The Pell Grant was created in 1972 to assist low-income college students. This table provides information on percentages of students who were Pell Grant recipients for the academic year 2001-2002 at schools of various types in a certain state.
a. Use a calculator or computer to find the mean and standard deviation of percentages of students with Pell Grants at private schools.
b. Use a calculator or computer to find the mean and standard deviation of percentages of students with Pell Grants at state schools.
c. Use a calculator or computer to find the mean and standard deviation of percentages of students with Pell Grants at state-related schools.
d. The highest mean is for state-related schools. Explain why it might be misleading to report that the percentage of students receiving Pell Grants is highest at state-related schools.
e. For which type of school are the Pell Grants most evenly allocated, in the sense that percentages for all schools of that type are most similar to each other?
f. Explain why side-by-side stemplots may be a better choice of display than side-byside boxplots for this data set.
g. When deciding whether to use side-byside stemplots or boxplots, are we mainly concerned with data production, displaying and summarizing data, probability, or statistical inference?