la salle college antipolo - · pdf filemr. elpidio quirino spent 3 hours and 46 minutes...

LA SALLE COLLEGE ANTIPOLO 1985 LA SALLE AVENUE, TOWN & COUNTRY HEIGHTS SAN LUIS, ANTIPOLO CITY, 1870 RIZAL, PHILIPPINES

MTH114: Intermediate Statistics

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LA SALLE COLLEGE ANTIPOLO 1985 LA SALLE AVENUE, TOWN & COUNTRY HEIGHTS SAN LUIS, ANTIPOLO CITY, 1870 RIZAL, PHILIPPINES

FIRST SEMESTER, AY 2015 – 2016

BMTH2: Mathematics of Investment

Problem Set # 1

Part I: Introduction to Statistics Direction: Identify what is being asked in each of the following. Write your answer/answers on the

space provided for. Please avoid erasures.

1. The five steps in statistical investigation are _________________, _________________, _________________,

____________________, and __________________.

2. A ________________________ is typically a very large collection of individuals or measurements

about which we desire information.

3. A ___________________ is the calculated measure of some characteristics of a sample.

4. A parameter is the measure of some characteristics of a ______________________.

5. The number of ripe mangoes in a box is an example of _________________ data.

6. The basic objective of _______________________________ is that of obtaining a sample, inspecting this

sample, and then making inferences about the unknown characteristics of the population

from which the sample was drawn.

7. ___________________________ is a method of presenting data that shows the component part of a

whole.

8. ___________________________ is data obtained from original source by means of actual observations

or interviews.

9. Attribute data is also called ____________________________.

10. _______________________________________ is the procedure used to collect the sample data.

Part II: Types of Data

Direction: Identify the type of datum each of the given below. Write your answer on the space

provided for. Write Discrete Data if it is discrete, Continuous Data if it is continuous, and Qualitative Data if it is qualitative. Please avoid erasures.

11. Mr. Jose Rizal said he weighed 125 pounds, to the nearest pound.

12. Ms. Gabriela Silang was 48 years old on her last birthday.

13. Mr. Apolinario Mabini used 3 ½ cups of flour in his red velvet cupcakes.

14. Ms. Melchora Aquino bought a can of tomato sauce which weighs 1.48 kilograms.

15. 45,678 applicants took the entrance examination and only 34,598 passed.

16. Mr. Juan Luna’s height is 6 feet and 3 inches.

17. Mr. Diego Silang’s monthly salary is 56,789 pesos.

18. Lolo Andres Bonifacio died at the age of 86.

19. In a diving competition, the third diver received a score of 7.8.

20. The favorite dictionary of Mr. Antonio Luna is 7.89 inches thick.

21. Last semester, Mr. Lapu-lapu got a grade of 3.75 in his Foundation of Mathematics coursework.

22. The capacity of a 3 ½ floppy disk is 1.44 megabytes.

23. Mr. Jose P. Laurel bought an iPhone 6 Plus with 64 gigabytes memory.

24. Ms. Gloria Arroyo is one of the female Presidents of the Republic of the Philippines.

25. There are 3 students in Intermediate Statistics class of Mr. Migo Mendoza.

26. Mr. Ramon Magsaysay brought a 500ml bottle of glutathione.

27. Most of the students in La Salle College Antipolo are Roman Catholic.

28. Most avid users of iPhone prefer Gold rather than Silver.

29. Mr. Fidel Ramos was 7 pounds when he was born.

30. Most of the respondents agreed that SONA of President Aquino was better than TSONA of VP Binay.

31. Mr. Elpidio Quirino spent 3 hours and 46 minutes waiting for his friend in Starbucks Café.

32. There were 123,456 Directioners during the concert of One Direction last March 2015.

33. Mr. Joseph Estrada solved 75 problems in his Physics Problem Set.

34. Ms. Cory Aquino’s shoe size is 12 and a half inches.

35. Mrs. Imelda Marcos is a widow of Mr. Ferdinand Marcos.

36. A stun gun can shock a thief 50,000 volts.

37. The American flag has 50 stars.

38. There are 50 states in United States of America.

39. Most of the respondents can speak either Tagalog or Waray.

40. The population of the Philippines is 100,096,496 as of July 2014.

Part III: Types of Population

Direction: Identify the type of population each of the given below. Write your answer on the space

provided for. Write Infinite Population if it is infinite and Finite Population if it is finite. Please avoid

erasures.

