LEADER:
MIRASOL, Jester T.
MEMBERS:
MARIÑAS, Carl Lester D.
MENDOZA, Rico D.
PEDRANO, John Mark R.
SOTTO, Mark Anthony A.
PROFESSOR:
Mr. Mark Ronoele Gonzalvo
THE GROUP 3 PRESENTERS
CARL LESTER D. MARIÑAS
RICO D. MENDOZA
JOHN MARK R. PEDRANO
JESTER T. MIRASOL
MARK ANTHONY A. SOTTO
Republic of the Philippines
EULOGIO “Amang” RODRIGUEZ
INSTITUTE OF SCIENCE AND TECHNOLOGY
Nagtahan, Sampaloc, Manila
COLLEGE OF ENGINEERING
SURVEY ON CIVIL ENGINEERING STUDENTS OF EULOGIO AMANG
RODRIGUEZ INSTITUTE OF SCIENCE AND TECHNOLOGY –
MANILA CAMPUS ABOUT THEIR FAVORITE
DATE OF THE MONTH (1-31)
OVERVIEW
DATA COLLECTION
DATA PRESENTATION
GRAPHICAL REPRESENTATION
MEASURE OF CENTRAL TENDENCY
MEASURE OF POSITION
MEASURE OF VARIABILITY
GROUP 3
DATA
COLLECTION
GROUP 3
DATA
COLLECTION
1ST YEAR CE STUDENTS
2ND YEAR CE STUDENTS
3RD YEAR CE STUDENTS
4TH YEAR CE STUDENTS
GROUP 3
DATA
COLLECTION
Snowball Sampling was employed
as the group reached out few
students from each year level and
let those students relay the google
form to their classmates via their
respective Group Chats.
SNOWBALL SAMPLING is a sampling method used by
researchers to generate a pool of participants for a
research study through referrals made by individuals
who share a particular characteristic of research
interest with the target population (Frey, 2018).
GROUP 3
DATA
COLLECTION
The survey targets 25 respondents
each from 1st year to 3rd year and
15 respondents from 4th year.
QUOTA SAMPLING is defined as a non-probability
sampling method in which researchers create a sample
involving individuals that represent a population
(QuestionPro Survey Software, 2022).
GROUP 3
DATA
COLLECTION
To finally obtain the target
number of respondents, simple
random sampling technique was
used through ‘Wheel of Names'
method which was done per year
level.
SIMPLE RANDOM SAMPLING is a
randomly selected subset of a population.
In this sampling method, each member of
the population has an exactly equal chance
of being selected (Thomas, 2020).
