Exam 3: Numerical Descriptive Measures

TABLE 3-10 The time period from 2000 to 2003 saw a great deal of volatility in the value of stocks. The data in the following table represent the total rate of return of the Dow Jones Industrial Index, the Standard & Poor's 500, the Russell 2000 Index, and the Wilshire 5000 Index from 2000 to 2003. Year DJIA SP500 Russell2000 Wilshire5000 2003 25.30 26.40 45.40 29.40 2002 -15.01 -22.10 -21.58 -20.90 2001 -5.44 -11.90 -1.03 -10.97 2000 -6.20 -9.10 -3.02 -10.89 -Referring to Table 3-10, calculate the geometric mean rate of return the Russell 2000 Index.

$\text { TABLE 3-8 }$ Given below is the frequency distribution of the number of defective tomatoes in 50 different shipments. Defective Items Frequency 0 but less than 5 35 5 but less than 10 7 10 but less than 15 5 15 but less than 20 2 20 but less than 25 1 25 but less than 30 0 -Referring to Table 3-8, what is the approximate variance?

As a general rule, an observation is considered an extreme value if its Z score is less than 3.

The coefficient of variation is a measure of relative variation.

According to the Chebyshev rule, at least 93.75% of all observations in any data set are contained within a distance of how many standard deviations around the mean?

According to the empirical rule, if the data form a "bell-shaped" normal distribution, percent of the observations will be contained within 1 standard deviation around the arithmetic mean.

The interquartile range is a measure of central tendency in a set of data.

A population with 200 elements has an arithmetic mean of 10. From this information, it can be shown that the population standard deviation is 15.

$\text { TABLE 3-9 }$ In the 2002- 2003 academic year, many public universities in the United States raised tuition and fees due to a decrease in state subsidies. The change in the cost of tuition, a shared dormitory room, and the most popular meal plan from the 2001- 2002 academic year for a sample of 10 public universities were as follows: $1589, $593, $1223, $869, $423, $1720, $708, $1425, $922 and $308. -Referring to Table 3-9, what is the standard deviation of the change in the cost?

The rate of return for the S&P 500 over a seven- year period is - 0.029, - 0.061, - 0.493,- 0.286, - 0.160, - 0.186 and - 0.224. The geometric mean rate of return is _____.

TABLE 3-4 The stem-and-leaf display below represents the number of cargo manifests approved by customs inspectors of the Port of New York in a sample of 35 days. Stem Leaves 1H 67889 2L 0011122223333444 2H 5566678899 3L 1122 Note (1): 1H means the "high teens" - 15, 16, 17, 18, or 19; 2L means the "low twenties" - 20, 21, 22, 23, or 24; 2H means the "high twenties" - 25, 26, 27, 28, or 29, etc. Note (2): For this sample, the sum of the observations is 838, the sum of the squares of the observations is 20,684, and the sum of the squared differences between each observation and the mean is 619.89. -Referring to Table 3-4, the coefficient of variation of the customs data is_________ percent.

An economics professor bases his final grade on homework, two midterm examinations, and a final examination. The homework counts 10% toward the final grade, while each midterm examination counts 25%. The remaining portion consists of the final examination. If a student scored 95% in homework, 70% on the first midterm examination, 96% on the second midterm examination, and 72% on the final, his final average is 79.8%.

TABLE 3-1 Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid and have no private health insurance. The ages of 25 uninsured senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92 -Referring to Table 3-3, the five-number summary of the data in this sample consists of___,____ , ___,____ ,___ and____ .

In left-skewed distributions, which of the following is the correct statement?

TABLE 3-5 The rate of return of a Fortune 500 company over the past 15 years are: 3.17%, 4.43%, 5.93%, 5.43%, 7.29%, 8.21%, 6.23%, 5.23%, 4.34%, 6.68%, 7.14%, -5.56%, -5.23%, -5.73%, -10.34% -Referring to Table 3-5, compute the arithmetic mean rate of return.

TABLE 3-3 The stem-and-leaf display below represents the number of vitamin supplements sold by a health food store in a sample of 16 days. Stem Leaves 1H 99 2L 0023 2H 567 3L 034 3H 4L 1 Note (1): 1H means the "high teens" - 15, 16, 17, 18, or 19; 2L means the "low twenties" - 20, 21, 22, 23, or 24; 2H means the "high twenties" - 25, 26, 27, 28, or 29, etc. Note (2): For this sample, the sum of the observations is 448, the sum of the squares of the observations is 13,356, and the sum of the squared differences between each observation and the mean is 812. -Referring to Table 3-3, the standard deviation of the number of vitamin supplements sold in this sample is ___.

TABLE 3-9 In the 2002- 2003 academic year, many public universities in the United States raised tuition and fees due to a decrease in state subsidies. The change in the cost of tuition, a shared dormitory room, and the most popular meal plan from the 2001- 2002 academic year for a sample of 10 public universities were as follows: $1589, $593, $1223, $869, $423, $1720, $708, $1425, $922 and $308. -Referring to Table 3-9, are the data skewed? If so, how?

The rate of return for Microsoft's stock over a seven- year period is 0.527, 0.145, 0.684, 1.146, 0.564, 0.883 and 0.436. The geometric mean rate of return is ______ .

In a boxplot, the box portion represents the data between the first and third quartile values.

In exploratory data analysis, a boxplot can be used to illustrate the median, quartiles, and extreme values.