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Algebra 1 Interactive Chalkboard
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2. Splash Screen

3. Lesson 13-1 Sampling and Bias Lesson 13-2 Introduction to Matrices
Lesson 13-3 Histograms
Lesson 13-4 Measures of Variation
Lesson 13-5 Box-and-Whisker Plots
Contents

4. Example 1 Classify a Random Sample
Example 2 Identify Sample as Biased or Unbiased
Example 3 Identify and Classify a Biased Sample
Example 4 Identify the Sample
Lesson 1 Contents

5. Retail Each day, a department store chain selects one male and one female shopper randomly from each of their 57 stores, and asks them survey questions about their shopping habits.
Identify the sample and suggest a population from which it was selected.
Answer: The sample is 57 male and 57 female shoppers each day. The population is shoppers in the chain’s stores.
Example 1-1a

6. Classify the sample as simple, stratified, or systematic.
Retail Each day, a department store chain selects one male and one female shopper randomly from each of their 57 stores, and asks them survey questions about their shopping habits.
Classify the sample as simple, stratified, or systematic.
The population is divided into similar, nonoverlapping groups.
Answer: This is a stratified random sample.
Example 1-1b

7. b. Classify the sample as simple, stratified, or systematic.
At an automobile factory, every tenth item is checked for quality controls.
a. Identify the sample and suggest a population from which it was selected.
b. Classify the sample as simple, stratified, or systematic.
Answer: The sample is every tenth item. The population is all of the products that are manufactured in the factory.
Answer: This is a systematic random sample.
Example 1-1c

8. Identify the sample as biased or unbiased. Explain your reasoning.
Student Council The student council surveys the students in one classroom to decide the theme for the spring dance.
Identify the sample as biased or unbiased. Explain your reasoning.
The sample includes only students in one classroom.
Answer: The sample is biased.
Example 1-2a

9. Identify the sample as biased or unbiased. Explain your reasoning.
School The Parent Association surveys the parents of every fifth student on the school roster to decide whether to hold a fundraiser.
Identify the sample as biased or unbiased. Explain your reasoning.
The parents are picked using a systematic method.
Answer: The sample is unbiased.
Example 1-2b

10. Identify each sample as biased or unbiased. Explain your reasoning.
a. A local news station interviews one person on every street in Los Angeles to give their opinion on their mayor. 
b. A statistics company calls every twentieth person in Cleveland’s telephone directory to find out his or her favorite sports team in Ohio  
Answer: The sample is unbiased because the sample is picked using a stratified method.
Answer: The sample is biased because it will not be representative of the entire state.
Example 1-2c

11. Community The maintenance chairperson of a neighborhood association has been asked by the association to survey the residents of the neighborhood to find out when to hold a neighborhood clean up day. The chairperson decides to ask her immediate neighbors, and the neighbors in the houses directly across the street from her house.
Identify the sample, and suggest a population from which it was selected.
Answer: The sample is the chairperson’s immediate neighbors and the neighbors across the street. The population is the residents of the neighborhood.
Example 1-3a

12. Community The maintenance chairperson of a neighborhood association has been asked by the association to survey the residents of the neighborhood to find out when to hold a neighborhood clean up day. The chairperson decides to ask her immediate neighbors, and the neighbors in the houses directly across the street from her house.
Classify the sample as a convenience sample, or a voluntary response sample.
Answer: This is a convenience sample because the chairperson asked only her closest neighbors.
Example 1-3b

13. Mark, a college journalist, wanted to find out what the average student in the United States does on the weekend. He decides to interview people in his dorm.
a. Identify the sample, and suggest a population from which it was selected.  
b. Classify the sample as a convenience sample, or a voluntary response sample. 
Answer: The sample is college students in his dorm. The population is all college students.
Answer: This is a convenience sample because Mark asked students who lived in the same building as him.
Example 1-3c

14. Answer: The sample is a group of parents of the graduating seniors.
School The high school Parent Association sent a letter to the parents of all graduating seniors asking them to return the enclosed ballot if they had a preference on where the graduation party was to be held.
Identify the sample.
Answer: The sample is a group of parents of the graduating seniors.
Example 1-4a