GROUP 3
DATA
COLLECTION
FINAL
TABULATED
LISTS
FAVORITE DATE
OF THE MONTH
1
13. Castillo, Monica E.
13
14. Tamosa, Reynante R.
7
15. Zabat, Ulysses Xandrex L.
29
2. Lacanilao, Lizel G.
30
16. Yumang, Vincent L.
26
3. Dela Cruz, James R.
7
17. Galang, Ronalyn S.
3
4. Abejero, Welmor A.
17
18. Manaloto, Jonard M.
1
5. Varias, Gerielle Louisee DG.
26
19. Mendeja, Christelle L.
29
6. Justo, Princess Anne I.
17
20. Sarmiento, Khalia
4
7. Escarro, Caryll Joy C.
17
21. Arevalo, Aila Marie P.
28
8. Estrada, Aldrin Daniel L.
26
22. Introlizo, Jeffrey
25
9. Bonot, Jedraleen D.
31
23. Rodrigo, Andrei
17
10. Kempiz, Alwayne
26
24. Mabugay, Ricky A Jr.
17
11. Villaceran, Franz-Yari S.
27
25. Acuña, Kurt Daniel
25
12. Barbosa, John Steven D.
15
NAME
1. Netrua, Glyza Mae DC.
13. Priego, Jeffrey L.
3
14. Balasbas, Stefany Mary Joy P.
9
1. Ambon, Hannah Marie L.
FAVORITE DATE
OF THE MONTH
7
15. Velasquez, Andrea
31
2. Delos Reyes, Carl Bryan Y.
3
16. Manalo, Cedric D.
14
3. Bicar, Denver
5
17. Pena, Reign Marie L.
17
4. Yamamoto, Kazayuki G.
21
18. Caampued, Annie C.
13
5. Geuvarra, Drey Matthew F.
15
19. Buntalan, Jecell
26
6. Santos, Criselda Joy N.
8
20. Balolot, Mark Genesis L.
29
7. Gepollo, Missy S.
14
21. Mopal, Gethel M.
28
8. Acibar, Cherrie Mae B.
7
22. Selda, Ydel Mae R.
22
9. Lorenzo, Igi Mark R.
7
23. Lumugdang, Ralfh Robert P.
24
10. Abello, Andrea Joyce S.
17
24. Buensalida, Jovell P.
4
11. Esteras, Fevonica Reign S.
19
25. Anaviso, Daniel F.
9
12. Panaligan, Jherlyn May D.
12
NAME
NAME
1. Gabilan, Joey Albert
FAVORITE DATE
OF THE MONTH
6
13. Manrique, Jessel C.
7
14. Orellana, Karla Mikaela M.
9
15. Arizobal, Emmanuel A.
18
2. Serrato, Mary Chris A.
10
16. Alcober, Jay-Ar C.
28
3. Arcueno, Jeruz V.
18
17. Jocson, Lorraine Ann N.
28
4. Tulaylay, Hannah Rica DS.
12
18. Agot, Romeo Tito S.
16
5. Serrano, John Angelo P.
17
19. Callanta, Ara Mae F.
17
6. Telan, Ian Migelle G.
21
20. Diaz, Janelle R.
6
7. Gomez, John Anthony I.
14
21. Pacinos II, Edwin R.
12
8. Velasco, Kin Oliver P.
28
22. De Jesus, Carla Angelica C.
16
9. Dacca, Gilbert A.
13
23. Calturan, Lady Ann G.
22
10. Fadriquela, Ilver M.
5
24. De Jesus, Aldren E.
26
11. Brin, Raymond L.
21
25. Razos, Billy James C.
4
12. Perez, Jerome J.
1
NAME
1. Biscocho, Royell Cris P.
2. Sedaba, Mae Joy U.
3. Bueno, Apple C.
4. Catapia, Alyssa Joy M.
5. Aliodin, Sittie Ainie L.
6. Biñas, Lester
7. Cuevas, Jayson
8. Cabali, John Leonard M.
9. Montañez, John Paul B.
10. Ordiales, Joe Angelica C.
11. Galero, Marvin Zandro R.
12. Buynay, Marven B.
13. Pascua, Raymond A.
14. Baleta, Andrea Nicole R.
15. Dinaguit, Jamia Mae A.
FAVORITE DATE OF THE MONTH
30
11
12
31
10
19
4
12
1
1
9
7
19
30
28
1
27
30
15
7
13
17
7
26
29
17
26
17
3
26
1
31
29
26
4
28
8
14
25
14
17
17
7
13
17
7
26
25
17
29
7
19
28
3
12
22
5
3
24
21
9
4
15
31
9
6
21
12
10
1
16
18
7
22
12
9
26
17
18
4
21
28
30
14
28
11
28
16
12
13
17
31
5
6
10
19
4
12
1
1
9
7
19
30
28
ARRAY
(Largest to Smallest)
The favorite date of the month (1-31) of EARIST - Manila CE students arranged from largest to smallest.
31
31
31
30
30
30
29
29
29
28
28
28
28
28
28
27
26
26
26
26
26
26
25
25
24
22
22
21
21
21
19
19
19
18
18
17
17
17
17
17
17
17
17
17
16
16
15
15
14
14
14
13
13
13
12
12
12
12
12
11
10
10
9
9
9
9
8
7
7
7
7
7
7
7
6
6
5
5
4
4
4
4
3
3
3
1
1
1
1
1
ARRAY
(Smallest to Largest)
