Following are boxplots comparing the amount of econozole

The weather in Los Angeles is dry most of the time, but it can be quite rainy in the winter. The rainiest month of the year is February. The following table presents the annual rainfall in Los Angeles, in inches, for each February from 1965 to 2006. 0.2 3.7 1.2 13.7 1.5 0.2 1.7 0.6 0.1 8.9 1.9 5.5 0.5 3.1 3.1 8.9 8.0 12.7 4.1 0.3 2.6 1.5 8.0 4.6 0.7 0.7 6.6 4.9 0.1 4.4 3.2 11.0 7.9 0.0 1.3 2.4 0.1 2.8 4.9 3.5 6.1 0.1 a. Construct a stem-and-leaf plot for these data. b. Construct a histogram for these data. c. Construct a dotplot for these data. d. Construct a boxplot for these data. Does the box-plot show any outliers?

Forty-five specimens of a certain type of powder were analyzed for sulfur trioxide content. Following are the results, in percent. The list has been sorted into numerical order. 14.1 14.4 14.7 14.8 15.3 15.6 16.1 16.6 17.3 14.2 14.4 14.7 14.9 15.3 15.7 16.2 17.2 17.3 14.3 14.4 14.8 15.0 15.4 15.7 16.4 17.2 17.8 14.3 14.4 14.8 15.0 15.4 15.9 16.4 17.2 21.9 14.3 14.6 14.8 15.2 15.5 15.9 16.5 17.2 22.4 a. Construct a stem-and-leaf plot for these data. b. Construct a histogram for these data. c. Construct a dotplot for these data. d. Construct a boxplot for these data. Does the box-plot show any outliers?

Refer to Table 1.2 (in Section 1.2). Construct a stem-and-leaf plot with the ones digit as the stem (for values greater than or equal to 10 the stem will have two digits) and the tenths digit as the leaf. How many stems are there (be sure to include leafless stems)? What are some advantages and disadvantages of this plot, compared to the one in Figure 1.6 (page 26)?

A certain reaction was run several times using each of two catalysts, A and B. The catalysts were supposed to control the yield of an undesirable side product. Results, in units of percentage yield, for 24 runs of catalyst A and 20 runs of catalyst B are as follows: a. Construct a histogram for the yields of each catalyst. b. Construct comparative boxplots for the yields of the two catalysts. c. Using the boxplots, what differences can be seen between the results of the yields of the two catalysts?

For the following data: a. Make a scatterplot of y versus x. Is the relationship between x and y approximately linear, or is it nonlinear? b. Compute the natural logarithm of each y value. This is known as making a log transformation of y. Make a scatter plot of ln y versus x. Is the relationship between x and ln y approximately linear, or is it nonlinear? c. In general, it is easier to work with quantities that have an approximate linear relationship than with quantities that have a nonlinear relationship. For these data, do you think it would be easier to work with x and y or with x and ln y? Explain.

Following are measurements of soil concentrations (in mg/kg) of chromium (Cr) and nickel (Ni) at 20 sites in the area of Cleveland, Ohio. These data are taken from the article “Variation in North American Regulatory Guidance for Heavy Metal Surface Soil Contamination at Commercial and Industrial Sites” (A. Jennings and J. Ma, J Environment Eng, 2007:587–609). Cr: 34 1 511 2 574 496 322 424 269 140 244 252 76 108 24 38 18 34 30 191 Ni: 23 22 55 39 283 34 159 37 61 34 163 140 32 23 54 837 64 354 376 471 a. Construct a histogram for each set of concentrations. b. Construct comparative boxplots for the two sets of concentrations. c. Using the boxplots, what differences can be seen between the two sets of concentrations?

Sketch a histogram for which a. The mean is greater than the median. b. The mean is less than the median. c. The mean is approximately equal to the median.

