Exam 3: Numerical Descriptive Measures

According to the empirical rule,if the data form a "bell-shaped" normal distribution,_____________ percent of the observations will be contained within 2 standard deviations around the arithmetic mean.

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 variance of the customs data is _____________ .

If the values are all the same (so that there is no variation in the datA.,the range,interquartile range,variance and standard deviation will all equal zero.

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

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

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 standard deviation of the customs data 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,what type of shape does the distribution of the sample appear to have?

The mode is easier to compute than the geometric mean.

Instruction 3-10 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 1 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 3-10,the five-number summary of the data in this sample consists of _____________ ,_____________ ,_____________ ,_____________ ,_____________ .

In general,which of the following descriptive summary measures cannot be easily approximated from a boxplot?

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

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

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

The larger the Z score,the further is the distance from the observation to the median.

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

If a set of data is perfectly symmetrical,the _________must be identical to the median.

Instruction 3-11B The stem-and-leaf display below represents the number of cargo manifests approved by customs inspectors of the Port of Brisbane in a sample of 35 days. Stem Leaves 1 67889 2L 0011122223333444 2H 5566678899 3L 1122 -Referring to Instruction 3-11B,construct a box-and-whisker plot of this sample.

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

Which measure of central tendency can be used for both numerical and categorical variables?

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