The favorite date of the month (1-31) of EARIST - Manila CE students arranged from smallest to largest.
1
1
1
1
1
3
3
3
4
4
4
4
5
5
6
6
7
7
7
7
7
7
7
8
9
9
9
9
10
10
11
12
12
12
12
12
13
13
13
14
14
14
15
15
16
16
17
17
17
17
17
17
17
17
17
18
18
19
19
19
21
21
21
22
22
24
25
25
26
26
26
26
26
26
27
28
28
28
28
28
28
29
29
29
30
30
30
31
31
31
Stem – and – Leaf Diagram
STEM
LEAVES
0
1 1 1 1 1 3 3 3 4 4 4 4 5 5 6 6 7 7 7 7 7 7 7 8 9 9 9 9
1
0 0 1 2 2 2 2 2 3 3 3 4 4 4 5 5 6 6 7 7 7 7 7 7 7 7 7 8 8 9 9 9
2
1 1 1 2 2 4 5 5 6 6 6 6 6 6 7 8 8 8 8 8 8 9 9 9
3
1 1 1
Frequency Distribution Table
CLASSES
TALLY
CLASS
FREQUENCY
MARK (X)
LIMIT
BOUNDARY
Lower
Upper
Lower
Upper
RELATIVE
FREQUENCY
CUMULATIVE
FREQUENCY
<cf
>cf
1–5
IIIII IIIII
IIII
14
3
1
5
0.5
5.5
0.156
14
90
6 – 10
IIIII IIIII
IIIII I
16
8
6
10
5.5
10.5
0.178
30
76
11 – 15
IIIII IIIII
IIII
14
13
11
15
10.5
15.5
0.156
44
60
16 – 20
IIIII IIIII
IIIII I
16
18
16
20
15.5
20.5
0.178
60
46
21 – 25
IIIII III
8
23
21
25
20.5
25.5
0.089
68
30
26 – 30
IIIII IIIII
IIIII IIII
19
28
26
30
25.5
30.5
0.211
87
22
31 – 35
III
3
33
31
35
30.5
35.5
0.033
90
3
TOTAL
90
1.001
HISTOGRAM
CLASS BOUNDARY
CLASSES
LOWER
UPPER
CLASS MARK
(x)
FREQUENCY
1–5
14
0.5
5.5
3
6 – 10
16
5.5
10.5
8
11 – 15
14
10.5
15.5
13
16 – 20
16
15.5
20.5
18
21 – 25
8
20.5
25.5
23
26 – 30
19
25.5
30.5
28
31 – 35
13
30.5
35.5
33
TOTAL
90
FREQUENCY POLYGON
CLASSES
FREQUENCY
20
CLASS MARK
(x)
19
18
16
14
3
6 – 10
16
8
11 – 15
14
13
16 – 20
16
18
14
FREQUENCY
1–5
16
14
16
14
12
10
8
8
6
4
21 – 25
8
23
26 – 30
19
28
31 – 35
13
TOTAL
90
33
3
2
0
0
0
3
8
13
18
CLASS MARK
23
28
33
0
38
OGIVE
(Less than Cumulative Frequency)
1–5
14
14
CLASS BOUNDARY
90
LOWER
UPPER
80
0.5
5.5
6 – 10
16
30
5.5
10.5
11 – 15
14
44
10.5
15.5
16 – 20
16
60
15.5
20.5
21 – 25
8
68
20.5
25.5
26 – 30
19
87
25.5
30.5
CUMULATIVE FREQUENCY
CUMULATIVE
CLASSES FREQUENCY FREQUENCY
> cf
100
87
90
68
70
60
60
50
44
40
30
30
20
10
14
0
0
31 – 35
13
TOTAL
90
90
30.5
35.5
0,5
5,5
10,5
15,5
20,5
CLASS BOUNDARY
25,5
30,5
35,5
OGIVE
(Greater than Cumulative Frequency)
1–5
14
90
CLASS BOUNDARY
90
LOWER
UPPER
80
0.5
5.5
6 – 10
16
76
5.5
10.5
11 – 15
14
60
10.5
15.5
16 – 20
16
46
15.5
20.5
21 – 25
8
30
20.5
25.5
26 – 30
19
22
25.5
30.5
CUMULATIVE FREQUENCY
CUMULATIVE
CLASSES FREQUENCY FREQUENCY
> cf
100
90
76
70
60
60
46
50
40
30
30
22
20
10
3
0
0
31 – 35
13
TOTAL
90
3
30.5
35.5
0,5
5,5
10,5
15,5
20,5
CLASS BOUNDARY
25,5
30,5
35,5
Pie Chart
SECTOR
OCCUPIED IN
THE PIE CHART
CLASSES
FREQUENCY
RELATIVE
FREQUENCY
1–5
14
0.156
56⁰
6 – 10
16
0.178
64⁰
11 – 15
14
0.156
56⁰
16 – 20
16
0.178
64⁰
21 – 25
8
0.089
32⁰
26 – 30
19
0.211
76⁰
31 – 35
3
0.033
12⁰
TOTAL
90
1.001
360⁰
MEAN
CLASSES
TALLY
FREQUENCY
(f)
1–5
IIIII IIIII IIII
14
6 – 10
11 – 15
16 – 20
21 – 25
26 – 30
31 – 35
TOTAL
IIIII IIIII
IIIII I
IIIII IIIII IIII
IIIII IIIII
IIIII I
IIIII III
IIIII IIIII IIIII
IIII
III
CLASS
MARK
(x)
fx
3
42
16
8
128
14
13
182
16
18
288
8
23
184
19
28
532
3
33
99
90
1,455
𝑓𝑥
𝑥=
𝑛
𝑥=
𝑥
𝑥
14 3 +16 8 +14 13 +16 18 +8 23 +19 28 +3(33)
90
42+128+182+288+184+532+99
=
90
1455
=
90
𝒙 = 𝟏𝟔. 𝟏𝟕
∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑴𝒆𝒂𝒏 𝒊𝒔 𝟏𝟔. 𝟏𝟕.
MEDIAN
c=5
CLASSES
FREQUENCY
(f)
CUMULATIVE
FREQUENCY (<cf)
1–5
14
14
6 – 10
16
30
11 – 15
14
44 𝑪𝑭<
16 𝒇𝒎 = 𝟏𝟔
𝑴𝒆𝒅𝒊𝒂𝒏
60
𝑪𝒍𝒂𝒔𝒔
21 – 25
8
68
𝑇ℎ𝑒 45𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒
4𝑡ℎ class.
