Select Program Area --Select Program Area-- ESE HOME Accountability, Partnership, & Assistance Adult & Community Learning Amazing Educators BOE Advisory Councils Board of Elementary & Secondary Education Career/Vocational Technical Education Charter Schools College and Career Readiness Compliance/Monitoring (PQA) Conferences, Workshops and Trainings Curriculum & Instruction Digital Learning District & School Assistance Centers (DSACs) District & School Turnaround District Review, Analysis, & Assistance Tools Educator Evaluation Educator Licensure Tests (MTEL) Educator Licensure Educational Proficiency Plan (EPP) Edwin ELAR Log In Employment Opportunities: ESE English Language Learners Every Student Succeeds Act (ESSA) Family Literacy High School Equivalency (HSE) Testing Program Grants/Funding Opportunities Information Services Laws & Regulations Literacy LEAP Project MCAS MCAS Appeals METCO Office for Food and Nutrition Programs Performance Assessment for Leaders (PAL) Planning and Research Professional Development Race to the Top (RTTT) RETELL Safe and Supportive Schools School and District Profiles/Directory School Finance School Redesign Science, Technology Engineering, and Mathematics (STEM) Security Portal | MassEdu Gateway Special Education Special Education Appeals Special Education in Institutional Settings Student and Family Support Title I/Federal Support Programs Systems for Student Success (SfSS)
 Students & Families Educators & Administrators Teaching, Learning & Testing Data & Accountability Finance & Funding About the Department Education Board

# Massachusetts Comprehensive Assessment System

Question 10: Open-Response
A snow day occurs when school is canceled for the day because of bad winter weather. The box below shows the number of snow days at Andrew's school during each of the past six winters.
 2,  5,  5,  3,  4,  5
1. For the past six winters, what was the median number of snow days per winter at Andrew's school? Show or explain how you got your answer.
2. For the past six winters, what was the mean number of snow days per winter at Andrew's school? Show or explain how you got your answer.
3. For the past six winters, what was the mean absolute deviation of the number of snow days per winter at Andrew's school? Show or explain how you got your answer.
Maria lives in another state. The box below shows the number of snow days at Maria's school during each of the past six winters.
 0,  2,  9,  3,  1,  3
1. At which school, Andrew's or Maria's, is the number of snow days per winter more predictable? Explain your reasoning. Use specific data from both schools in your explanation.

### Scoring Guide and Sample Student WorkSelect a score point in the table below to view the sample student response.

ScoreDescription
4 The student response demonstrates an exemplary understanding of the Statistics and Probability concepts involved in using measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. The student finds the median, mean, and mean absolute deviation of two sets of data and then compares them.
4
3 The student response demonstrates a good understanding of the Statistics and Probability concepts involved in using measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. Although there is significant evidence that the student was able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result, the response merits 3 points.
2 The student response demonstrates a fair understanding of the Statistics and Probability concepts involved in using measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points.
1 The student response demonstrates a minimal understanding of the Statistics and Probability concepts involved in using measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
0 The student response contains insufficient evidence of the Statistics and Probability concepts involved in using measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations to merit any points.

Note: There are 2 sample student responses for Score Point 4.