Exam 3: Numerical Descriptive Measures

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

In a set of numerical data, the value for Q2 is always halfway between Q1 and Q3.

TABLE 3-9 In the 2002- 2003 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 2001- 2002 academic year for a sample of 10 public universities were as follows: $1589, $593, $1223, $869, $423, $1720, $708, $1425, $922 and $308. -Referring to Table 3-9, what is the coefficient of variation of the change in cost?

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 and 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 Table 3-1, calculate the standard deviation of the ages of the uninsured senior citizens correct to the nearest hundredth of a year.

In a right-skewed distribution

A boxplot is a graphical representation of a 5-number summary.

TABLE 3-8 Given below is the frequency distribution of the number of defective tomatoes in 50 different shipments. Def ective 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 Table 3-8, what is the approximate standard deviation?

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 range of the rate of return?

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

$\text { TABLE 3-3 }$ 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 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 Table 3-3, the median number of vitamin supplements sold in this sample is___

The 5-number summary consists of the smallest observation, the first quartile, the median, the third quartile, and the largest observation.

$\text { TABLE 3-7 }$ Given below is the frequency distribution of the 12-month rate of return achieved by 30 stocks. 12- month Rate of Return Number of Funds -0.10 but less than 0.0 3 0.0 but less than 0.1 5 01 but less than 0.2 6 0.2 but less than 0.3 10 0.3 but less than 0.4 6 -Referring to Table 3-7, what is the approximate variance?

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

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

The line drawn within the box of the boxplot always represents the median.

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.

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

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

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. $11\quad15\quad23\quad29\quad19\quad22\quad21\quad20\quad15\quad25\quad17$ -Referring to Table 3-2, the first quartile of the carbohydrate amounts is ____grams.

According to the empirical rule, if the data form a "bell-shaped" normal distribution, percent of the observations will be contained within 3 standard deviations around the arithmetic mean.