26 – 30
19
87
∴ 𝑻𝒉𝒆 𝑴𝒆𝒅𝒊𝒂𝒏 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟒𝒕𝒉 𝒄𝒍𝒂𝒔𝒔
31 – 35
TOTAL
3
90
90
𝑳𝒎 = 𝟏𝟓. 𝟓 16 – 20
𝒏 = 𝟗𝟎
𝑛
𝑀𝑒𝑑𝑖𝑎𝑛 𝐶𝑙𝑎𝑠𝑠 =
2
90
𝑀𝑒𝑑𝑖𝑎𝑛 𝐶𝑙𝑎𝑠𝑠 =
2
𝑀𝑒𝑑𝑖𝑎𝑛 𝐶𝑙𝑎𝑠𝑠 = 𝟒𝟓
(45𝑡ℎ 𝑑𝑎𝑡𝑎 𝑜𝑟 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛)
(16 – 20).
MEDIAN
𝑥 = 𝐿𝑚 +
𝑳𝒐𝒘𝒆𝒓 𝑩𝒐𝒖𝒏𝒅𝒂𝒓𝒚 𝒐𝒇 𝑴𝒆𝒅𝒊𝒂𝒏 𝑪𝒍𝒂𝒔𝒔 (𝑳𝒎 ) = 𝟏𝟓. 𝟓
𝑥 = 15.5 +
𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝒐𝒇 𝑴𝒆𝒅𝒊𝒂𝒏 𝑪𝒍𝒂𝒔𝒔 (𝒇𝒎 ) = 𝟏𝟔
𝑪𝒖𝒎𝒖𝒍𝒂𝒕𝒊𝒗𝒆 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝒐𝒇 𝒕𝒉𝒆 𝑪𝒍𝒂𝒔𝒔
𝒑𝒓𝒆𝒄𝒆𝒅𝒊𝒏𝒈 𝒕𝒉𝒆 𝑴𝒆𝒅𝒊𝒂𝒏 𝑪𝒍𝒂𝒔𝒔(𝑪𝑭< ) = 𝟒𝟒
𝑓𝑚
90
−44
2
16
∙𝑐
𝑥 = 15.5 +
1
16
∙5
𝑥 = 15.5 +
5
16
𝑥 = 15.5 +
45 −44
∙
16
𝑥 = 15.5 +
1
16
𝑻𝒐𝒕𝒂𝒍 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 (𝒏) = 𝟗𝟎
𝑪𝒍𝒂𝒔𝒔 𝑺𝒊𝒛𝒆 (𝒄) = 𝟓
𝑛
2
( ) −𝐶𝐹<
∙5
5
∙5
𝑥 = 15.5 + 0.31
𝒙 = 𝟏𝟓. 𝟖𝟏
∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑴𝒆𝒅𝒊𝒂𝒏 𝒊𝒔 𝟏𝟓. 𝟖𝟏.
MODE
𝒄=𝟓
𝑳𝒎𝒐 = 𝟐𝟓. 𝟓
CLASSES
FREQUENCY
(f)
1–5
14
6 – 10
16
11 – 15
14
16 – 20
16
21 – 25
8
𝒇𝟏 = 𝟖
19
𝑴𝒐𝒅𝒂𝒍 𝑪𝒍𝒂𝒔𝒔
3
𝒇𝟐 = 𝟑
26 – 30
𝒇𝒎𝒐 = 𝟏𝟗
31 – 35
TOTAL
𝒏 = 𝟗𝟎
90
𝐓𝐡𝐞 𝐦𝐚𝐱𝐢𝐦𝐮𝐦 𝐟𝐫𝐞𝐪𝐮𝐞𝐧𝐜𝐲 𝐢𝐬 𝟏𝟗
𝐚𝐧𝐝 𝐢𝐭 𝐚𝐩𝐩𝐞𝐚𝐫𝐬 𝐰𝐢𝐭𝐡𝐢𝐧
𝐭𝐡𝐞 𝟔𝐭𝐡 𝐜𝐥𝐚𝐬𝐬.
∴ 𝑻𝒉𝒆 𝒎𝒐𝒅𝒂𝒍 𝒄𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆
𝟔𝒕𝒉 𝒄𝒍𝒂𝒔𝒔 (26 – 30).
MODE
𝑥 = 𝐿𝑚𝑜 +
𝑳𝒐𝒘𝒆𝒓 𝑩𝒐𝒖𝒏𝒅𝒂𝒓𝒚 𝒐𝒇 𝑴𝒐𝒅𝒂𝒍 𝑪𝒍𝒂𝒔𝒔 (𝑳𝒎𝒐 ) = 𝟐𝟓. 𝟓
𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝒐𝒇 𝑴𝒐𝒅𝒂𝒍 𝑪𝒍𝒂𝒔𝒔 (𝒇𝒎𝒐 ) = 𝟏𝟗
𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒍𝒂𝒔𝒔 𝒑𝒓𝒆𝒄𝒆𝒅𝒊𝒏𝒈 𝒕𝒉𝒆
𝑴𝒐𝒅𝒂𝒍 𝑪𝒍𝒂𝒔𝒔 (𝒇𝟏 ) = 𝟖
𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒍𝒂𝒔𝒔 𝒂𝒇𝒕𝒆𝒓 𝒕𝒉𝒆
𝑴𝒐𝒅𝒂𝒍 𝑪𝒍𝒂𝒔𝒔(𝒇𝟐 ) = 𝟑
𝑓𝑚𝑜 −𝑓1
2(𝑓𝑚𝑜 )−𝑓1 −𝑓2
𝑥 = 25.5 +
19−8
∙
2(19)−8−3
𝑥 = 25.5 +
11
∙
27
5
55
27
∙𝑐
𝑥 = 25.5 +
5
𝑥 = 25.5 + 2.04
𝒙 = 𝟐𝟕. 𝟓𝟒
𝑻𝒐𝒕𝒂𝒍 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 (𝒏) = 𝟗𝟎
𝑪𝒍𝒂𝒔𝒔 𝑺𝒊𝒛𝒆 (𝒄) = 𝟓
∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑴𝒐𝒅𝒆 𝒊𝒔 𝟐𝟕. 𝟓𝟒.