41. Number of questions in the preliminary examination in Mathematics of Investment.

42. Number of dust in the sky.

43. Number of ants living on Earth.

44. Number of squids in the sea.

45. Number of Mathematics teachers in the whole world.

46. Number of Nike running shoes in United States of America.

47. Set of integers.

48. Set of real numbers.

49. Set of natural numbers from 1 to 1,000.

50. Number of islands in the Philippines.

51. Number of stars in the galaxy.

52. Number of words in two Webster dictionaries.

53. Number of books in DLSU library.

54. Number of atoms in human body.

55. Number of planets in the solar system.

56. Number of Ms. Universe title holders.

57. Number of viruses in human body.

58. Number of good bacteria in human body.

59. Number of pebbles all over the world.

60. Number of flies all over the world.

Part IV: Variable and Observed Value

Direction: Identify if the given below has variable or has observed value. Write your answer on the

space provided for. Write Variable if it has variable and Observed Value if it shows observed value.

Please avoid erasures.

61. The focus of the research paper was on the marital status of the respondents.

62. Most of the respondents are Born Again Christian.

63. There were 567 Rizalenos took part in the recent study of Department of Health.

64. The teacher would like to determine the favorite color of her students in her Art class.

65. The teacher found out that most of her students are female.

66. La Salle Greenhills is an all-male school.

67. The in-demand shoe size in the market is 10 inches.

68. A group of students in Enderun College would like to determine the favorite food of Filipinos.

69. The recent study of Olay Philippines will still focus on skin complexion.

70. The focus of the study conducted by Science Education Department was about losing weight.

71. There are four kinds pain killer drugs used in the experiment conducted by UP Medicine students.

72. The respondents of the study are students of the College of Education.

73. Eighty percent of the respondents of the study conducted were taking Bachelor of Science in International Relations and on their second year.

74. The focus of the experiment is the effect of social media networking sites on the study habits of La Salle College Antipolo freshmen students.

75. Most of the respondents of study about dating are single.

76. The top grossing Filipino movies of all time is The Amazing Praybeyt Benjamin.

77. Ms. Jennilyn Mercado topped the FHM survey on 100 sexiest woman in the world.

78. Mr. Dagul wrote on the questionnaire his height was 2 feet and 3 inches.

79. Most of the respondents monthly salary are ranging from P10,000.00 to P19,999.00.

80. The focus of the study was the eating habits of kids ages 2 to 7 years old.

Part V: Independent and Dependent Variables

Direction: Identify the type of variables each of the items has below. Write your answer on the space

provided for. Write Independent Variable if it is has independent variable and Dependent Variable if

it has dependent variable. Please avoid erasures.

81. The research found out that students performed well in computer-aided instruction compare to traditional instruction.

82. The research would like to determine the effect Outcome-Based Education among La Salle College Antipolo freshmen students.

83. The experiment will determine the effect of three weigh loss pills.

84. The genres of music have effects on mood of employees working in BPO companies.

86. The researchers found out that abnormal sleeping pattern has an effect on the way people process information on their minds.

87. The study will determine the employability of De La Salle University-Manila Education graduates of 2014.

88. The study will measure the Intelligent Quotient of freshmen students of Harvard University.

89. The Worktext in Selected Topics in History of Mathematics found useful in studying History and Philosophy of Mathematics course.

90. The study will develop a module in teaching of Genetics.

91. The students will analyze the novel of Paulo Coelho entitled “Veronica Decides to Die” using Psychoanalytic Theory of Sigmund Freud.

