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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 creditrating
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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 Spring '10
 PARVINI
 Statistics, Mean, data values

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