𝐐𝟏
Quartile 1
CLASSES
FREQUENCY
1-5
14
Lq=5.5 6-10
fq = 16 16
30
11-15
14
44
16-20
16
60
21-25
8
68
26-30
19
87
31-35
3
90
TOTAL
n = 90 90
C=5
CF<
CF< = 14
𝑛𝑘
𝑞=
4
90 ∙ 1
𝑞=
4
90
𝑞=
4
𝒒 = 𝟐𝟐. 𝟓
14
Quartile
Class
𝑇ℎ𝑒 22.5𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒
2𝑛𝑑 class.
∴ 𝑻𝒉𝒆 𝑸𝒖𝒂𝒓𝒕𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟐𝒏𝒅 𝒄𝒍𝒂𝒔𝒔
(6 – 10).
𝐐𝟏
Quartile 1
Lower Boundary of Quartile
Class (Lq) = 5.5
𝑄1 = 𝐿𝑞 +
Frequency of Quartile
Class (fq ) = 16
𝑄1 = 5.5 +
Cumulative Frequency of the Class
immediately preceding the
Quartile Class (CF< ) = 14
Total Frequency (n) = 90
Class Size (c) = 5
𝑄1 = 5.5 +
kn
4 − CF
<
f𝑞
8.5
𝑄1 = 5.5 +
∙5
16
.𝑐
1 ∙ 90
4 − 14
16
𝑄1 = 5.5 + 0.53125 5
.5
22.5 − 14
.5
16
𝑄1 = 5.5 + 2.66
𝑸𝟏 = 𝟖. 𝟏𝟔
∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑸𝟏 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟖. 𝟏𝟔.
𝐐𝟑
C=5
Quartile 3
CLASSES
FREQUENCY
CF<
1-5
14
14
6-10
16
30
11-15
14
44
16-20
16
Lq= 20.5 21-25
fq = 8
CF< = 60
𝑛𝑘
𝑞=
4
90 ∙ 3
𝑞=
4
270
𝑞=
4
𝒒 = 𝟔𝟕. 𝟓
60
8
68
26-30
19
87
31-35
3
90
TOTAL
n = 90 90
Quartile
Class
𝑇ℎ𝑒 67.5𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒
5𝑡ℎ class.
∴ 𝑻𝒉𝒆 𝑸𝒖𝒂𝒓𝒕𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟓𝒕𝒉 𝒄𝒍𝒂𝒔𝒔
(21 – 25).
𝐐𝟑
Quartile 3
Lower Boundary of Quartile
Class (Lq) = 20.5
𝑄3 = 𝐿𝑞 +
Frequency of Quartile
Class (fq ) = 8
𝑄3 = 20.5 +
Cumulative Frequency of the Class
immediately preceding the
Quartile Class (CF< ) = 60
Total Frequency (n) = 90
Class Size (c) = 5
𝑄3 = 20.5 +
kn
4 − CF
<
f𝑞
7.5
𝑄3 = 20.5 +
∙5
16
.𝑐
3 ∙ 90
4 − 14
16
𝑄3 = 20.5 + 0.9375 5
.5
67.5 − 14
.5
16
𝑄3 = 20.5 + 4.69
𝑸𝟑 = 𝟐𝟓. 𝟏𝟗
∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑸𝟑 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟐𝟓. 𝟏𝟗.
𝐃𝟏
C=5
Ld = 0.5
Decile 1
CLASSES
FREQUENCY
CF< = 0
CF<
𝑛𝑘
𝑑=
10
90 ∙ 1
𝑑=
10
90
𝑑=
10
𝒅=𝟗
14 Decile Class
1-5
fd = 14 14
6-10
16
30
11-15
14
44
16-20
16
60
21-25
8
68
26-30
19
87
31-35
3
90
TOTAL
n = 90 90
𝑇ℎ𝑒 9𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒
1𝑠𝑡 class.
∴ 𝑻𝒉𝒆 𝑫𝒆𝒄𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟏𝒔𝒕 𝒄𝒍𝒂𝒔𝒔
(1 – 5).