92. The experiment determined that Facebook had a tremendous effect on the aggressive behavior of teenagers.

93. The study will determine the effect of X-ray radiation on infants.

94. Education leaders in Canada found out that Wi-Fi has health risk.

95. The study about employment satisfaction found out that teaching staffs have high satisfaction rates compare to non-teaching staffs.

96. The study will determine the key factors in internet advertising.

97. The study revealed that high weather temperature contributes to crime rates.

98. The study found out that teenagers in Korea and Japan have high risk of committing suicide due to pressure in their studies.

99. The study will determine the effect of prayers as a daily classroom routine in the behavior of students.

100. TIMMS revealed that Singapore and Korea were top performers in Math and Science subjects.

Part VI: Determining Samples from the Population

Direction: Given the population, marginal error/s and/or confidence level/s compute for the

number of samples each of the population has below. Write your solution on the space provided for.

Please avoid erasures.

101-105. N = 6,530 and e = 5%

Solution:

106-110. N = 7,000 and e = 10%

Solution:

111-115. N = 2,800 and e = 1%

Solution:

116-120. N = 10,280 and the confidence level is 95%

Solution:

121-125. N = 18,470 and the confidence level is 90%

Solution:

126-130. N=32,460 and the confidence level is 99%

Solution:

131-135. N=560 and e = 1%

Solution:

136-140. N = 1,000 and e = 10%

Solution:

141-145. N = 80,000 and confidence level is 90%

Solution:

146-150. N = 90 and e = 5%

Solution:

151-155. N = 900 and confidence level is 99%

Solution:

156-160. N=23,000 and e = 1%

Solution:

161-165. N = 143,000 and confidence level is 95%

Solution:

166-170. N = 500,000 and e = 10%

Solution:

171-175. N = 9,000,000 and confidence level is 99%

Solution:

176-180. N = 13,000 and e = 1%

Solution:

181-185. N = 5,000,000 and e = 5%

Solution:

186-190. N = 10,000 and confidence levels are 99% and 90%

Solution:

191-195. N = 20 and confidence levels are 99% and 95%

Solution:

196-200. N = 10 and e = 1% and 5%

Solution:

Direction: Solve for the following problem. Do what is instructed. Write your solution on the space

provided for. Please avoid erasures.

201-220. A researcher wants to make a study on the IQ of 4,000 high school students. Determine the

sample size if he decides to have (a) 99%, (b) 95% and (c) 90% confidence coefficients.

Solution:

221-250. Using stratified sampling technique, show how the researcher will gather the sample from

the population in the above mentioned problem. Complete the table.

Year Level Number of

Students

1% 5% 10%

Freshmen 1,050

Sophomore 1,005

Junior 980

Senior 965

N=4,000 n= n= n=

Solution:

251-255. A researcher wants to make a socio-economic survey on 900 workers of a shoe factory. If

he allows 10% marginal error, how many workers must he take into his sample?

Solution:

256-260. Using systematic sampling make a list of the elements included in the sample for

abovementioned problem.

Solution:

Part VII: Graphical Presentations

Direction: Do what is instructed. Please complete the table with necessary information. Create your

graphical presentation/s using MS Word tools, then have it printed and paste it on the space provided

for. Please follow the guidelines in creating graphical presentations.

261-275. The number of each type of operations performed at a general hospital is listed below.

Type of Operations Number of Cases

(f)

Relative Frequencies

(rf) Thoracic 26

Bones and Joints 43

EENT 55

General 100

Abdominal 112

Urologic 73

Proctologic 62

Neurosurgery 19

N=490

Present the data in graphical forms such as (a) bar chart and (b) pie chart.

