In 1998, a total of 116,517 students took the Advanced Placement examination in Calculus

In Exercises 1–6, write the sum in expanded form. \(\sum_{i=1}^{7} x_{i}\)

In Exercises 1–6, write the sum in expanded form. \(\sum_{i=1}^{5}\left(x_{i}-\bar{x}\right)\)

In Exercises 1–6, write the sum in expanded form. \(\frac{1}{7} \sum_{i=1}^{7} x_{i}\)

In Exercises 1–6, write the sum in expanded form. \(\frac{1}{5} \sum_{i=1}^{5}\left(x_{i}-\bar{x}\right)\)

In Exercises 1–6, write the sum in expanded form. \(\frac{1}{5} \sum_{i=1}^{5}\left(x_{i}-\bar{x}\right)^{2}\)

In Exercises 1–6, write the sum in expanded form. \(\sqrt{\frac{1}{5} \sum_{i=1}^{5}\left(x_{i}-\bar{x}\right)^{2}}\)

In Exercises 7–10, write the sum in sigma notation. \(x_{1} f_{1}+x_{2} f_{2}+x_{3} f_{3}+\cdots+x_{8} f_{8}\)

In Exercises 7–10, write the sum in sigma notation. \(\left(x_{1}-\bar{x}\right)^{2}+\left(x_{2}-\bar{x}\right)^{2}+\cdots+\left(x_{10}-\bar{x}\right)^{2}\)

In Exercises 7–10, write the sum in sigma notation. \(\frac{1}{50}\left[\left(x_{1}-\bar{x}\right)^{2}+\left(x_{2}-\bar{x}\right)^{2}+\cdots+\left(x_{50}-\bar{x}\right)^{2}\right]\)

In Exercises 7–10, write the sum in sigma notation. \(\sqrt{\frac{1}{7}\left[\left(x_{1}-\bar{x}\right)^{2}+\left(x_{2}-\bar{x}\right)^{2}+\cdots+\left(x_{7}-\bar{x}\right)^{2}\right]}\)

In each case, identify whether the number described is a parameter or a statistic. (a) The average score on last week’s quiz was 73.4. (b) About 13% of the human population is left-handed. (c) In a study of laboratory rats, 93% became aggressive when deprived of sleep.

In each case, identify whether the average described is a mean, median, or mode. (a) The average Irish child with red hair also has freckles. (b) The pitcher’s earned run average is 2.35. (c) The choir lined up with tall people in the back, short people in front, and people of average height in the middle.

In Exercises 3–6, find the mean of the data set. {12, 23, 15, 48, 36}

In Exercises 3–6, find the mean of the data set. {4, 8, 11, 6, 21, 7}

In Exercises 3–6, find the mean of the data set. {32.4, 48.1, 85.3, 67.2, 72.4, 55.3}

In Exercises 3–6, find the mean of the data set. {27.4, 3.1, 9.7, 32.3, 12.8, 39.4, 73.7}

In Exercises 7 and 8, find the mean population of the six states listed in Table 9.15 (page 702) for the indicated year. 1900

In Exercises 7 and 8, find the mean population of the six states listed in Table 9.15 (page 702) for the indicated year. 1990

In Exercises 9 and 10, find the mean of the indicated data. The number of satellites (moons), from the data in Table 9.19.

In Exercises 9 and 10, find the mean of the indicated data. The area of the continents, from the data in Table 9.20.

Find the median of the data in Table 9.19. (See Exercise 9.)

Find the median of the data in Table 9.20. (See Exercise 10.)

Determine the average annual home run production for Willie Mays and for Mickey Mantle for their career totals of 660 over 22 years and 536 over 18 years, respectively. Who had the greater production rate?

A painting crew in State College, Pennsylvania, painted 12 houses in 5 days, and a crew in College Station, Texas, painted 15 houses in 7 days. Determine the average number of houses per day each crew painted. Which crew had the greater rate?

The Hip-Hop House produced 1147 scooter skirts in 4 weeks, and What-Next Fashion produced 1516 scooter skirts in 4 weeks. Which company had the greater production rate?

Per capita income (PCI) is an average found by dividing a nation’s gross national product (GNP) by its population. India has 882,575,000 people and a GNP of 311 billion dollars, and Mexico has 87,715,000 people and a GNP of 218 billion dollars. Determine the PCI for India and for Mexico. Which nation has the greater income per person?

Find the median and mode of the numbers in Table 9.18 on page 711 (weights in grams of newly hatched loon chicks).

In 1998, a total of 116,517 students took the Advanced Placement examination in Calculus AB. From the frequency table below, find the mean score in Calculus AB in 1998. (Source: The College Board.)

In 1998, a total of 26,784 students took the Advanced Placement examination in Calculus BC. From the frequency table below, find the mean score in Calculus BC in 1998. (Source:The College Board.)