𝐃𝟏
Decile 1
Lower Boundary of Decile
Class (Ld) = 0.5
𝐷1 = 𝐿𝑑 +
Frequency of Decile
Class (fq ) = 14
𝐷1 = 0.5 +
Cumulative Frequency of the Class
immediately preceding the Decile
Class (CF< ) = 0
Total Frequency (n) = 90
Class Size (c) = 5
𝐷1 = 0.5 +
kn
10 − CF
<
f𝑑
1 ∙ 90
10 − 0
14
9−0
.5
14
.𝑐
𝐷1 = 0.5 +
9
∙5
14
𝐷1 = 0.5 + 0.64 5
.5
𝐷1 = 0.5 + 3.21
𝑫𝟏 = 𝟑. 𝟕𝟏
∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑫𝟏 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟑. 𝟕𝟏.
𝐃𝟒
C=5
Decile 4
CLASSES
FREQUENCY
CF<
1-5
14
14
6-10
16
Ld = 10.5 11-15
fd = 14
CF< = 30
𝑛𝑘
𝑑=
10
90 ∙ 4
𝑑=
10
360
𝑑=
10
𝒅 = 𝟑𝟔
30
14
44 Decile Class
16-20
16
60
21-25
8
68
26-30
19
87
31-35
3
90
TOTAL
n = 90 90
𝑇ℎ𝑒 36𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒
3𝑟𝑑 class.
∴ 𝑻𝒉𝒆 𝑫𝒆𝒄𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟑𝒓𝒅 𝒄𝒍𝒂𝒔𝒔
(11 – 15).
𝐃𝟒
Decile 4
Lower Boundary of Decile
Class (Ld) = 10.5
𝐷4 = 𝐿𝑑 +
Frequency of Decile
Class (fq ) = 14
𝐷4 = 10.5 +
Cumulative Frequency of the Class
immediately preceding the Decile
Class (CF< ) = 30
Total Frequency (n) = 90
Class Size (c) = 5
𝐷4 = 10.5 +
kn
10 − CF
<
f𝑑
𝐷4 = 10.5 +
.𝑐
4 ∙ 90
10 − 30
14
36 − 30
.5
14
6
∙5
14
𝐷4 = 10.5 + 0.4286 5
.5
𝐷4 = 10.5 + 2.14
𝑫𝟒 = 𝟏𝟐. 𝟔𝟒
∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑫𝟒 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟏𝟐. 𝟔𝟒.
𝐃𝟖
C=5
Decile 8
CLASSES
FREQUENCY
CF<
1-5
14
14
6-10
16
30
11-15
14
44
16-20
16
60
21-25
8
Ld = 25.5 26-30
fd = 19
CF< = 68
𝑛𝑘
𝑑=
10
90 ∙ 24
𝑑=
10
720
𝑑=
10
𝒅 = 𝟕𝟐
68
19
87 Decile Class
31-35
3
90
TOTAL
n = 90 90
𝑇ℎ𝑒 72𝑛𝑑 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒
6𝑡ℎ class.
∴ 𝑻𝒉𝒆 𝑫𝒆𝒄𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟔𝒕𝒉 𝒄𝒍𝒂𝒔𝒔
(26 – 30).
𝐃𝟖
Decile 8
Lower Boundary of Decile
Class (Ld) = 25.5
𝐷8 = 𝐿𝑑 +
Frequency of Decile
Class (fq ) = 19
𝐷8 = 25.5 +
Cumulative Frequency of the Class
immediately preceding the Decile
Class (CF< ) = 68
Total Frequency (n) = 90
Class Size (c) = 5
𝐷8 = 25.5 +
kn
10 − CF
<
f𝑑
𝐷8 = 25.5 +
.𝑐
8 ∙ 90
10 − 68
19
72 − 68
.5
19
4
∙5
14
𝐷8 = 25.5 + 0.21 5
.5
𝐷8 = 25.5 + 1.05
𝑫𝟖 = 𝟐𝟔. 𝟓𝟓
∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑫𝟖 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟐𝟔. 𝟓𝟓.
𝐏𝟐𝟒
Percentile 24
CLASSES
FREQUENCY
1-5
14
Lp = 5.5 6-10
fp = 16 16
30
11-15
14
44
16-20
16
60
21-25
8
68
26-30
19
87
31-35
3
90
TOTAL
n = 90 90
C=5
CF<
CF< = 14
𝑛𝑘
𝑝=
100
90 ∙ 24
𝑝=
100
2160
𝑝=
100
𝒑 = 𝟐𝟏. 𝟔
14
Percentile
Class
𝑇ℎ𝑒 21.6𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒
2𝑛𝑑 class.
∴ 𝑻𝒉𝒆 𝑷𝒆𝒓𝒄𝒆𝒏𝒕𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟐𝒏𝒅 𝒄𝒍𝒂𝒔𝒔
(6 – 10).
