3-2 example16

3-2 example16 - Student: Grady Sinlonton Colu'se:...

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Unformatted text preview: Student: Grady Sinlonton Colu'se: 1\-Iat11119: E1e111e11ta1y Statistics - Spring 2010 - C‘RN: 49239 Instructor: Shawn Pan-'ini - 16 weeks Date: 3.-"'18.-"'10 Book: Triola: E1e111e11ta1y Statistics. Me Time: 11:27 ALI Because the mean is very sensitive to extreme values, it is not a resistant measure of center. The trimmed mean is more resistant. To find the 10% trimmed mean for a data set, first arrange the data in order, then delete the bottom 10% of the values and the top 10% of the values, then calculate the mean of the remaining values. For the following credit-rating scores, find (a) the mean, (b) the 10% trimmed mean, and (c) the 20% trimmed mean. How do the results compare? 1'05 208 7’78 812 299 7’97 712 676 7’66 61 1 698 841 W2 535 654 562 241 7’9] 696 254 a. The arithmetic mean, or the mean, of a set of data is the measure of center found by adding the data values and dividing the total by the number of data values. 2;: (— sum of all data values mean = — n (— number of data values In order to calculate the mean, first sum all the data values. 2 x = 14,403 Then divide the sum by the number of data values to get the mean, The number of values is 20. -2x X: 11 11,658 16 220.4 Thus, the mean is 220.4. b. In order to calculate the 10% trimmed mean, first arrange the data in order of increasing magnitude. 535 562 61 1 654 676 696 698 1'05 1'08 212 1'41 254 766 722 2'18 T91 29? 7’99 812 841 Then determine how many data values you must delete from the bottom and the top of the arranged data values. Delete 2 values from the bottom and the top. Page 1 Student: Grady Sinlonton Colu'se: 1\-Iat11119: Elenlentaiy Statistics - Spring 3010 - C‘RN: 49339 Instructor: Shawn Pan-'ini - 16 weeks Date: 3.-"'18.-"'10 Book: T1‘iola: Elenlentaiy Statistics. Me Time: 11:37 ALI 611 654 6?6 696 698 7"05 7’08 712 T4] 1'54 T66 T72 1'78 T9] 379'? 799 Next sum all 16 data values above. 2;, = 11,658 Then divide the sum by the number of data values to get the 10% trimmed mean, rounding to one decimal place. The number ot‘values is 16. 11,658 = 728.6 Thus, the 10% trimmed mean is ?28.6. c. In order to calculate the 20% trimmed mean, first determine how many data values you must delete from the bottom and the top of the arranged data values. Delete 4 values from the bottom and the top. 676 696 698 T05 T08 'i'12 7’41 754 7"66 7’72 778 791 Next sum all 12 data values above. 2:; = 8?97 Then divide the sum by the number of data values to get the 20% trimmed mean, rounding to one decimal place. The number of values is 12. 8797 —= ?33.] 12 Therefore, the 20% trimmed mean is "£311. Examine the results to see if the results show a trend of increasing or decreasing values as the percentage of trim increases. Based on that, determine if the distribution of the data is skewed to the right, left, or neither. Page 3 ...
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This note was uploaded on 05/21/2010 for the course MATH 49239 taught by Professor Parvini during the Spring '10 term at Mesa CC.

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3-2 example16 - Student: Grady Sinlonton Colu'se:...

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