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MODULE
8
Multi-Variable Categorical Data
Study Guide Review
Essential Question: How can you use multi-variable categorical data to solve real-world problems?
ASSESSMENT AND INTERVENTION
KEY EXAMPLE
(Lesson 8.1)
The principal of a high school surveyed 9th and 10th graders as to whether they want to go on a field trip to the museum, zoo, or botanical garden. The results of the survey are in the following table. Complete the table. Preferred Field Trip
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Grade
Museum
Zoo
Botanical Garden
9 th
42
28
31
52
62
80
93
10 th
MODULE PERFORMANCE TASK
Total
70
42 + 28 + 31 = 101 70 - 42 = 28
Mathematical Practices: MP.1, MP.2, MP.3, MP.4, MP.6 S-ID.5
Grade 9 © Houghton Mifflin Harcourt Publishing Company
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142
categorical data (datos categóricos) conditional relative frequency (frecuencia relativa condicional) frequency table (tabla de frecuencia) joint relative frequency (frecuencia relativa conjunta) marginal relative frequency (frecuencia relativa marginal) quantitative data (datos cuantitativos) relative frequency (frecuencia relativa)
Total who prefer the museum - 9th graders who prefer the museum Find the grand total.
Preferred Field Trip
SUPPORTING STUDENT REASONING
r Review methods for drawing circle graphs, histograms, and bar graphs3FNJOETUVEFOUTPG UIFBEWBOUBHFTBOEEJTBEWBOUBHFTPGFBDIUZQFPG EJTQMBZ
Total
Key Vocabulary
8
Find the 9th grade row total.
70 + 80 + 93 = 243 and 101 + 142 = 243
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MODULE
STUDY GUIDE REVIEW
Museum
Zoo
Botanical Garden
Total
th
42
28
31
101
10 th
28
52
62
142
Total
70
80
93
243
KEY EXAMPLE
(Lesson 8.2)
The principal wants to know if the percent of 10th graders who prefer the zoo is greater than the percent of total students who prefer the zoo. Find the conditional relative frequency of 10th graders who prefer the zoo and the marginal relative frequency of students who prefer the zoo. Compare the results. The percent of 10th graders who prefer the zoo is given by the conditional relative frequency: Number of 10 th graders who prefer the zoo _ ____ = 52 ≈ 0.37 142 Total number of 10th graders The percent of total students who prefer the zoo is given by the marginal relative frequency: Number of students who prefer the zoo _ ____ = 80 ≈ 0.33. 243 Total number of students th Since 37% > 33%, the percent of 10 graders who prefer the zoo is greater than the percent of total students who prefer the zoo. Module 8
371
Study Guide Review
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371
Module 8
SCAFFOLDING SUPPORT CONTINUED
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DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-B;CA-B DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-B;CA-B
DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-B;CA-B
EXERCISES 1.
SAMPLE SOLUTION
Complete the two-way frequency table. Interpret the meaning of the number in the starred cell of the table. (Lesson 8.1)
1.
Preferred Mode of Transportation Age
Bike
Car
Bus
Total
Adults
25
3
12
40
Teenagers Total
5
28
12
45
30
*31
24
85
31 is the total number of people surveyed who prefer cars. 2.
A middle school student surveyed middle school and high school teachers on whether they preferred to have their students write in pen. (Lesson 8.2)
Prefer Students Use Pen Grade Level
Yes
No
Total
Middle School
3
18
21
High School
7
12
19
Total
10
30
40
Attend Camp
Visit a National Park
Grades 7–9
0.125
0.2
0.075
Grades 10–12
0.35
0.1
0.15
2.
Students’ Preferences Grade 7-9
80 Number
Are middle school teachers or high school teachers more likely to prefer that their students use pen? Explain. 36.8% is greater than 14.3%, so a greater percent of high school teachers prefer that their students use pen.
Grade 10-12
60 40 20
MODULE PERFORMANCE TASK
Survey Says?