𝐏𝟐𝟒
Percentile 24
Lower Boundary of Percentile
Class (Lp) = 5.5
𝑃24 = 𝐿𝑝 +
Frequency of Percentile
Class (fp ) = 16
𝑃24 = 5.5 +
Cumulative Frequency of the Class
immediately preceding the Decile
Class (CF< ) = 14
Total Frequency (n) = 90
Class Size (c) = 5
𝑃24 = 5.5 +
kn
100 − CF
<
f𝑝
𝑃24 = 5.5 +
.𝑐
24 ∙ 90
100 − 14
16
21.6 − 14
.5
16
7.6
∙5
16
𝑃24 = 5.5 + 0. 475 5
.5
𝑃24 = 5.5 + 3.38
𝑷𝟐𝟒 = 𝟕. 𝟖𝟖
∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑷𝟐𝟒 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟕. 𝟖𝟖.
𝐏𝟑𝟏
Percentile 31
CLASSES
FREQUENCY
1-5
14
Lp = 5.5 6-10
fp = 16 16
30
11-15
14
44
16-20
16
60
21-25
8
68
26-30
19
87
31-35
3
90
TOTAL
n = 90 90
C=5
CF<
CF< = 14
𝑛𝑘
𝑝=
100
90 ∙ 24
𝑝=
100
2790
𝑝=
100
𝒑 = 𝟐𝟕. 𝟗
14
Percentile
Class
𝑇ℎ𝑒 27.9𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒
2𝑛𝑑 class.
∴ 𝑻𝒉𝒆 𝑷𝒆𝒓𝒄𝒆𝒏𝒕𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟐𝒏𝒅 𝒄𝒍𝒂𝒔𝒔
(6 – 10).
𝐏𝟑𝟏
Percentile 31
Lower Boundary of Percentile
Class (Lp) = 5.5
𝑃31 = 𝐿𝑝 +
Frequency of Percentile
Class (fp ) = 16
𝑃31 = 5.5 +
Cumulative Frequency of the Class
immediately preceding the Decile
Class (CF< ) = 14
Total Frequency (n) = 90
Class Size (c) = 5
𝑃31 = 5.5 +
kn
100 − CF
<
f𝑝
𝑃31 = 5.5 +
.𝑐
31 ∙ 90
100 − 14
16
27.9 − 14
.5
16
13.9
∙5
16
𝑃31 = 5.5 + 0. 8688 5
.5
𝑃31 = 5.5 + 4.34
𝑷𝟑𝟏 = 𝟗. 𝟖𝟒
∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑷𝟑𝟏 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟗. 𝟖𝟒.
𝐏𝟒𝟒
Percentile 44
CLASSES
FREQUENCY
CF<
1-5
14
14
6-10
16
Lp = 10.5 11-15
fp = 14 14
44
16-20
16
60
21-25
8
68
26-30
19
87
31-35
3
90
TOTAL
n = 90 90
C=5
CF< = 30
𝑛𝑘
𝑝=
100
90 ∙ 44
𝑝=
100
3960
𝑝=
100
𝒑 = 𝟑𝟗. 𝟔
30
Percentile
Class
𝑇ℎ𝑒 39.6𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒
3𝑟𝑑 class.
∴ 𝑻𝒉𝒆 𝑷𝒆𝒓𝒄𝒆𝒏𝒕𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟑𝒓𝒅 𝒄𝒍𝒂𝒔𝒔
(11 – 15).
𝐏𝟒𝟒
Percentile 44
Lower Boundary of Percentile
Class (Lp) = 10.5
𝑃44 = 𝐿𝑝 +
Frequency of Percentile
Class (fp ) = 14
𝑃44 = 10.5 +
Cumulative Frequency of the Class
immediately preceding the Decile
Class (CF< ) = 30
Total Frequency (n) = 90
Class Size (c) = 5
𝑃44 = 10.5 +
kn
100 − CF
<
f𝑝
𝑃44 = 10.5 +
.𝑐
44 ∙ 90
100 − 30
14
39.6 − 30
.5
14
9.6
∙5
14
𝑃44 = 10.5 + 0. 6857 5
.5
𝑃44 = 10.5 + 3.43
𝑷𝟒𝟒 = 𝟏𝟑. 𝟗𝟑
∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑷𝟒𝟒 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟏𝟑. 𝟗𝟑.
𝐏𝟖𝟖
Percentile 88
CLASSES
FREQUENCY
CF<
1-5
14
14
6-10
16
30
11-15
14
44
16-20
16
60
21-25
8
Lp = 25.5 26-30
fp = 19 19
87
31-35
3
90
TOTAL
n = 90 90
C=5
CF< = 68
𝑛𝑘
𝑝=
100
90 ∙ 88
𝑝=
100
7920
𝑝=
100
𝒑 = 𝟕𝟗. 𝟐
68
Percentile
Class
𝑇ℎ𝑒 79.2𝑛𝑑 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒
6𝑡ℎ class.
∴ 𝑻𝒉𝒆 𝑷𝒆𝒓𝒄𝒆𝒏𝒕𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟔𝒕𝒉 𝒄𝒍𝒂𝒔𝒔
(26 – 30).