15. Suggest a population from which the sample was selected.
School The high school Parent Association sent a letter to the parents of all graduating seniors asking them to return the enclosed ballot if they had a preference on where the graduation party was to be held.
Suggest a population from which the sample was selected.
Answer: The population is all of the parents of the graduating seniors.
Example 1-4b

16. Answer: The sample is biased. It is a voluntary response sample.
School The high school Parent Association sent a letter to the parents of all graduating seniors asking them to return the enclosed ballot if they had a preference on where the graduation party was to be held.
State whether the sample is unbiased (random) or biased. If unbiased, classify it as simple, stratified, or systematic. If biased, classify it as convenience or voluntary response.
The sample includes only the parents of the graduating seniors who return the ballot. Therefore, the reported preference is not likely to be representative of all of the parents.
Answer: The sample is biased. It is a voluntary response sample.
Example 1-4c

17. b. Suggest a population from which the sample was selected.
A large company wants to make sure that all of their employees are working their scheduled hours. The accountant states that the first 50 people to voluntarily submit their time cards will be reviewed for accuracy.
a. Identify the sample.   
b. Suggest a population from which the sample was selected.  
Answer: The sample is 50 of the workers.
Answer: The population is all of the workers.
Example 1-4c

18. Answer: The sample is biased. It is a voluntary response.
A large company wants to make sure that all of their employees are working their scheduled hours. The accountant states that the first 50 people to voluntarily submit their time cards will be reviewed for accuracy.
c. State whether the sample is unbiased (random) or biased. If unbiased, classify it as simple, stratified, or systematic. If biased, classify it as convenience or voluntary response.   
Answer: The sample is biased. It is a voluntary response.
Example 1-4c

19. End of Lesson 1

20. Example 1 Name Dimensions of Matrices Example 2 Add Matrices
Example 3 Subtract Matrices
Example 4 Perform Scalar Multiplication
Lesson 2 Contents

21. This matrix has 3 rows and 1 column.
State the dimensions of the matrix. Then identify the position of the circled element in the matrix.
This matrix has 3 rows and 1 column.
Answer: It is a 3-by-1 matrix. The circled element is the second row and the first column.
Example 2-1a

22. This matrix has 3 rows and 4 columns.
State the dimensions of the matrix. Then identify the position of the circled element in the matrix.
This matrix has 3 rows and 4 columns.
Answer: It is a 3-by-4 matrix. The circled element is the first row and the fourth column.
Example 2-1b

23. Answer: 1 by 2; first row, first column
State the dimensions of each matrix. Then identify the position of the circled element in the matrix. a. b.
Answer: 1 by 2; first row, first column
Answer: 2 by 4; second row, third column
Example 2-1c

24. = Find the sum. If the sum does not exist, write impossible.
Definition of matrix addition =
Example 2-2a

25. Answer: = Simplify.
Example 2-2a

26. Find the sum. If the sum does not exist, write impossible.
Since the first matrix is a 2 by 2 matrix and the second matrix is a 3 by 3 matrix, the matrices do not have the same dimensions.
Answer: It is impossible to add these matrices.
Example 2-2b

27. Find the sum. If the sum does not exist, write impossible.a. b.
Answer: impossible
Answer:
Example 2-2c

28. College Football The Division 1-A current football coaches with the five best overall records as of 2000 are listed below.
Overall Record
Bowl Record
Coach
Won
Lost
Tied
Joe Paterno
322 90 3 20 9 1
Bobby Bowden
315 87 4 17 6
Lou Holtz
224
110 7 11 8 2
Jackie Sherrill
172 93
Ken Hatfield
147
104
Example 2-3a

29. Use subtraction of matrices to determine the regular season records of these coaches.
Example 2-3a

30. Answer: Regular Season Record Coach Won Lost Tied Joe Paterno 302 81 2
Bobby Bowden
298 3
Lou Holtz
213
102 5
Jackie Sherrill
164 87 4
Ken Hatfield
143 98
Example 2-3a

31. Four performing theaters have seating capacities listed below.
Overall Seating Capacity
Number of Seats in the Balcony
Theater
Left Section
Middle Section
Right Section
King Theater
1065
640
385
180
Falcon Theater
840
620
210
190
Emerald Theater
615
550
175
140
Daisy Theater
530
410
160
120
Example 2-3b

