An experiment measuring the percent shrinkage on drying of

The following is a sample of prices, rounded to the nearest cent, charged per gallon of standard unleaded gasoline in the San Francisco Bay area in June 1997. 3.88, 3.90, 3.93, 3.90, 3.93, 3.96, 3.88, 3.94, 3.96, 3.88, 3.94, 3.99, 3.98 Represent these data in (a) a frequency table; (b) a relative frequency line graph.

Explain how a pie chart can be constructed. If a data value had relative frequency r, at what angle would the lines defining its sector meet?

The following are the estimated oil reserves, in billions of barrels, for four regions in the Western Hemisphere. United States 38.7 South America 22.6 Canada 8.8 Mexico 60.0 Represent these data in a pie chart.

The following table gives the average travel time to work for workers in each of the 50 states as well as the percentage of those workers who use public transportation. (a) Represent the data relating to the average travel times in a histogram. (b) Represent the data relating to the percentage of workers using public transportation in a stem and leaf plot.

Choose a book or article and count the number of words in each of the first 100 sentences. Present the data in a stem and leaf plot. Now choose another book or article, by a different author, and do the same. Do the two stem and leaf plots look similar? Do you think this could be a viable method for telling whether different articles were written by different authors?

The following table gives the number of commercial airline accidents and the total number of resulting fatalities in the United States in the years from 1985 to 2006. (a) Represent the number of yearly airline accidents in a frequency table. (b) Give a frequency polygon graph of the number of yearly airline accidents. (c) Give a cumulative relative frequency plot of the number of yearly airline accidents. (d) Find the sample mean of the number of yearly airline accidents. (e) Find the sample median of the number of yearly airline accidents. (f ) Find the sample mode of the number of yearly airline accidents. (g) Find the sample standard deviation of the number of yearly airline accidents.

(Use the table from Problem 6.) (a) Represent the number of yearly airline fatalities in a histogram. (b) Represent the number of yearly airline fatalities in a stem and leaf plot. (c) Find the sample mean of the number of yearly airline fatalities. (d) Find the sample median of the number of yearly airline fatalities. (e) Find the sample standard deviation of the number of yearly airline fatalities.

The sample mean of the weights of the adult women of town A is larger than the sample mean of the weights of the adult women of town B. Moreover, the sample mean of the weights of the adult men of town A is larger than the sample mean of the weights of the adult men of town B. Can we conclude that the sample mean of the weights of the adults of town A is larger than the sample mean of the weights of the adults of town B? Explain your answer.

Using the table given in Problem 4, find the sample mean and sample median of the average travel time for those states in the (a) northeast; (b) midwest; (c) south; (d) west.

A total of 100 people work at company A, whereas a total of 110 work at company B. Suppose the total employee payroll is larger at company A than at company B. (a) What does this imply about the median of the salaries at company A with regard to the median of the salaries at company B? (b) What does this imply about the average of the salaries at company A with regard to the average of the salaries at company B?

The sample mean of the initial 99 values of a data set consisting of 198 values is equal to 120, whereas the sample mean of the final 99 values is equal to 100. What can you conclude about the sample mean of the entire data set (a) Repeat when sample mean is replaced by sample median. (b) Repeat when sample mean is replaced by sample mode.

The following table gives the number of pedestrians, classified according to age group and sex, killed in fatal road accidents in England in 1922. (a) Approximate the sample means of the ages of the males. (b) Approximate the sample means of the ages of the females. (c) Approximate the quartiles of the males killed. (d) Approximate the quartiles of the females killed.

The following are the percentages of ash content in 12 samples of coal found in close proximity: 9.2, 14.1, 9.8, 12.4, 16.0, 12.6, 22.7, 18.9, 21.0, 14.5, 20.4, 16.9 Find the (a) sample mean, and (b) sample standard deviation of these percentages.

The sample mean and sample variance of five data values are, respectively, x =104 and s2 =16. If three of the data values are 102, 100, 105, what are the other two data values?

