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# ISE361_HW1answers_F03 - ISE 361 Homework One 8 a Number...

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ISE 361 Homework One Fall 2003 8 a. Number observations equal 2 x 2 x 2=8 10 a. 5 | 9 units = MPa 6 | 33588 7 | 00234677889 8 | 127 9 | 077 stem: ones 10| 7 leaf: tenths 11| 368 What constitutes large or small variation usually depends on the application at hand, but an often-used rule of thumb is: the variation tends to be large whenever the spread of the data (the difference between the largest and smallest observations) is large compared to a representative value. Here, “Large” means that the percentage is closer to 100% than it is to 0%. For this data, the spread is 11 – 5 = 6, which constitutes 6/8 = .75 or 75%, of the typical data value of 8 . Most researchers would call this a large amount of variation. b. The data display is not perfectly symmetric around some middle representative value. There tends to be some positive skewness in this data. c. Outliers are data points that appear to be very different from the pack. There appear to be no outliers in this data. d. There are 4 values greater than 10. The proportion of data values that exceed 10 is 4/27 = 0.148, about 15% 17 c. The center is somewhere around 2 or 3 and it shows some positive skewness in the data. The histogram also shows a lot of spread/variation in this data. 18. a. The most interesting feature of the histogram is the heavy positive skewness of the data. b. From the frequency distribution (or from the histogram), the number of authors who published at least 5 papers is 33+28+19+…+5+3+3 =144, so the proportion who published 5 or more papers is 144/1309 = .11 or 11%. Similarly, by adding frequencies and dividing by n = 1309, the proportion who publishes 10 or more papers is 39/1309 = .0298, or about 3%. The proportion who published more than 10 papers (i.e., 11 or more) is 32/1309 = .0245, or about 2.5%.

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ISE 361 Homework One c. No. Strictly speaking, the class described by “>or =15” has no upper boundary, so it
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ISE361_HW1answers_F03 - ISE 361 Homework One 8 a Number...

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