Massachusetts Comprehensive Assessment System

2018, Grade 10 Mathematics

Question 41: Open-Response

Reporting Category: Statistics and Probability
Standard: 10.D.1 - Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data.
Standard: CCSS.Math.Content.HSS-ID.A.2 - Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.*

The histogram below shows the heights, in inches, of the students in Landon's class.

How many of the students in Landon's class are at least 65 inches tall? Show or explain how you got your answer.
What fraction of the students in Landon's class are between 65 and 68 inches tall? Show or explain how you got your answer.
What could be the median height of the students in Landon's class? Show or explain how you got your answer.

Landon's teacher will add her height to the data. She is 65 inches tall.

Will the new median height be less than, equal to, or greater than the median height you found in part (c)? Explain your reasoning.

Scoring Guide and Sample Student Work

Select a score point in the table below to view the sample student response.

Score	Description
4	The student response demonstrates an exemplary understanding of the Statistics and Probability concepts involved in using statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets. The student interprets a histogram and considers how the median might change when new data is added.
4
3	The student response demonstrates a good understanding of the Statistics and Probability concepts involved in using statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets. 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 statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets. 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 statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets.
0	The student response contains insufficient evidence of an understanding of the Statistics and Probability concepts involved in using statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets to merit any points.

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

Grade 10 Mathematics

Question 17: Number and Quantity

Question 20: Algebra and Functions

Question 21: Algebra and Functions

Question 36: Geometry

Question 41: Statistics and Probability

Question 42: Geometry

Return to the MCAS 2018 Student Work Directory

Last Updated: December 6, 2022