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Unformatted text preview: 1 8 1 6 1 4 1 2 1 0 8 6 4 2 8 0 0 7 0 0 6 0 0 5 0 0 4 0 0 3 0 0 2 0 0 1 0 0 N u m b e r o f p a p e r s Frequency HW Set 1: Due 4/6 in quiz session. HW1: hw_A (at the end of lecture 1), 1.8 (a,b), 1.18 (a,b; by hand, or by computer). HW2: hw_B and hw_C (end of lecture 2), 1.19(a,b,c), 1.20(c), 1.24(a). HW3: 1.28, 1.30, 1.32. HW4: hw_D, hw_E (end of lecture 4), 1.34(a), 1.37 (warning: some book answers are wrong). 8. (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 published 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%. 18. (a) The classes overlap. For example, the classes 2030 and 3040 both contain the number 30, which happens to coincide with one of the data values, so it would not be clear which class to put this observation in. (b) The histogram appears below: Hw_B. A histogram of the raw data appears below: 1 0 0 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 3 0 2 0 1 0 C o n c e n tr a tio n ( p p m ) R e la tive fr e q u e n c y After transforming the data by taking logarithms (base 10), a histogram of the log 10 data is shown below. The shape of this histogram is much less skewed than the histogram of the original data. Hw_C. (a) Proportion(x ≤ 3) = .10 + .15 + .20 + .25 = .70. Proportion(x < 3) = Proportion(x ≤ 2) = .10 + .15 + .20 = .45....
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 Spring '08
 Frequency, Probability distribution, Decimal, probability density function, Histogram, Density estimation

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