In this problem, you will use data from the 2018 Grade 10 Mathematics MCAS to investigate evidence of achievement gaps in standardized test score at the school level. The mcas data contains information on 355 schools in Massachusetts. Scores on the MCAS are classified into levels: warning/failing, needs improvement, proficient, and advanced. Students who score in the "proficient" category are said to "demonstrate a solid understanding of challenging subject matter", while those in the "advanced" category are said to "demonstrate a comprehensive and in-depth understanding of rigorous subject matter"; the variable PA_perc represents the percentage of students at a school who score at the proficient or advanced level.

The descriptions of the variables are as follows.

Variable Description

PA_perc percentage of students scoring proficient or advanced

class_size average class size

math_class_size average math class size

student_teacher_ratio student to teacher ratio

attendance_rate average percentage of days attended across students

number_of_students total number of students who took the exam

largest_minority largest minority group among the student body

white_less50 coded TRUE if less than 50% of students are white

exp_per_pupil average expenditures per pupil in USD

econ_dis percentage of economically disadvantaged students

Some additional background on certain variables:

- Whether a student is economically disadvantaged is a proxy measure for student family income; a student is considered economically disadvantaged if they are participating in one or more of the following programs: the Supplemental Nutrition Assistance Program (SNAP),

the Transitional Assistance for Families with Dependent Children (TAFDC), the Department

of Children and Families' (DCF) foster care program, MassHealth (Medicaid).

- Expenditures per pupil is a proxy measure for the amount of funding available to a school

district. This variable is measured by district (i.e., constant for schools in the same district).

Briefly summarize features of the sampled schools, focusing on the percentage of students

scoring at the proficient/advanced levels, the average expenditures per student,

and the percentage of economically disadvantaged students. Reference appropriate

numerical and graphical summaries as needed.