Bar Chart Pie Chart

276-295. Thirty preschoolers were asked of their favorite color, the responses were as follows:

Student Favorite

Color Student

Favorite

Color Student

Favorite

Color 1 Yellow 11 Blue 21 Pink

2 Green 12 Red 22 Pink

3 Green 13 Pink 23 Red

4 Red 14 Blue 24 Violet

5 Blue 15 Violet 25 Green

6 Red 16 Green 26 Blue

7 Pink 17 Green 27 Yellow

8 Yellow 18 Red 28 Blue

9 Blue 19 Blue 29 Pink

10 Pink 20 Red 30 Red

Create a frequency distribution and present the data in graphical forms (a) bar chart and

(b) pie chart.

n= 100%

Present the data using graphical forms.

Bar Chart Pie Chart

296-315. Forty elementary students were asked for their favorite fruit juice flavor. The data

collected were as follows:

Orange Strawberry Pineapple Mango Orange Mango Apple Grapes

Orange Apple Grapes Mango Apple Mango Grapes Strawberry

Pineapple Mango Apple Orange Grapes Strawberry Mango Mango

Grapes Grapes Apple Apple Mango Pineapple Apple Orange

Orange Pineapple Mango Grapes Orange Grapes Pineapple Apple

Create a frequency distribution and present the data using (a) bar chart, (b) line chart and

(c) pie chart.

n= 100%


Bar Chart

Line Chart

Pie Chart

Part VIII: Ungrouped Frequency Distribution




316-340. The time spent, in minutes, by 25 students in their travel from their house to their school

is presented.

45 25 45 35 35

35 15 25 45 15

25 55 35 5 25

5 25 15 25 65

25 45 25 55 45

Construct an ungrouped frequency distribution.

n= 100%

Present the data in graphical forms.

Bar Chart

Line Chart

Pie Chart

341-365. Fifty students were asked for the number of children in their family. The data collected

were as follows.

2 6 2 5 4 3 4 5 4 6

3 3 2 1 3 2 4 3 3 3

3 2 1 5 3 2 3 4 4 4

4 4 3 6 7 3 2 4 2 3

1 1 1 4 5 1 1 2 5 2


n= 100%


Bar Chart

Line Chart

Pie Chart

366-390. Sixty students were asked for the number of hours they spend watching TV during

Sunday night. The data collected were as follows.

3 2 4 3 5 0 2 5 3 3 3 2

4 3 1 3 3 3 3 0 4 2 4 1

3 0 2 2 4 5 3 2 4 2 4 3

3 2 4 3 3 2 4 3 2 4 4 2

5 3 4 3 1 2 4 3 3 3 2 2


n= 100%


Bar Chart

Line Chart

Pie Chart

391-415. The number of pigs born per liter last year at the Big Pig Farm are given in the following

list:

8 11 6 13 10 9 7 14 11 12 10

4 6 5 6 11 7 12 13 10 7 10

6 9 11 8 10 7 11 8 9 13 8

5 14 9 11 7 9 9 11 12 9 7

9 7 8 12 13 11 10 9 8 12 9


n= 100%


Bar Chart

Line Chart

Pie Chart

416-440. Ms. Honeygirl Pulot-pukyutan opened her coin bank and counted her savings to be

P2,158.50. Her 12-centavo coins totaled P6.00. Her 5-centavo coins, P20.00. Her 10-centavo

coins, P20.00. Her 25-centavo coins, P62.50. There were P300.00 1-peso coins. While the

5-peso coins were P250.00 and 10-peso coins, P500.00. Complete the grouped frequency

distribution.

Coins Tallies f rf 1 centavo

5 centavos

10 centavos

25 centavos

1 peso

5 pesos

10 pesos

n= 100%


Bar Chart

Line Chart

Pie Chart

441-465. Ms. Mary Christmas Aguinaldo withdrew a total of P6,500.00 for the Christmas

“aguinaldos”. The bank teller gave her two bundles of P10.00 bill worth P1,000.00 each;

two bundles of P20.00 bill worth P1,500.00; P50.00 bill worth P1,000.00; and P100.00 bill

worth P2,000.00. Complete the ungrouped frequency distribution below.

