Percentages of economically disadvantaged students are listed for 17 middle schools and 12 high schools in a certain school district around the year 2000.
a. Are the data values formatted with a column for values of quantitative responses and a column for values of a categorical explanatory variable, or are they formatted with two columns of quantitative responses (one for each of two categorical groups)?
b. Find the five-number summary values for middle schools.
c. Find the five-number summary values for high schools.
d. Neither type of school has outlier values. Construct a side-by-side boxplot to display percentages of disadvantaged students in the two types of schools.
e. Are the centers comparable? If not, which type of school tends to have higher percentages of economically disadvantaged students?
f. Suppose students are classified as being economically disadvantaged based on a form that must be completed by parents regarding household income, and sent in to make students eligible for free or reduced school lunches. Explain how this could bring about a difference in reported percentages for the two types of schools.
g. Disadvantaged students might tend to drop out before they have completed high school. Explain how this could bring about a difference in reported percentages for the two types of schools.
h. Are the spreads comparable? If not, which type of school tends to have more variable percentages of economically disadvantaged students?
i. The shapes of the two distributions are similar: Are they markedly leftskewed, fairly symmetric, or markedly right-skewed?
j. Considering the shapes of the distributions, do mean and standard deviation do a good job of summarizing centers and spreads?