The figure below is a histogram showing the distribution of serum cholesterol level for a sample of men. Use the histogram to answer the following questions: a. Is the percentage of men with cholesterol levels above 240 mg/dL closest to 30%, 50%, or 70%? b. In which interval are there more men: 240–260 mg/dL or 280–340 mg/dL? Equation Transcription: Text Transcription: 240 mg/dL 240-340 mg/dL (mg/dL)

The histogram below presents the compressive strengths of a sample of concrete blocks hardened for 28 days. One rectangle from the histogram is missing. What is its height?

The following table presents the number of students absent in a middle school in northwestern Montana for each school day in January 2008. a. Construct a boxplot. b. There was a snowstorm on January 27. Was the number of absences the next day an outlier?

Refer to Table 1.5 (in Section 1.3). a. Using the class intervals in the table, construct a histogram in which the heights of the rectangles are equal to the relative frequencies. b. Compare the histogram in part (a) with the histogram in Figure 1.9, for which the heights are the densities. Are the shapes of the histograms the same? c. Explain why the heights should not be set equal to the relative frequencies in this case. d. Which classes are visually exaggerated by making the heights equal to the relative frequencies?

Refer to Table 1.4 (in Section 1.3). a. Using the class intervals in the table, construct a histogram in which the heights of the rectangles are equal to the frequencies. b. Using the class intervals in the table, construct a histogram in which the heights of the rectangles are equal to the densities. c. Compare the histograms in parts (a) and (b) with the histogram in Figure 1.8, for which the heights are the relative frequencies. Are the shapes of the histograms the same?

Which of the following statistics cannot be determined from a boxplot? i. The median ii. The mean iii. The first quartile iv. The third quartile v. The interquartile range

A sample of 100 resistors has an average resistance of \(50\ \Omega\) and a standard deviation of \(5\ \Omega\). A second sample of 100 resistors has an average resistance of \(100\ \Omega\) and a standard deviation of \(5\ \Omega\). If the two samples are combined, the standard deviation of all 200 resistances will be . i. less than \(5\ \Omega\) ii. greater than \(5\ \Omega\) iii. equal to \(5\ \Omega\) iv. can’t tell from the information given (Hint: Don’t do any calculations. Just try to sketch, very roughly, histograms for each sample separately, then for the combined sample.) Equation Transcription: Text Transcription: 50 ohms 5 ohms 100 ohms 5 ohms 5 ohms 5 ohms

Following are boxplots comparing the amount of econozole nitrate (in \(\mu \mathrm{g/cm^2}\)) absorbed into skin for a brand name and a generic antifungal ointment (from the article “Improved Bioequivalence Assessment of Topical Dermatological Drug Products Using Dermatopharmacokinetics.” B. N’Dri-Stempfer, W. Navidi, R. Guy, and A. Bunge, Pharmaceutical Research, 2009:316–328). True or false: a. The median amount absorbed for the brand name drug is greater than the 25th percentile of the amount absorbed for the generic drug. b. The median amount absorbed for the brand name drug is greater than the median amount absorbed for the generic drug. c. About half the sample values for the brand name drug are between 2 and 3. d. There is a greater proportion of values outside the box for the brand name drug than for the generic drug. e. Both samples are skewed to the right. f. Both samples contain outliers. Equation Transcription: Text Transcription: {mu}g/cm^2 ({mu}g/cm^2)

Following are summary statistics for two data sets, A and B. a. Compute the interquartile ranges for both A and B. b. Do the summary statistics for A provide enough information to construct a boxplot? If so, construct the boxplot. If not, explain why. c. Do the summary statistics for B provide enough information to construct a boxplot? If so, construct the boxplot. If not, explain why.

Match each histogram to the boxplot that represents the same data set.

Refer to the asphalt data in Example 1.12 (page 18). a. Construct a boxplot for the asphalt data. b. Which values, if any, are outliers? c. Construct a dotplot for the asphalt data. d. For purposes of constructing boxplots, an outlier is defined to be a point whose distance from the nearest quartile is more than 1.5 IQR. A more general, and less precise, definition is that an outlier is any point that is detached from the bulk of the data. Are there any points in the asphalt data set that are outliers under this more general definition, but not under the boxplot definition? If so, which are they?

Match each scatterplot to the statement that best describes it.