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The following table shows the distribution of scores on the SAT Mathematics test for 2011 college-bound seniors. Score 700-800 600-690 500-590 400-490 Number of Students 111,893 304,037 481,170 498,944 Proportion of Students 0.0679 0.1846 0.2921 0.3029

The following table shows the distribution of scores on the SAT Mathematics test for 2011 college-bound seniors. Score 700-800 600-690 500-590 400-490 Number of Students 111,893 304,037 481,170 498,944 Proportion of Students 0.0679 0.1846 0.2921 0.3029

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The table displays the distribution of scores on the SAT Mathematics test for 2011 college-bound seniors. The data is organized as follows: | Score | Number of Students | Proportion of Students | |---------|--------------------|-----------------------| | 700–800 | 111,893 | 0.0679 | | 600–690 | 304,037 | 0.1846 | | 500–590 | 481,170 | 0.2921 | | 400–490 | 498,944 | 0.3029 | | 300–390 | 210,645 | | | 200–290 | 40,434 | | | **Total** | **1,647,123** | **1.0000** | **Source:** 2011 College-Bound Seniors Total Group Report, College Board. This data can be used to analyze the mathematical proficiency of students in the 2011 cohort. Below the table, there are some exercises: a. **Exercise:** Identify the two missing numbers in the third column (proportion of students). b. **Exercise:** From a random sample of 1,000 scores, calculate the expected number of students scoring in the category 700–800 and in the category 400–490. c. **Exercise:** Create a stacked bar graph to compare this distribution with that of SAT Critical Reading scores. d. **Exercise:** Discuss whether the two populations are homogeneous, providing reasoning for your answer.
Transcribed Image Text:The table displays the distribution of scores on the SAT Mathematics test for 2011 college-bound seniors. The data is organized as follows: | Score | Number of Students | Proportion of Students | |---------|--------------------|-----------------------| | 700–800 | 111,893 | 0.0679 | | 600–690 | 304,037 | 0.1846 | | 500–590 | 481,170 | 0.2921 | | 400–490 | 498,944 | 0.3029 | | 300–390 | 210,645 | | | 200–290 | 40,434 | | | **Total** | **1,647,123** | **1.0000** | **Source:** 2011 College-Bound Seniors Total Group Report, College Board. This data can be used to analyze the mathematical proficiency of students in the 2011 cohort. Below the table, there are some exercises: a. **Exercise:** Identify the two missing numbers in the third column (proportion of students). b. **Exercise:** From a random sample of 1,000 scores, calculate the expected number of students scoring in the category 700–800 and in the category 400–490. c. **Exercise:** Create a stacked bar graph to compare this distribution with that of SAT Critical Reading scores. d. **Exercise:** Discuss whether the two populations are homogeneous, providing reasoning for your answer.
**Table Analysis:** The table presents the distribution of ages among male and female actors who secured regular roles in pilot episodes for new television series. This data includes the number of actors whose ages could be determined, except for a few (8 males and 5 females). | Age | Number of Males | Number of Females | |----------|-----------------|-------------------| | 0–9 | 13 | 7 | | 10–19 | 31 | 29 | | 20–29 | 73 | 95 | | 30–39 | 116 | 88 | | 40–49 | 52 | 21 | | 50–59 | 33 | 19 | | 60 and over | 13 | 10 | | **Total** | **331** | **269** | *Source: James J. Jones, The 2011 Pilot Report, Premier Talent Group.* **Bar Graph Analysis:** The first bar graph illustrates the total number of actors (both male and female) across different age groups: - It shows that males generally have higher numbers across most age categories, particularly in the 30–39 and 40–49 age brackets. - Females have higher numbers only in the 20–29 age group. The second bar graph displays the percentage distribution of actors within each gender: - While the percentage distribution is similar across age groups, the differences in total numbers are apparent. - For males, the 30–39 age group constitutes the largest percentage. - For females, the 20–29 age group is the most significant. **Questions:** a. Observe how the two graphs highlight different facets of the data. The first graph shows absolute numbers, while the second offers a percentage view within each gender. b. The groups are not homogeneous. Males are more prevalent in most age brackets except for 20–29, where females are more represented. This difference in distribution highlights the disparity in age representation between genders in pilot roles.
Transcribed Image Text:**Table Analysis:** The table presents the distribution of ages among male and female actors who secured regular roles in pilot episodes for new television series. This data includes the number of actors whose ages could be determined, except for a few (8 males and 5 females). | Age | Number of Males | Number of Females | |----------|-----------------|-------------------| | 0–9 | 13 | 7 | | 10–19 | 31 | 29 | | 20–29 | 73 | 95 | | 30–39 | 116 | 88 | | 40–49 | 52 | 21 | | 50–59 | 33 | 19 | | 60 and over | 13 | 10 | | **Total** | **331** | **269** | *Source: James J. Jones, The 2011 Pilot Report, Premier Talent Group.* **Bar Graph Analysis:** The first bar graph illustrates the total number of actors (both male and female) across different age groups: - It shows that males generally have higher numbers across most age categories, particularly in the 30–39 and 40–49 age brackets. - Females have higher numbers only in the 20–29 age group. The second bar graph displays the percentage distribution of actors within each gender: - While the percentage distribution is similar across age groups, the differences in total numbers are apparent. - For males, the 30–39 age group constitutes the largest percentage. - For females, the 20–29 age group is the most significant. **Questions:** a. Observe how the two graphs highlight different facets of the data. The first graph shows absolute numbers, while the second offers a percentage view within each gender. b. The groups are not homogeneous. Males are more prevalent in most age brackets except for 20–29, where females are more represented. This difference in distribution highlights the disparity in age representation between genders in pilot roles.
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The distribution of scores for the SAT mathematics test is as follows:

Score Number of students Proportion of students
700-800 111893 0.0679
600-690 304037 0.1846
500-590 481170 0.2921
400-490 498944 0.3029
300-390 210645  
200-290 40434  
Total 1647123 1.0000
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