In Exercises 20 and 21 use the data in Table 9.16 (page 703). (a) Find the average (mean) of the indicated temperatures for Beijing. (b) Find the weighted average using the number of days in the month as the weight. (Assume no leap year.) (c) Compare your results in parts (a) and (b). Do the weights have an effect on the average? Why or why not? Which average is the better indicator for these temperatures? The monthly high temperatures

In Exercises 20 and 21 use the data in Table 9.16 (page 703). (a) Find the average (mean) of the indicated temperatures for Beijing. (b) Find the weighted average using the number of days in the month as the weight. (Assume no leap year.) (c) Compare your results in parts (a) and (b). Do the weights have an effect on the average? Why or why not? Which average is the better indicator for these temperatures? The monthly low temperatures

In Exercises 22–25, determine the five-number summary, the range, and the interquartile range for the sets of data specified. Identify any outliers. The annual home run production data for Mark McGwire and Barry Bonds in Table 9.6 (page 696).

In Exercises 22–25, determine the five-number summary, the range, and the interquartile range for the sets of data specified. Identify any outliers. The annual home run production data for Willie Mays and Mickey Mantle in Table 9.13 (page 701).

In Exercises 22–25, determine the five-number summary, the range, and the interquartile range for the sets of data specified. Identify any outliers. The following average annual wind speeds at 44 climatic data centers around the United States: 9.0, 6.9, 9.1, 9.2, 10.2, 12.5, 12.0, 11.2, 12.9, 10.3, 10.6, 10.9, 8.7, 10.3, 11.0, 7.7, 11.4, 7.9, 9.6, 8.0, 10.7, 9.3, 7.9, 6.2, 8.3, 8.9, 9.3, 11.6, 10.6, 9.0, 8.2, 9.4, 10.6, 9.5, 6.3, 9.1, 7.9, 9.7, 8.8, 6.9, 8.7, 9.0, 8.9, 9.3

In Exercises 22–25, determine the five-number summary, the range, and the interquartile range for the sets of data specified. Identify any outliers. The following salaries for employees in one department of the Garcia Brothers Company (in thousands of dollars): 33.5, 35.3, 33.8, 29.3, 36.7, 32.8, 31.7, 37.3, 33.5, 28.2, 34.8, 33.5, 29.7, 38.5, 32.7, 34.8, 34.2, 31.6, 35.4

In Exercises 26–28, make (a) a boxplot and (b) a modified boxplot for the data. The annual home run production data for Mark McGwire in Table 9.6 (page 696)

In Exercises 26–28, make (a) a boxplot and (b) a modified boxplot for the data. The annual home run production data for Barry Bonds in Table 9.6 (page 696)

In Exercises 26–28, make (a) a boxplot and (b) a modified boxplot for the data. The annual CD shipments in Table 9.9 (page 699)

In Exercises 29 and 30, refer to the wind speed data analyzed in Exercise 24. Some wind turbine generators, to be efficient generators of power, require average wind speeds of at least 10.5 mph. Approximately what fraction of the climatic centers are suited for these wind turbine generators?

In Exercises 29 and 30, refer to the wind speed data analyzed in Exercise 24. If technology improves the efficiency of the wind turbines so that they are efficient in winds that average at least 7.5 mph, approximately what fraction of the climatic centers are suited for these improved wind generators?

In Exercises 31 and 32, use simultaneous boxplots of the annual home run production data for Willie Mays and Mickey Mantle in Table 9.13 (page 701) to answer the question. (a) Which data set has the greater range? (b) Which data set has the greater interquartile range?

In Exercises 31 and 32, use simultaneous boxplots of the annual home run production data for Willie Mays and Mickey Mantle in Table 9.13 (page 701) to answer the question. Write a paragraph explaining the difference in home run production between Willie Mays and Mickey Mantle.

In Exercises 33–38, find the standard deviation and variance of the data set. (Since the data set is the population under consideration, use \(\sigma\) in each case, rather than s.) {23, 45, 29, 34, 39, 41, 19, 22}

In Exercises 33–38, find the standard deviation and variance of the data set. (Since the data set is the population under consideration, use \(\sigma\) in each case, rather than s.) {28, 84, 67, 71, 92, 37, 45, 32, 74, 96}

In Exercises 33–38, find the standard deviation and variance of the data set. (Since the data set is the population under consideration, use \(\sigma\) in each case, rather than s.) The CD shipment data in Table 9.9 (page 699)

In Exercises 33–38, find the standard deviation and variance of the data set. (Since the data set is the population under consideration, use \(\sigma\) in each case, rather than s.) The cassette shipment data in Table 9.10 (page 700)

In Exercises 33–38, find the standard deviation and variance of the data set. (Since the data set is the population under consideration, use \(\sigma\) in each case, rather than s.) The data in Exercise 24

In Exercises 33–38, find the standard deviation and variance of the data set. (Since the data set is the population under consideration, use \(\sigma\) in each case, rather than s.) The data in Exercise 25

Mark McGwire’s annual home run production (Table 9.6, page 696) ranges from a low of 3 to a high of 70. Is either of these numbers an outlier by the 1.5 X IQR criterion?

