Exam 3: Numerical Descriptive Measures

In perfectly symmetrical distributions, which of the following is not a correct statement?

TABLE 3-7 Given below is the frequency distribution of the 12-month rate of return achieved by 30 stocks. 12- month Rate of Return Number of Funds -0.10 but less than 0.0 3 0.0 but less th an 0.1 5 0.1 but less than 0.2 6 0.2 but less than 0.3 10 0.3 but less than 0.4 6 -Referring to Table 3-7, what is the approximate mean rate of return?

$\text { TABLE 3-1 }$ 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 first quartile of the ages of the uninsured senior citizens.

$\text { TABLE 3-2 }$ 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, what type of shape does the distribution of the sample appear to have?

$\text { TABLE 3-2 }$ 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 arithmetic mean carbohydrates in this sample is _____grams.

$\text { TABLE 3-3 }$ 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 range of the number of vitamin supplements sold in this sample 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 variance of the customs data is ___.

The coefficient of variation is a measure of central tendency in the data.

If the arithmetic mean of a numerical data set exceeds the median, the data are considered to be _____skewed.

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 range in the carbohydrate amounts is ____grams.

The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5 is 1.9.

$\text { TABLE 3-3 }$ 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 interquartile range of the number of vitamin supplements sold in this sample is ____.

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 variance of the number of vitamin supplements sold in this sample is ______.

$\text { TABLE 3-1 }$ 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, calculate the arithmetic mean age of the uninsured senior citizens to the nearest hundredth of a year.

TABLE 3-6 The rate of return of an Internet Service Provider over a 10- year period are: 10.25%, 12.64%, 8.37%, 9.29%, 6.23%, 42.53%, 29.23%, 15.25%, 21.52%, -2.35%. -Referring to Table 3-6, what is the shape of the distribution for the rate of return?

$\text { TABLE 3-10 }$ 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 Wilshire 5000 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 Wilshire 5000 Index.

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 1 67889 2 0011122223333444 2 5566678899 3 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 interquartile range of the customs data is ____.

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, construct a boxplot for the rate of return.

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, what type of shape does the distribution of the sample appear to have?

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 median carbohydrate amount in the cereal is____ grams.