Exam 3: Numerical Descriptive Measures

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. The ages of 25 senior citizens were as follows: -Referring to Table 3-1, determine which of the following is the correct statement.

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, 15, 23, 29, 19, 22, 21, 20 ,15, 25, 17 -Referring to Table 3-2, the coefficient of variation of the carbohydrate amounts is ________ percent.

If the distribution of a data set were perfectly symmetrical, the distance from Q₁ to the median would always equal the distance from Q₃ to the median in a boxplot.

TABLE 3-3 The ordered array below represents the number of vitamin supplements sold by a health food store in a sample of 16 days. 19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41 Note: For this sample, the sum of the values is 448, and the sum of the squared differences between each value and the mean is 812. -Referring to Table 3-3, the five-number summary of the data in this sample consists of ________, ________, ________, ________, ________.

You were told that the 1ˢᵗ, 2ⁿᵈ and 3ʳᵈ quartiles of female students' weight at a major university are 95 lbs, 125 lbs, and 138 lbs. What percentage of the students weigh less than 95 lbs?

If the data set is approximately bell-shaped, the empirical rule will more accurately reflect the greater concentration of data close to the mean as compared to the Chebyshev rule.

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. The ages of 25 senior citizens were as follows: -Referring to Table 3-1, calculate the coefficient of variation of the ages of the senior citizens.

The coefficient of variation measures variability in a data set relative to the size of the arithmetic mean.

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

According to the Chebyshev rule, at least what percentage of the observations in any data set are contained within a distance of 2 standard deviations around the mean?

TABLE 3-4 The ordered array below represents the number of cargo manifests approved by customs inspectors at the Port of New York in a sample of 35 days: 16, 17, 18, 18, 19, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 28, 28, 29, 29, 31, 31, 32, 32 Note: For this sample, the sum of the values is 838, and the sum of the squared differences between each value and the mean is 619.89. -Referring to Table 3-4, the five-number summary for the data in the customs sample consists of ________, ________, ________, ________, ________.

TABLE 3-12 Energy drink consumption has continued to gain in popularity since the 1997 debut of Red Bull, the current leader in the energy drink market. Given below are the exam scores and the number of 12-ounce energy drinks consumed by 10 college students within a week prior to the exam. -Referring to Table 3-12, for a student who has consumed a high number of energy drinks within the week prior to the exam, you will expect his/her exam score to

In a right-skewed distribution,

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

The line drawn within the box of the boxplot always represents the arithmetic mean.

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

TABLE 3-7 In a recent 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 previous academic year for a sample of 10 public universities were as follows: $1,589, $593, $1,223, $869, $423, $1,720, $708, $1425, $922 and $308. -Referring to Table 3-7, what is the mean and median change in the cost?

The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5 is 4.05.

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, what is the shape of the distribution for the rate of return?

TABLE 3-4 The ordered array below represents the number of cargo manifests approved by customs inspectors at the Port of New York in a sample of 35 days: 16, 17, 18, 18, 19, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 28, 28, 29, 29, 31, 31, 32, 32 Note: For this sample, the sum of the values is 838, and the sum of the squared differences between each value and the mean is 619.89. -Referring to Table 3-4, construct a boxplot of this sample.