Visit a Foreign Country
Attend Camp
Visit a National Park
Grades 7–9
25
40
15
Grades 10–12
70
20
30
r Make a table showing the relative frequency of each of the six categories in the table compared to the results for the entire table. r Make a circle graph, histogram, or bar graph showing the frequencies or relative frequencies of each of the six categories in the table. r Write and answer at least five questions involving conditional relative probability that can be answered by referring to the table. r Describe any trends you see in the data. Use your own paper to work on the task. Use numbers, words, or algebra to explain how you reached your conclusion.
372
n eig y or ntr F u sit o Vi C
© Houghton Mifflin Harcourt Publishing Company
Students in grades 7–12 were surveyed about which of the following they would most like to do during 2 weeks of a summer vacation: visit a foreign country, attend camp, or visit a national park. The students were divided into two groups, Grades 7–9 and Grades 10–12. Here are the results:
Module 8
Visit a Foreign Country
Study Guide Review
SAMPLE SOLUTION CONTINUED
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4. Attending camp is the most popular activity in Grades 7–9 and the least popular in Grades 10–12. As students grow older they appear to grow more interested in travel, such as by visiting a foreign country or a national park. In both grade categories, students prefer visiting a foreign country to visiting a national park.
DISCUSSION OPPORTUNITIES r "TLTUVEFOUTUPEFTDSJCFBOEKVTUJGZUIFUSFOETJOUIFEBUBUIBUUIFZEFUFDUFE r %JTDVTTXIJDIPGUIFUISFFHJWFONFUIPETJTCFTUGPSEJTQMBZJOHUIFEBUB BOEXIZ
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nd te p At am C
it Vis al n tio ark Na P
3. a. What is the conditional relative probability that a student who chose “Attend Camp” is in 1 Grades 10–12? __ 3 b. What is the conditional relative probability that a student who chose “Visit a National 2 Park” is in Grades 10–12? __ 3 c. What is the probability that a student in Grades 10–12 did NOT choose “Visit a Foreign 5 Country”? ___ 12 d. What is the conditional relative probability that if a student is in Grades 7–9, the student 3 chose “Visit a National Park”? ___ 16 e. What is the conditional relative probability that a student who chose “Visit a National Park” is in Grades 7–12? 1
Assessment Rubric 2 points: Student correctly solves the problem and explains his/her reasoning. 1 point: Student shows good understanding of the problem but does not fully solve or explain his/her reasoning. 0 points: Student does not demonstrate understanding of the problem.
Study Guide Review 372
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MODULE
9
MODULE
STUDY GUIDE REVIEW
One-Variable Data Distributions
Study Guide Review
Essential Question: How can you use one-variable data distributions to solve real-world problems?
ASSESSMENT AND INTERVENTION
KEY EXAMPLE
(Lesson 9.2)
The dot plot given shows the high score of 12 members of a bowling club. A new member joins whose high score is 294. Determine if the new score is an outlier.
x x x x x x x x x x x x
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276
280
284
288
292
Key Vocabulary
9
histogram (histograma) interquartile range IQR (rango entre cuartiles) mean (media) median (mediana) normal curve (curva normal) normal distribution (distribución normal) outlier (valor extremo) range (rango de un conjunto de datos)
296
High Score
The scores are 278, 278, 280, 282, 282, 284, 284, 284, 286, 286, 286, 288, and 294.
MODULE PERFORMANCE TASK
Median = 284
280 + 282 Q 1 = _ = 281 2
286 + 286 Q 3 = _ = 286 2
A data value is an outlier if x < Q 1 - 1.5(IQR) or if x > Q 3 + 1.5(IQR).
IQR = 286 - 281 = 5
Since 294 > 286 + 1.5(5), the new score is an outlier.
Mathematical Practices: MP.1, MP.2, MP.4, MP.5 S-ID.1, S-ID.2, S-ID.3
SUPPORTING STUDENT REASONING
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429
Module 9
KEY EXAMPLE © Houghton Mifflin Harcourt Publishing Company
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(Lesson 9.4)
A machine produces plastic skateboard wheels with diameters that are normally distributed with a mean diameter of 52 mm and a standard deviation of 0.15 mm. 34% 34% Find the percent of wheels made by the machine that 2.35% 0.15% 0.15% 2.35% have a diameter of less than 51.7 mm. 13.5% 13.5% 0.3 _____ =2 52 - 51.7 = 0.3 0.15 x ± 1σ 51.7 is 2 standard deviations below the mean. The percent of data that is 2 standard deviations below the mean is 0.15% + 2.35% = 2.5%. 2.5% of the wheels have a diameter less than 51.7 mm.