32. Number of Seats on the Main Floor
Use subtraction of matrices to find the seating capacities on the main floors of the theaters.
Answer:
Number of Seats on the Main Floor
Theater
Left Section
Middle Section
Right Section
King Theater
680
460
Falcon Theater
630
430
Emerald Theater
440
410
Daisy Theater
370
290
Example 2-3b

33. Definition of scalar multiplication
Substitution
Definition of scalar multiplication
Simplify.
Answer:
Example 2-4a

34. Answer:
Example 2-4b

35. End of Lesson 2

36. Example 1 Determine Information from a Histogram
Example 2 Compare Data in Histograms
Example 3 Create a Histogram
Lesson 3 Contents

37. Student Population In what measurement class does the median occur
Student Population In what measurement class does the median occur? Use the histogram below to determine your answer.
First, add up the frequencies to determine the number of students in homeroom classes at Central High School.
Example 3-1a

38. Answer: The median occurs in the 20-25 measurement class.
There are 24 homeroom classes, so the middle data value is between the 12th and 13th data values. Both the 12th and 13th data values are located in the measurement class.
Answer: The median occurs in the measurement class.
Example 3-1a

39. Answer: Only two homeroom classes have fewer than 10 students.
Student Population Describe the distribution of the data in the histogram shown below.
Answer: Only two homeroom classes have fewer than 10 students.
There is a gap in the 5-10 measurement class.
Most of the homeroom classes have at least 15 students.
The distribution is skewed to the right.
Example 3-1b

40. Answer each question about the histogram shown below.
a. In what measurement class does the median occur?
b. Describe the distribution of the data.
Answer: $10-$20 measurement class
Answer: Only seven items cost more than $30. Most equipment costs less than $30. The distribution is skewed to the left.
Example 3-1c

41. A Class A B The medians are about the same.
Multiple-Choice Test Item Use the data in the histograms to determine which class has a greater median test score.
A Class A B The medians are about the same.
C Class B D Cannot be determined
Example 3-2a

42. Read the Test Item
You have two histograms depicting the test scores of two classes. You are asked to determine which class has a greater median test score.
Solve the Test Item
Study the histograms carefully. The measurement classes and the frequency scales are the same for each histogram. The distribution for Class A is skewed to the right, and the distribution for Group B is skewed to the right. This would indicate that the median heights are about the same. To check this assumption, locate the measurement class of each median.
Example 3-2a

43. Answer: The median heights are about the same. The answer is B.
Group A
Group B
The median is between the 12th and 13th data values. The median is in the measurement class.
The median is between the 12th and 13th data values. The median is in the measurement class.
Answer: The median heights are about the same. The answer is B.
Example 3-2a

44. A City A B The medians are about the same.
Multiple-Choice Test Item Use the data in the histograms to determine which city has a greater median age.
A City A B The medians are about the same.
C City B D Cannot be determined
Answer: C
Example 3-2b

45. Step 1 Identify the greatest and least values in the data set.
Football Create a histogram to represent the following scores of top 25 winning college football teams during one week of the 2001 season.
43, 52, 38, 36, 42, 46, 26, 38, 38, 31, 38, 37, 38, 48, 45, 27, 47, 35, 35, 26, 47, 24, 41, 21, 32
Step 1 Identify the greatest and least values in the data set.
The scores range from 21 to 52 points.
Step 2 Create measurement classes of equal width.
For these data, use measurement classes from 20 to 55 with a 5-point interval for each class.
Example 3-3a

46. Step 3 Create a frequency table using the measurement classes.1 | 5
|||| 3
||| 9
|||| |||| 2 ||
Frequency
Tally
Score Intervals
Example 3-3a

47. Step 4 Draw the histogram.
Use the measurement classes to determine the scale for the horizontal axis and the frequency values to determine the scale for the vertical axis. For each measurement class, draw a rectangle as wide as the measurement class and as tall as the frequency for the class. Label the axes and include a descriptive title for the histogram.
Example 3-3a

48. Answer:
Example 3-3a

49. Create a histogram to represent the attendance at the weekly meeting of the Math Club.
75, 58, 71, 67, 73, 58, 67, 78, 65, 77, 72, 68, 76, 64, 72, 57, 71, 75, 64, 74, 60, 54, 66, 74
Answer:
Example 3-3b