Is it possible for the standard deviation of a set to be negative? To be zero? Explain your answer in both cases.

In 1995, scores on the Scholastic Aptitude Tests were re-scaled to their original mean (500) with an approximate standard deviation of 100. SAT scores in the general population have a normal distribution. (a) Approximately what percentage of the 1995 scores fell between 400 and 600? (b) Approximately what percentage of the 1995 scores fell below 300? (c) By 2001 the national average on the SAT Math section had risen to 514. Is this number a parameter or a statistic?

In 2001, the national mean ACT Math score was 20.7, with an approximate standard deviation of 6. ACT scores in the general population have a normal distribution. (a) Approximately what percentage of the 2001 scores were higher than 26.7? (b) Approximately what ACT Math score would one need to make in 2001 to be ranked among the top 2.5% of all who took the test? (c) Writing to Learn Mean ACT scores are published state by state. If we add up the 50 state means and divide by 50, will the result be a good estimate for the national mean score? Explain your answer.

The median is strongly affected by outliers. Justify your answer.

The length of the box in a boxplot is the interquartile range. Justify your answer.

You may use a graphing calculator when solving Exercises 45–48. The plot of a normal distribution will be (A) Symmetric. (B) Skewed left. (C) Skewed right. (D) Lower in the middle than at the ends. (E) Of no predictable shape.

You may use a graphing calculator when solving Exercises 45–48. A frequency table for a set of 25 quiz grades is given below. What is the mean of the data? (A) 7.00 (B) 7.28 (C) 7.35 (D) 7.60 (E) 7.86

You may use a graphing calculator when solving Exercises 45–48. Professor Mitchell grades the exams of his 30 students and finds that the scores have a mean of 81.3 and a median of 80.5. He later determines that the top student deserves 9 extra points for a misgraded proof. After the error is corrected, the scores have (A) A mean of 81.3 and a median of 80.5. (B) A mean of 81.6 and a median of 80.5. (C) A mean of 81.6 and a median of 80.8. (D) A mean of 90.3 and a median of 80.5. (E) A mean of 90.3 and a median of 89.5.

You may use a graphing calculator when solving Exercises 45–48. If the calorie contents of robin eggs are normally distributed with a mean of 25 and a standard deviation of 1.2, then 95% of all robin eggs will have a calorie content in the interval (A) [21.4,28.6] (B) [22,28] (C) [22.6,27.4] (D) [23,27] (E) [23.8,26.2]

List a set of data for which the inequality holds. (a) Mode < median < mean (b) Median < mean < mode (c) Mean < mode < median

List a set of data for which the equation or inequality holds. (a) Standard deviation < interquartile range (b) Interquartile range < standard deviation (c) Range = interquartile range

Is it possible for the standard deviation of a data set to be greater than the range? Explain.

Why can we find the mode of categorical data but not the mean or median?

Draw a boxplot for which the inequality holds. (a) Median < mean (b) 2 X interquartile range < range (c) Range < 2 X interquartile range

Construct a set of data with median 5, mode 6, and mean 7.

The average life expectancies for males and females in South American nations were given in Table 9.12 (page 701). To find an overall average life expectancy for males or females in all of these nations, we would need to weight the national data according to the various national populations. Table 9.21 is an extension of Table 9.12, showing the populations (in millions). Assume that males and females appear in roughly equal numbers in every nation. In Exercises 55 and 56, use the data in Table 9.21 to find the mean life expectancy for each group. Women living in South American nations

The average life expectancies for males and females in South American nations were given in Table 9.12 (page 701). To find an overall average life expectancy for males or females in all of these nations, we would need to weight the national data according to the various national populations. Table 9.21 is an extension of Table 9.12, showing the populations (in millions). Assume that males and females appear in roughly equal numbers in every nation. In Exercises 55 and 56, use the data in Table 9.21 to find the mean life expectancy for each group. Men living in South American nations

A plant manufactures ball bearings to the purchaser’s specifications, rejecting any output with a diameter that deviates more than 0.1 mm from the specified value. If the ball bearings are produced with the specified mean and a standard deviation of 0.05 mm, what percentage of the output will be rejected?

A machine fills 12-ounce cola cans with a mean of 12.08 ounces of cola and a standard deviation of 0.04 ounce. Approximately what percentage of the cans will actually contain less than the advertised 12 ounces of cola?