Peso Bills Tallies f rf P10.00

P20.00

P50.00

P100.00

n= 100%


Bar Chart

Line Chart

Pie Chart

Part IX: Grouped Frequency Distribution




466-505. The table below shows the gold scores attained by golfers in a tournament. Complete the

cumulative frequency distribution and construct the graphs.

Classes f Class

Marks rf

Class

Boundaries

Lower

Exact

Limits

Upper

Exact

Limits

f≤ f≥

70-79 3

80-89 16

90-99 31

100-109 38

110-119 36

120-129 25

130-139 19

140-149 10

150-159 3

160-169 3

170-179 1

N=185 100%

Histogram

Frequency Polygon

Ogive

506-545. The table below shows the scores attained by 155 high school graduates in an entrance

examination for college in La Salle College Antipolo. Complete the cumulative frequency

distribution and construct the graphs.

Classes f Class

Marks rf

Class

Boundaries

Lower

Exact

Limits

Upper

Exact

Limits

f≤ f≥

33-40 9

41-48 14

49-56 11

57-64 16

65-72 24

73-80 21

81-88 18

89-96 12

97-104 14

105-112 9

113-120 7

N=155 100%

Histogram

Frequency Polygon

Ogive

546-595. The 25 second year students contributed the following amount, in peso, for the “Buwan ng

Wika” celebration:

15 20 30 80 50

47 43 50 25 35

50 50 80 78 60

72 65 30 62 53

75 78 50 40 35

Cumulative Frequency Distribution:

Classes f Class

Marks rf

Class

Boundaries

Lower

Exact

Limits

Upper

Exact

Limits

f≤ f≥

N= 100%

Determine the (a) range, (b) class interval using three methods, and (c) class width. Write

your solution on the space provided for.

Range

Class Interval

Sturges’ Rule

Class Width Square Root Rule

Rice Rule

Present your data using graphical tools.

Histogram

Frequency Polygon

Ogive

596-630. From the 50 scores below, construct a frequency distribution, using a class interval of 5.

48 56 53 60 43 65 62 72 38 66

32 37 60 49 56 62 73 63 52 52

38 42 56 71 48 59 42 55 66 63

70 35 39 67 32 48 37 35 39 73

63 50 48 50 44 50 52 43 42 70

Classes f Class

Marks rf

Class

Boundaries

Lower

Exact

Limits

Upper

Exact

Limits

f≤ f≥

N= 100%

Histogram

Frequency Polygon

Ogive

631-660. The speed of 55 cars were measured by a radar device of a city street. Use 5 class intervals

and construct the cumulative frequency distribution.

23 21 26 38 16 23 48 18 24 23 21

33 32 22 32 32 34 25 27 25 33 26

18 29 28 24 24 28 29 25 27 28 29

43 27 22 41 41 30 31 52 22 23 25

20 18 26 35 35 24 43 38 22 23 27


Classes f Class

Marks rf

Class

Boundaries

Lower

Exact

Limits

Upper

Exact

Limits

f≤ f≥

N= 100%

Present your data using graphical tools:

Histogram

Frequency Polygon

Ogive

661-700. The following are a collection of IQ scores. Use class interval of 9 in constructing

cumulative frequency distribution.

69 84 91 96 100 103 105 109 115 122

74 86 92 96 101 103 105 110 115 122

74 86 92 98 101 103 105 110 116 124

75 87 92 98 101 103 105 110 116 125

76 88 93 99 101 103 106 111 117 126

77 88 94 99 101 103 106 113 117 129

79 88 95 99 102 103 106 113 118 129

81 89 95 100 102 104 107 114 120 130

83 89 95 100 102 104 108 114 121 133

84 91 95 100 102 104 109 115 121 139


Classes f Class

Marks rf

Class

Boundaries

Lower

Exact

Limits

Upper

Exact

Limits

f≤ f≥

N= 100%

Present your data using graphical tools:

Histogram

Frequency Polygon

Ogive

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