Suppose you are given the average pay of all working people in each of the 50 states of the United States. (a) Do you think that the sample mean of the averages for the 50 states will equal the value given for the entire United States? (b) If the answer to part (a) is no, explain what other information aside from just the 50 averages would be needed to determine the sample mean salary for the entire country. Also, explain how you would use the additional information to compute this quantity.

The following data represent the lifetimes (in hours) of a sample of 40 transistors: 112, 121, 126, 108, 141, 104, 136, 134 121, 118, 143, 116, 108, 122, 127, 140 113, 117, 126, 130, 134, 120, 131, 133 118, 125, 151, 147, 137, 140, 132, 119 110, 124, 132, 152, 135, 130, 136, 128 (a) Determine the sample mean, median, and mode. (b) Give a cumulative relative frequency plot of these data.

An experiment measuring the percent shrinkage on drying of 50 clay specimens produced the following data: 18.2 21.2 23.1 18.5 15.6 20.8 19.4 15.4 21.2 13.4 16.4 18.7 18.2 19.6 14.3 16.6 24.0 17.6 17.8 20.2 17.4 23.6 17.5 20.3 16.6 19.3 18.5 19.3 21.2 13.9 20.5 19.0 17.6 22.3 18.4 21.2 20.4 21.4 20.3 20.1 19.6 20.6 14.8 19.7 20.5 18.0 20.8 15.8 23.1 17.0 (a) Draw a stem and leaf plot of these data. (b) Compute the sample mean, median, and mode. (c) Compute the sample variance. (d) Group the data into class intervals of size 1 percent starting with the value 13.0, and draw the resulting histogram. (e) For the grouped data acting as if each of the data points in an interval was actually located at the midpoint of that interval, compute the sample mean and sample variance and compare this with the results obtained in parts (b) and (c). Why do they differ?

A computationally efficient way to compute the sample mean and sample variance of the data set x1, x2, . . . , xn is as follows. Let x j = j _ i=1 xi j , j =1, . . . , n be the sample mean of the first j data values, and let s2 j = j _ i=1 (xi xj)2 j 1 , j =2, . . . , n be the sample variance of the first j, j 2, values. Then, with s2 1 =0, it can be shown that xj+1 = xj + xj+1 xj j +1 and s2 j+1 = 1 1 j s2 j +(j +1)(xj+1 xj)2 (a) Use the preceding formulas to compute the sample mean and sample variance of the data values 3, 4, 7, 2, 9, 6. (b) Verify your results in part (a) by computing as usual. (c) Verify the formula given above for xj+1 in terms of x j .

Use the data of Table 2.5 to find the (a) 90 percentile of the average temperature for January; (b) 75 percentile of the average temperature for July.

Find the quartiles of the following ages at death as given in obituaries of the New York Times in the 2 weeks preceding 1 August 2013. 92, 90, 92, 74, 69, 80, 94, 98, 65, 96, 84, 69, 86, 91, 88 74, 97, 85, 88, 68, 77, 94, 88, 65, 76, 75, 60 69, 97, 92, 85, 70, 80, 93, 91, 68, 82, 78, 89

The universities having the largest number of months in which they ranked in the top 10 for the number of google searches over the past 114 months (as of June 2013) are as follows. University Number of Months in Top 10 Harvard University 114 University of Texas, Austin 114 University of Michigan 114 Stanford University 113 University of California Los Angeles (UCLA) 111 University of California Berkeley 97 Penn State University 94 Massachusetts Institute of Technology (MIT) 66 University of Southern California (USC) 63 Ohio State University 52 Yale University 48 University of Washington 33 (a) Find the sample mean of the data. (b) Find the sample variance of the data. (c) Find the sample quartiles of the data.

Use the part of the table given in Problem 4 that gives the percentage of workers in each state that use public transportation to get to work to draw a box plot of these 50 percentages.

Represent the data of Problem 20 in a box plot.

The average particulate concentration, in micrograms per cubic meter, was measured in a petrochemical complex at 36 randomly chosen times, with the following concentrations resulting: 5, 18, 15, 7, 23, 220, 130, 85, 103, 25, 80, 7, 24, 6, 13, 65, 37, 25, 24, 65, 82, 95, 77, 15, 70, 110, 44, 28, 33, 81, 29, 14, 45, 92, 17, 53 (a) Represent the data in a histogram. (b) Is the histogram approximately normal?

