Exam 3: Numerical Descriptive Measures

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

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 box-and-whisker plot.

Instruction 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 who 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 Instruction 3-1,calculate the variance of the ages of the uninsured senior citizens correct to the nearest hundredth of a year squared.

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

Instruction 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 Instruction 3-3,the third quartile of the number of vitamin supplements sold in this sample is _____________ .

Instruction 3-2 The data below represents 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 Instruction 3-2,the arithmetic mean carbohydrates in this sample is _____________ grams.

Instruction 3-5 The rate of return of a listed Australian 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 Instruction 3-5,compute the geometric mean rate of return.

Instruction 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 Instruction 3-3,the range of the number of vitamin supplements sold in this sample is _____________ .

When preparing statistical information,it is important to be conscious of errors in the objectivity of your _____________ .

Instruction 3-4 The ordered array below represents the number of cargo manifests approved by customs inspectors at the Port of Brisbane 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 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 Instruction 3-4,the range of the customs data is _____________ .

Instruction 3-9 The data below represents 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 Instruction 3-9,the five-number summary of the carbohydrate amounts consists of _____________ ,_____________ ,_____________ ,_____________ ,_____________ .

Instruction 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 Instruction 3-8,what is the approximate standard deviation?

Instruction 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 Instruction 3-3,the first quartile of the number of vitamin supplements sold in this sample is _____________ .

Instruction 3-15 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-grams energy drinks consumed by 10 college students within a week prior to the exam. Exam Scores 75 92 84 64 64 86 81 61 73 93 Number of Drinks 5 3 2 4 2 7 3 0 1 0 -Referring to Instruction 3-15,you will expect a decrease in the amount of energy drink consumed within the week prior to the exam to be associated with _____________ .

A boxplot is a graphical representation of a five-number summary.

What is a measure of variation or dispersion in a set of data?

An economics lecturer bases his final grade on tutorial work,two mid-semester tests,and a final examination.The tutorial work counts 10% toward the final grade,while each mid-semester test counts 25%.The remaining portion consists of the final examination.If a student scored 95% in tutorial work,70% on the first mid-semester test,96% on the second mid-semester test,and 72% on the final exam,his final average would be _________.

If the mean is equal to the median,the distribution is symmetrical or has zero skewness.

Instruction 3-4 The ordered array below represents the number of cargo manifests approved by customs inspectors at the Port of Brisbane 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 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 Instruction 3-4,the first quartile of the customs data is _____________ .

Instruction 3-11 The ordered array below represents the number of cargo manifests approved by customs inspectors at the Port of Brisbane 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 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 Instruction 3-11,construct a boxplot of this sample.