50. End of Lesson 3

51. Example 2 Find the Quartiles and the Interquartile Range
Example 1 Find the Range
Example 2 Find the Quartiles and the Interquartile Range
Example 3 Identify Outliers
Lesson 4 Contents

52. Answer: The range of the yardage is or 1799 yards.
Collage Football The teams with the top 15 offensive yardage gains for the 2000 season are listed in the table. Find the range of the data.
Team
Yardage
Air Force
Boise St.
Clemson
Florida St.
Georgia Tech
Idaho
Indiana
Kentucky
Miami
Michigan
Nebraska
Northwestern
Purdue
Texas
Tulane
4971
5459
4911
6588
4789
4985
4830
4900
5069
5059
5232
5183
4825
4989
The greatest amount of yardage gains is 6588, and the least amount of yardage gains is 4789.
Answer: The range of the yardage is or 1799 yards.
Example 4-1a

53. Baseball The baseball players with the top 12 all-time runs batted in (RBI) are listed in the table. Find the range of the data.
Player
RBI
Hank Aaron
Cap Anson
Ty Cobb
Jimmie Foxx
Lou Gehrig
Willie Mays
Eddie Murray
Stan Musial
Mel Ott
Babe Ruth
Ted Williams
Carl Yastrzemski
2297
2076
1937
1922
1995
1903
1917
1951
1860
2213
1839
1844
Answer: 458 RBI
Example 4-1b

54. Area (thousand square miles)
Geography The areas of the 5 largest states are listed in the table. Find the median, the lower quartile, the upper quartile, and the interquartile range of the areas.
State
Area (thousand square miles)
Alaska
California
Montana
New Mexico
Texas
656
164
147
124
269
Explore You are given a table with the areas of the 5 largest states. You are asked to find the median, the lower quartile, the upper quartile, and the interquartile range.
Example 4-2a

55. Plan. First, list the areas from least to greatest. Then
Plan First, list the areas from least to greatest. Then find the median of the data. The median will divide the data into two sets of data. To find the upper and lower quartiles, find the median of each of these sets of data. Finally, subtract the lower quartile from the upper quartile to find the interquartile range.
Solve
median
Example 4-2a

56. Answer: The median is 164 thousand square miles.
The lower quartile is thousand square miles and the upper quartile is thousand square miles.
The interquartile range is – or 327 thousand square miles.
Examine Check to make sure that the numbers are listed in order. Since 135.5, 164, and divide the data into four equal parts, the lower quartile, median, and upper quartile are correct.
Example 4-2a

57. Area (thousand square miles)
Geography The following table shows the areas of some major U.S. cities. Find the median, the lower quartile, the upper quartile, and the interquartile range of the areas.
City
Area (thousand square miles)
Atlanta
Boston
Dallas
Indianapolis
Kansas City
Los Angeles
Miami
New York City
Philadelphia
Washington D.C.
136 47
378
352
317
467 34
322 68
Answer: The median is square miles. The lower quartile is 68 square miles. The upper quartile is 352 square miles. The interquartile range is 284 square miles.
Example 4-2b

58. [ ][ ] Identify any outliers in the following set of data. Stem Leaf 45 6 7 8 9
| 7 = 47 [ ][ ]
Step 1 Find the quartiles.
The brackets group the values in the lower half and the values in the upper half.
The boxes are used to find the lower quartile and upper quartile.
Example 4-3a

59. Step 2 Find the interquartile range.
The interquartile range is
Step 3 Find the outliers, if any.
An outlier must be 1.5(15) less than the lower quartile, 72, or 1.5(15) greater than the upper quartile, 87.
Answer: There are no values greater than Since 47 < 49.5, 47 is the only outlier.
Example 4-3a

60. Identify any outliers in the following set of data. Stem Leaf3 4 5 6 7
1 7
|1 = 31
Answer: 79 is the only outlier.
Example 4-3b

61. End of Lesson 4

62. Example 1 Draw a Box-and Whisker Plot
Example 2 Draw Parallel Box-and-Whisker Plots
Lesson 5 Contents

63. Ecology The average water level in Lake Travis in central Texas during August is a good indicator of whether the region has had normal rainfall, or is suffering from a drought. The following is a list of the water level in feet above sea level during August for the years 1990 to 2000.
674, 673, 678, 673, 670, 677, 653, 679, 664, 672, 645
Draw a box-and-whisker plot for these data.
Example 5-1a

