10TH GRADE
DATA ANALYSIS, STATISTICS AND PROBABILITY ANSWERS
1
Question 17
Casey placed six identical cards in a box. Each card was marked with one integer using
each of the integers 0, 1, 2, 3, 4, and 5 once. Casey drew two cards at random, one at a
time, without replacing the first card.
a. Make a list, chart, or diagram of the possible outcomes when choosing two cards
in this manner.
b. What is the probability that the sum of the integers on the two cards is greater
than 9?
c. Based on your response to part a., what is the most frequently occurring sum of
the integers? What is the probability that this sum will occur?
Scoring Guide
Score
Description
2
4
The student response demonstrates an exemplary understanding of the Data
Analysis and Probability concepts underlying the task.
3
The student response demonstrates good understanding of the Data Analysis and
Probability concepts underlying the task.
2
The student response contains fair evidence of understanding some aspect of the
Data Analysis and Probability concepts underlying the task. While some aspects
of the task are completed correctly, others are not. The mixed evidence provided
by the student merits no more than 2 points.
1
The student response contains only minimal evidence of understanding the Data
Analysis and Probability concepts underlying the task.
0
The student response contains insufficient evidence of understanding the Data
Analysis and Probability concepts underlying the task to merit any points.
Blank No Response.
2002 MCAS
Grade 10 Mathematics
Question # 17 - Score Point 4
3
4
5
6
7
8
9
Open Response Question 40
A class of 25 students is asked to determine approximately how much time the average
student spends on homework during a one-week period. Each student is to ask one of
his/her friends for the information, making sure that no one student is asked more than
once. The numbers of hours spent on homework per week are as follows:
8, 0, 25, 9, 4, 19, 25, 9, 9, 8, 0, 8, 25, 9, 8, 7, 8, 3, 7, 8, 5, 3, 25, 8, 10
a. Find the mean, median, and mode for these data. Explain or show how you found
each answer.
b. Based on this sample, which measure (or measures) that you found in part a best
describes the typical student? Explain your reasoning.
c. Describe a sampling procedure that would have led to more representative data.
Scoring Guide
Score
Description
4
The response demonstrates comprehensive understanding of mean, median,
mode, and effectively communicates information about the data and sampling
procedure.
3
The response demonstrates general understanding of mean, median, mode, and
communicates information about the data and sampling procedure.
2
The response demonstrates basic understanding of mean, median, mode, and/or
communicates information about the data and sampling procedure.
1
The response demonstrates minimal understanding of mean, median, mode,
and/or communicates information about the data and sampling procedure.
0
The response is incorrect or contains some correct work that is irrelevant to the
10
skill or concept being measured.
Blank No response.
Answer: (1)
11
Answer: (3)
Answer: (4)
Answer: 3
12
Answer:
Answer:
13
Answer:
14
Answer:
15
Answer:
16
Answer:
4pts-
3pts2pts1pt0pts-
17
ANSWER: D
ANSWER: D
18
ANSWER: C
ANSWER: C
19
ANSWER: C
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