A chemical engineer desiring to study the evaporation rate of water from brine evaporation beds obtained data on the number of inches of evaporation in each of 55 July days spread over 4 years. The data are given in the following stem and leaf plot, which shows that the smallest data value was .02 inches, and the largest .56 inches. .0 2, 6 .1 1, 4 .2 1, 1, 1, 3, 3, 4, 5, 5, 5, 6, 9 .3 0, 0, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 8, 9 .4 0, 1, 2, 2, 2, 3, 4, 4, 4, 5, 5, 5, 7, 8, 8, 8, 9, 9 .5 2, 5, 6 Find the (a) sample mean; (b) sample median; (c) sample standard deviation of these data. (d) Do the data appear to be approximately normal? (e) What percentage of data values are within 1 standard deviation of the mean?

The following are the grade point averages of 30 students recently admitted to the graduate program in the Department of Industrial Engineering and Operations Research at the University of California at Berkeley. 3.46, 3.72, 3.95, 3.55, 3.62, 3.80, 3.86, 3.71, 3.56, 3.49, 3.96, 3.90, 3.70, 3.61, 3.72, 3.65, 3.48, 3.87, 3.82, 3.91, 3.69, 3.67, 3.72, 3.66, 3.79, 3.75, 3.93, 3.74, 3.50, 3.83 (a) Represent the preceding data in a stem and leaf plot. (b) Calculate the sample mean x . (c) Calculate the sample standard deviation s. (d) Determine the proportion of the data values that lies within x }1.5s and compare with the lower bound given by Chebyshevs inequality. (e) Determine the proportion of the data values that lies within x }2s and compare with the lower bound given by Chebyshevs inequality.

Do the data in Problem 26 appear to be approximately normal? For parts (c) and (d) of this problem, compare the approximate proportions given by the empirical rule with the actual proportions.

Would you expect that a histogram of the weights of all the members of a health club would be approximately normal?

Use the data of Problem 16. (a) Compute the sample mean and sample median. (b) Are the data approximately normal? (c) Compute the sample standard deviation s. (d) What percentage of the data fall within x }1.5s? (e) Compare your answer in part (d) to that given by the empirical rule. (f ) Compare your answer in part (d) to the bound given by Chebyshevs inequality.

The following are the heights and starting salaries of 12 law school classmates whose law school examination scores were roughly the same. Height Salary 64 91 65 94 66 88 67 103 69 77 70 96 72 105 72 88 74 122 74 102 75 90 76 114 (a) Represent these data in a scatter diagram. (b) Find the sample correlation coefficient.

A random sample of individuals were rated as to their standing posture. In addition, the numbers of days of back pain each had experienced during the past year were also recorded. Surprisingly to the researcher these data indicated a positive correlation between good posture and number of days of back pain. Does this indicate that good posture causes back pain?

If for each of the fifty states we plot the paired data consisting of the average income of residents of the state and the number of foreign-born immigrants who reside in the state, then the data pairs will have a positive correlation. Can we conclude that immigrants tend to have higher incomes than native-born Americans? If not, how else could this phenomenon be explained?

A random group of 12 high school juniors were asked to estimate the average number of hours they study each week. The following give these hours along with the students grade point average. Hours GPA 6 2.8 14 3.2 3 3.1 22 3.6 9 3.0 11 3.3 12 3.4 5 2.7 18 3.1 24 3.8 15 3.0 17 3.9 Find the sample correlation coefficient between hours reported and GPA.

Verify property 3 of the sample correlation coefficient.

Verify property 4 of the sample correlation coefficient.

In a study of children in grades 2 through 4, a researcher gave each student a reading test. When looking at the resulting data the researcher noted a positive correlation between a students reading test score and height. The researcher concluded that taller children read better because they can more easily see the blackboard. What do you think? 3

A recent study yielded a positive correlation between breast-fed babies and scores on a vocabulary test taken at age 6. Discuss the potential difficulties in interpreting the results of this study.