Exam 3: Numerical Descriptive Measures

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.

SCENARIO 3-2 The data below represent the number 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 Scenario 3-2, is the carbohydrate amount in the cereal leptokurtic or platykurtic?

Which of the following measures is used to determine where the data is clustering?

SCENARIO 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 Scenario 3-3, the range of the number of vitamin supplements sold in this sample is_.

SCENARIO 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 Scenario 3-3, the variance of the number of vitamin supplements sold in this sample is _.

In left-skewed distributions, the distance from the smallest value to Q1 is greater than the distance from Q3 to the largest value.

When extreme values are present in a set of data, which of the following descriptive summary measures are most appropriate:

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

SCENARIO 3-2 The data below represent the number 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 Scenario 3-2, the kurtosis statistic for the carbohydrate amount in the cereal is_.

SCENARIO 3-2 The data below represent the number 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 Scenario 3-2, the coefficient of variation of the carbohydrate amounts ispercent.

3-22 Numerical Descriptive Measures The ordered array below represents the number of cargo manifests approved by customs inspectors of 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 Scenario 3-4, the coefficient of variation of the customs data is percent.

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

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.

SCENARIO 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 Scenario 3-3, the kurtosis statistic of the number of vitamin supplements sold in this sample is _.

According to the empirical rule, if the data form a "bell-shaped" normal distribution, percent of the observations will be contained within 1 standard deviation around the arithmetic mean.

SCENARIO 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 Scenario 3-7, are the data skewed? If so, how?

In right-skewed distributions, the distance from Q3 to the largest value is greater than the distance from the smallest observation to Q1.

SCENARIO 3-11 Given below are the closing prices for the Dow Jones Industrial Average (DJIA) and the Standard & Poor's (S&P) 500 Index over 10-weeks sometime in the past. Dow Jones 10,421 10,110 9,862 10,475 9,920 10,592 11,213 10,933 11,134 10,316 S\&P 500 1,379 1,356 1,343 1,410 1,389 1,463 1,529 1,499 1,516 1,355 -Referring to Scenario 3-11, for the week when the DJIA is high, you will expect the S&P index in that week to

SCENARIO 3-12 Given below are the rating and performance scores of 15 laptop computers. Performance Score 115 191 153 194 236 184 184 216 Overall Rating 74 78 79 80 84 76 77 92 Performance Score 185 183 189 202 192 141 187 Overall Rating 83 78 77 78 78 73 77 -Referring to Scenario 3-12, how will you classify the linear relationship between the performance scores and the rating?

SCENARIO 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 Scenario 3-5, what is the shape of the distribution for the rate of return?