Question

section i: multiple - choice. circle the letter corresponding to the best answer choice.

1. at the beginning of the school year, a high - school teacher asks every student in her classes to fill out a survey that asks for their age, gender, the number of years they have lived at their current address, their favorite school subject, and whether they plan to go to college after high school. which of the following best describes the types of variables that are being measured?

(a) five quantitative variables.
(b) two categorical variables and two quantitative variables.
(c) two categorical variables and three quantitative variables.
(d) three categorical variables and two quantitative variables.
the next three questions concern the following scenario: to the right is a dotplot of the adult literacy rates in 177 countries in 2008, according to the united nations. for example, the lowest literacy rate was 23.6%, in the african country of burkina faso.

1. the overall shape of this distribution is

(a) skewed to the right.
(b) skewed to the left.
(c) roughly symmetric.
(d) uniform.

1. the mean of this distribution (don’t try to find it) is

(a) very close to the median.
(b) clearly less than the median.
(c) clearly greater than the median.
(d) you can’t say because the mean is random.

1. based on the shape of this distribution, what numerical measures would best describe it?

(a) the median and the iqr.
(b) the mean and standard deviation.
(c) the mean and the quartiles.
(d) the median and the standard deviation.

Explanation:

Step1: Analyze question 1

Categorical variables: gender, whether they plan to go to college (binary - categorical). Quantitative variables: age, number of years lived at address, favorite school subject (age and number of years are numerical, favorite school subject - if we assume it's rated on a scale or something numerical). Wait no - age (quantitative), gender (categorical), number of years (quantitative), current address (categorical - but if we assume it's not used in a numerical way, wait the question says "types of variables". Wait age (quant), gender (cat), number of years (quant), favorite school subject (if it's like a ranking - quant, but usually in surveys, if it's just the name - but maybe the teacher is using a numerical scale. Wait no - actually, age (quant), gender (cat), number of years (quant), "whether they plan to go to college" (cat - binary: yes/no), current address (if it's just text - cat, but maybe not measured. Wait the variables measured: age (quant), gender (cat), number of years (quant), "whether they plan to go to college" (cat). So two categorical (gender, plan to college) and two quantitative (age, number of years). But wait the options: (B) two categorical and two quantitative. But wait the problem says "the types of variables that are being measured". Wait maybe the teacher is considering favorite school subject. If favorite school subject is like 1 = math, 2 = science etc. (quantitative as an ordinal variable). But usually, in basic stats, gender (cat), age (quant), number of years (quant), plan to college (cat). So two cat, two quant. But option (B) is two categorical and two quantitative. But wait the options: (C) two categorical and three quantitative. Wait no - age (quant), gender (cat), number of years (quant), plan to college (cat). So two cat, two quant. But option (B) is two categorical and two quantitative. But wait the first question's options: (B) two categorical and two quantitative. But wait maybe the teacher counts "favorite school subject" as quantitative (if it's ranked). But if it's just the name (like "math"), it's categorical. But the problem is from a stats context. In basic stats, age (quant), gender (cat), number of years (quant), plan to college (cat). So two cat (gender, plan), two quant (age, years). But option (B) is two categorical and two quantitative. But wait the options: (C) two categorical and three quantitative. No - unless favorite school subject is quantitative. If the survey has favorite school subject as a numerical rating (e.g., 1 - 10), then it's quantitative. But the problem says "asks for their age, gender, the number of years...". So age (quant), gender (cat), number of years (quant), "whether they plan..." (cat). So two cat, two quant. But option (B) is two categorical and two quantitative. But wait the first question's options: (B) two categorical and two quantitative. But wait maybe the teacher made a mistake. Wait no - another approach: Categorical variables: gender (male/female - cat), whether plan to college (yes/no - cat). Quantitative: age (number), number of years (number). So two cat, two quant. So question 1: (B) is wrong. Wait no - wait the options: (C) two categorical and three quantitative. No - unless favorite school subject. Wait the problem says "asks for their age, gender, the number of years they have lived at their current address, their favorite school subject, and whether they plan to go to college". So variables: age (quant), gender (cat), number of years (quant), favorite school subject (if it's a category - cat, if it's a rating - quant), whether plan (cat). If favorite school subject is a category (like "math", "history" - cat), then categorical variables: gender, favorite school subject, whether plan (three cat). Quantitative: age, number of years (two quant). But no option. Wait no - maybe the problem has a typo. Wait in standard textbook problems: age (quant), gender (cat), "number of years" (quant), "whether plan" (cat). So two cat (gender, plan), two quant (age, years). But option (B) is two categorical and two quantitative. But wait the options: (C) two categorical and three quantitative. No. Wait maybe the teacher considered "current address" as a variable. But the problem says "the types of variables that are being measured". If current address is just text - not measured (like not used in a numerical way). So back to: age (quant), gender (cat), number of years (quant), whether plan (cat). Two cat, two quant. But option (B) is two categorical and two quantitative. But wait the first question's options: (B) two categorical and two quantitative. But another approach: in statistics, variables: Categorical (nominal or ordinal - but if no order, nominal). Gender (nominal - cat), whether plan (nominal - cat). Quantitative (age - ratio, number of years - ratio). So two cat, two quant. So question 1: (B) is wrong. Wait no - wait the options: (C) two categorical and three quantitative. No. Wait maybe the problem counts "favorite school subject" as quantitative. If favorite school subject is on a scale (e.g., 1 - 5), then quantitative. So age (quant), gender (cat), number of years (quant), favorite school subject (quant), whether plan (cat). Then two cat (gender, plan), three quant (age, years, favorite). But option (C) is two categorical and three quantitative. But the problem says "the types of variables that are being measured". If the teacher is using favorite school subject as a numerical scale (quant), then yes. So question 1: (C). But this is a bit ambiguous. But in standard multiple - choice, if we assume favorite school subject is quantitative (e.g., 1 = least favorite, 5 = most favorite). Then two categorical (gender, plan) and three quantitative (age, years, favorite). So (C).

Step2: Analyze question 2

Looking at the dot - plot: the tail is on the left (lower literacy rates). A distribution is skewed to the left if the tail is on the left. So the overall shape is skewed to the left.

Step3: Analyze question 3

For a left - skewed distribution, the mean is less than the median. Because the mean is pulled by the lower values (in the left tail).

Step4: Analyze question 4

For a skewed distribution (left - skewed in this case), the median and IQR are the best measures. The mean is affected by skewness, while the median is more robust.

Answer:

1. C. two categorical variables and three quantitative variables.
2. B. skewed to the left.
3. B. clearly less than the median.
4. A. The median and the IQR.