64. Step 1 Determine the quartiles and any outliers.
Order the data from least to greatest. Use this list to determine the quartiles.
645, 653, 664, 670, 672, 673, 673, 674, 677, 678, 679
Determine the interquartile range.
Check to see if there are any outliers.
Any numbers less than or greater than are outliers. There are none.
Example 5-1a

65. Step 2 Draw a number line.
Assign a scale to the number line that includes the extreme values. Above the number line, place bullets to represent the three quartile points, any outliers, the least number that is not an outlier, and the greatest number that is not an outlier.
645
664
673
679
677
Example 5-1a

66. Step 3 Complete the box-and whisker plot.
Draw a box to designate the data between the upper and lower quartiles. Draw a vertical line through the point representing the median. Draw a line from the lower quartile to the least value that is not an outlier. Draw a line from the upper quartile to the greatest value that is not an outlier.
Example 5-1a

67. What does the box-and-whisker plot tell about the data?
Notice that the whisker and the box for the top half of the data is shorter than the whisker and box for the lower half of the data.
Answer: The upper half of the data are less spread out than the lower half of the data.
Example 5-1b

68. Average Yearly Rainfall For Some U.S. Cities
Ecology The average yearly rainfall is listed below for 11 major cities.
Average Yearly Rainfall For Some U.S. Cities
City
Rainfall(in.)
Chicago
Cleveland
Helena
Louisville
Milwaukee
Philadelphia
Portland
St. Louis
Tampa
Savannah
Seattle
33.34
35.40
11.37
43.56
30.94
41.42
37.39
33.91
46.73
49.70
38.60
a. Draw a box-and-whisker plot for these data.
b. What does the box-and-whisker plot tell you about the data?
Answer: Except for the outlier, the lower half of the data are less spread out than the upper half.
Example 5-1c

69. Draw a parallel box-and-whisker plot for the data.
Climate Pilar, who grew up on the island of Hawaii, is going to go to college in either Dallas or Nashville. She does not want to live in a place that gets too cold in the winter, so she decided to compare the average monthly low temperatures of each city.
Average Monthly
Low Temperatures (F)
Month
Dallas
Nashville
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sept.
Oct.
Nov.
Dec.
32.7
36.9
45.6
54.7
62.6 70
74.1
73.6
66.9
55.8
45.4
36.3
26.5
29.9
39.1
47.5
56.6
64.7
68.9
67.7
61.1
48.3
39.6
30.9
Draw a parallel box-and-whisker plot for the data.
Determine the quartiles and outliers for each city.
Example 5-2a

70. Neither city has any outliers.
Dallas 32.7, 36.3, 36.9, 45.4, 45.6, 54.7, 55.8, 62.6, 66.9, 70, 73.6, 74.1
Nashville 26.5, 29.9, 30.9, 39.1, 39.6, 47.5, 48.3, 56.6, 61.1, 64.7, 67.7, 68.9
Neither city has any outliers.
Draw the box-and-whisker plots using the same number line.
Example 5-2a

71. Answer:
Example 5-2a

72. Use the parallel box-and-whisker plots to compare the data.
Answer: The interquartile range of temperatures for both cities is about the same. However, all quartiles of the Dallas Temperatures are shifted to the right of those of Nashville, meaning Dallas has higher average low temperatures.
Example 5-2b

73. RBI for Top 12 Yankees and Rangers Hitters (2001)
Suppose a baseball manager has two job offers to manage the Yankees or the Rangers. He compares the teams using their average runs batted in (RBI) for their top twelve players.
a. Draw a parallel box-and- whisker plot for the data.
RBI for Top 12 Yankees and Rangers Hitters (2001)
Player
Yankees
Rangers 1 2 3 4 5 6 7 8 9 10 11 12
113 95 94 74 73 70 51 49 46 44 32 19
135
123 72 67 65 54 36 35 34 29 25
Example 5-2c

74. b. Use the parallel box-and-whisker plots to compare the data.
Answer:
b. Use the parallel box-and-whisker plots to compare the data.
Answer: The interquartile range of RBI for both teams is about the same. However, except for outliers, all of the Yankees RBI are shifted to the right of those of the Rangers, meaning the Yankees have a higher average RBI per person.
Example 5-2c

75. End of Lesson 5

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