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 for the Standard & Poor's 500.

In a perfectly symmetrical bell-shaped "normal" distribution

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 median of the customs data is _____.

Which of the arithmetic mean, median, mode, and geometric mean are resistant measures of central tendency?

Which of the following statistics is not a measure of central tendency?

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 3-1, identify the median age of the uninsured senior citizens.

The median of a data set with 20 items would be the average of the 10th and the 11th items in the ordered array.

The geometric mean is a measure of variation or dispersion in a set of data.

$\text { TABLE 3-2 }$ The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a sample of 11 different servings. $11\quad15\quad23\quad29\quad19\quad22\quad21\quad20\quad15\quad25\quad17$ -Referring to Table 3-2, the standard deviation of the carbohydrate amounts is ____grams.

TABLE 3-2 The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a sample of 11 different servings. $11\quad15\quad23\quad29\quad19\quad22\quad21\quad20\quad15\quad25\quad17$ -Referring to Table 3-2, the third quartile of the carbohydrate amounts is_____grams.

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 geometric mean rate of return.

$\text { TABLE 3-9 }$ 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 are the (absolute values of) the Z scores of the change in cost?

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 568 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 coefficient of variation of the number of vitamin supplements sold in this sample is_________ percent.

In a sample of size 40, the sample mean is 15. In this case, the sum of all observations in the sample is ΣXi = 600.

In left-skewed distributions, the distance from the smallest observation to Q1 exceeds the distance from Q3 to the largest observation.

TABLE 3-2 The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a sample of 11 different servings. $11\quad15\quad23\quad29\quad19\quad22\quad21\quad20\quad15\quad25\quad17$ -Referring to Table 3-2, the coefficient of variation of the carbohydrate amounts is _____percent.

The Z score of an observation measures how many standard deviations is the value from the mean.

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 arithmetic mean of the customs data is _____.