Exam 3: Numerical Descriptive Measures

Which descriptive summary measures are resistant statistics?

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, what is the skewness statistic of the change in the cost?

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 coefficient of variation of the number of vitamin supplements sold in this sample is percent.

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 first quartile of the number of vitamin supplements sold in this sample is _.

In a right skewed distribution, the distance from X smallest to Q1 isfrom Q3 to X largest.

SCENARIO 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: 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 Scenario 3-1, calculate the variance of the ages of the senior citizens correct to the nearest hundredth of a year squared.

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.

In a set of numerical data, the value for Q3 can never be smaller than the value forQ1.

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, is the change in the cost right- or left-skewed?

If a set of data is perfectly symmetrical, the arithmetic mean must be identical to the median.

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

A manufacturer of flashlight batteries took a sample of 130 batteries from a day's production and used them continuously until they were drained.The number of hours until failure is recorded.Given below is the boxplot of the number of hours it took to drain each of the 130 batteries.The distribution of the number of hours is

SCENARIO 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 Scenario 3-6, what is the shape of the distribution for the rate of return?

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 interquartile range of the number of vitamin supplements sold in this sample 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. $1115232919222120152517$ -Referring to Scenario 3-2, the range in the carbohydrate amounts is grams.

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

SCENARIO 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: 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 Scenario 3-1, determine the median age of the senior citizens.

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 3-8 The following table represents the assets in billions of dollars of the five largest bond funds sometime in the past. $\begin{array} { | l | c | } \hline \text { Bond Fund } & \text { Assets (Billions \$) } \\\hline \text { PIMCO Total Return Fund } & 246 \\\hline \text { Vanguard Total Bond Market Index Fund } & 110 \\\hline \text { Templeton Global Bond Fund } & 57 \\\hline \text { Vanguard Total Bond Market Index Fund II } & 56 \\\hline \text { Vanguard Inflation-Protected Securities } & 43 \\\hline\end{array}$ -Referring to Scenario 3-8, what are the variance and standard deviation for this population?

SCENARIO 3-10 The population of eight analysts at a software firm were asked to estimate the reuse rate when developing a new software system.The following data are given as a percentage of the total code written for a software system that is part of the reuse database. $50,62.5,37.5,75.0,45.0,47.5,15.0,25.0$ -Referring to Scenario 3-10, what are the variance and standard deviation of the total code that is part of the reuse database?