Module 9
429
x ± 2σ x ± 3σ
Study Guide Review
SCAFFOLDING SUPPORT
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DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-B;CA-B DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-B;CA-B
DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-B;CA-B
EXERCISES Find the mean, median, range, and interquartile range of each data set. (Lesson 9.1) {12, 12, 13, 14, 16, 20, 32}
total number of runs scored: 10,525 mean: 701.67 median: 712 range: 255
Median: 10
Median: 14
Range: 11
Range: 20
IQR: 5
IQR: 8
Make a box plot to represent the data set {28, 30, 32, 32, 34, 35, 36, 38}. (Lesson 9.3)
26
4.
American League:
Mean: 10.375
Mean: 17
3.
SAMPLE SOLUTION
{4, 8, 9, 9, 11, 12, 15, 15}
2.
28
30
32
34
36
38
National League: total number of runs scored: 9,730 mean: 648.67 median: 640 range: 270
40
The weights of a small box of Healthy Oats are normally distributed with a mean of 8.9 oz and a standard deviation of 0.1 oz. Find the probability that a randomly chosen box of Healthy Oats weighs more than 8.8 oz. Express the probability as a decimal. (Lesson 9.4)
The total number of runs scored by the American League, as well as the mean and median number of runs scored by the 15 teams, exceeded the National League figures by a substantial margin. The ranges of both leagues were similar, suggesting that the difference in run production between the top and bottom teams was about the same in both leagues.
0.84
MODULE PERFORMANCE TASK
Baseball Stats
One possible graphical representation of the data is a histogram for each league.
The table below gives the total number of runs scored by each of the 15 teams in each of baseball’s two major leagues, the American League and the National League, during the 2013 season.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
American
853
796
767
745
745
733
730
712
700
650
648
624
614
610
598
National
783
706
698
688
685
656
649
640
634
629
619
618
610
602
513
In this module you’ve learned many ways to analyze a set of data, both numerically and graphically. Which ways might be useful in helping someone to make sense of the statistics in the runs-scored table? Decide on the ones you’ll use and apply them, either through numerical calculations or pictorial representations or both. You may also explain why you decided not to calculate certain data measures. Use your own paper to work on the task. Use numbers, words, or algebra to explain how you reached your conclusion.
Module 9
430
National League
American League
Frequency
1
© Houghton Mifflin Harcourt Publishing Company
Team League
8
8
7
7
6
6
Frequency
1.
5 4 3
5 4 3
2
2
1
1
9 9 9 9 9 9 9 59 64 69 74 79 84 89 0– 0– 0– 0– 0– 0– 0– 55 60 65 70 75 80 85 Runs Scored
9 9 9 9 9 9 9 54 59 64 69 74 79 84 0– 0– 0– 0– 0– 0– 0– 50 55 60 65 70 75 80 Runs Scored
Study Guide Review
DISCUSSION OPPORTUNITIES
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r "TLTUVEFOUTUPTQFDVMBUFPOUIFSFTVMUTJGUIFZXFSFUPBOBMZ[FUIFDPNCJOFE TUBUJTUJDTGPSUIFUXPMFBHVFT Sample answer: The higher American League numbers would create a combined mean and a combined median greater than those of the National League when measured alone (combined mean: 675.17; combined median: 653). Without graphing, it is unclear whether the data would be roughly symmetric or skewed to the right.
7/25/14 7:56 PM
The American League histogram is not quite symmetric but is not strongly skewed in either direction. The National League histogram shows that the data are skewed to the right.
Assessment Rubric 2 points: Student correctly solves the problem and explains his/her reasoning. 1 point: Student shows good understanding of the problem but does not fully solve or explain his/her reasoning. 0 points: Student does not demonstrate understanding of the problem.
Study Guide Review 430