Book: Triola: Elementary Statistics, 11e Time: 11:19 ANI Since none of the amounts are repeated, there is no mode for this data set. ((1) The midrange is the measure of center that is the value midway between the maximum and minimum values in the original data set. The midrange is given by the following formula. maximum value + minimum value midran e = g 2 Start by identifying the maximum and minimum values of the data set. The data set is listed in ascending order on the right. The maximum value is 32,996. Per Capita Income \$23,492 \$25,098 \$26,183 \$32,191 \$32,996 The minimum value is 23,492. Now calculate the midrange of the data set. 32,996 + 23,492 2 28,244 midrange Thus, the midrange of the data set is \$28,244. Page 2 ...
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3-2 example6 - Student Grady Simonton Course Math119...

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