𝐏𝟖𝟖
Percentile 88
Lower Boundary of Percentile
Class (Lp) = 25.5
𝑃88 = 𝐿𝑝 +
Frequency of Percentile
Class (fp ) = 19
𝑃88 = 25.5 +
Cumulative Frequency of the Class
immediately preceding the Decile
Class (CF< ) = 68
Total Frequency (n) = 90
Class Size (c) = 5
𝑃88 = 25.5 +
kn
100 − CF
<
f𝑝
𝑃88 = 25.5 +
.𝑐
88 ∙ 90
100 − 68
19
79.2 − 68
.5
19
11.2
∙5
19
𝑃88 = 25.5 + 0.589 5
.5
𝑃88 = 25.5 + 2.95
𝑷𝟖𝟖 = 𝟐𝟖. 𝟒𝟓
∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑷𝟖𝟖 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟐𝟖. 𝟒𝟓.
𝐏𝟗𝟑
Percentile 93
CLASSES
FREQUENCY
CF<
1-5
14
14
6-10
16
30
11-15
14
44
16-20
16
60
21-25
8
Lp = 25.5 26-30
fp = 19 19
87
31-35
3
90
TOTAL
n = 90 90
C=5
CF< = 68
𝑛𝑘
𝑝=
100
93 ∙ 88
𝑝=
100
8370
𝑝=
100
𝒑 = 𝟖𝟑. 𝟕
68
Percentile
Class
𝑇ℎ𝑒 83.7𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒
6𝑡ℎ class.
∴ 𝑻𝒉𝒆 𝑷𝒆𝒓𝒄𝒆𝒏𝒕𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟔𝒕𝒉 𝒄𝒍𝒂𝒔𝒔
(26 – 30).
𝐏𝟗𝟑
Percentile 93
Lower Boundary of Percentile
Class (Lp) = 25.5
𝑃93 = 𝐿𝑝 +
Frequency of Percentile
Class (fp ) = 19
𝑃93 = 25.5 +
Cumulative Frequency of the Class
immediately preceding the Decile
Class (CF< ) = 68
Total Frequency (n) = 90
Class Size (c) = 5
𝑃93 = 25.5 +
kn
100 − CF
<
f𝑝
.𝑐
93 ∙ 90
100 − 68
19
83.7 − 68
.5
19
𝑃93
15.7
= 25.5 +
∙5
19
𝑃93 = 25.5 + 0.826 5
.5
𝑃93 = 25.5 + 4.13
𝑷𝟗𝟑 = 𝟐𝟗. 𝟔𝟑
∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑷𝟗𝟑 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟐𝟗. 𝟔𝟑.
QUARTILE DECILE PERCENTILE
𝑸𝟑 = 𝟐𝟓. 𝟏𝟗
𝑸𝟏 = 𝟖. 𝟏𝟔
𝑫𝟏 = 𝟑. 𝟕𝟏
𝑫𝟒 = 𝟏𝟐. 𝟔𝟒
𝑷𝟐𝟒 = 𝟕. 𝟖𝟖
𝑷𝟑𝟏 = 𝟗. 𝟖𝟒
𝑷𝟒𝟒 = 𝟏𝟑. 𝟗𝟑
𝑫𝟖 = 𝟐𝟔. 𝟓𝟓
𝑷𝟖𝟖 = 𝟐𝟖. 𝟒𝟓
𝑷𝟗𝟑 = 𝟐𝟗. 𝟔𝟑
𝟏
First Formula
FREQUENCY
(f)
CLASS MARK
(x)
fx
1-5
14
3
42
-13.16667
173.36120
2427.0568
6-10
16
8
128
-8.16667
66.69450
1067.112
11-15
14
13
182
-3.16667
10.02780
140.3892
16-20
16
18
288
1.83333
3.36110
53.7776
21-25
8
23
184
6.83333
46.69440
373.5552
26-30
19
28
532
11.83333
140.02770
2660.5263
CLASSES
𝒙−𝒙
𝒙−𝒙
𝟐
𝒇 𝒙−𝒙
𝟐
𝟐
𝒔𝟐 =
𝒇 𝒙−𝒙
𝒏−𝟏
𝟐
𝒔=
𝒇 𝒙−𝒙
𝒏−𝟏
𝑓𝑥
𝑛
1455
𝑥=
90
𝒙 = 𝟏𝟔. 𝟏𝟔𝟔𝟔𝟕
𝑥=
31-35
TOTAL
3
90
33
99
𝑓𝑥 = 1455
16.83333
283.36100
850.083
𝒇 𝒙−𝒙
𝟐
7772.5001
=
𝒔𝟐 =
𝑛 = 90
𝒇 𝒙−𝒙
𝒏−𝟏
𝟐
7572.5001
𝑠 =
90 − 1
2
𝑓𝑥 = 1455
𝒇 𝒙−𝒙
𝟐
= 7772.5001
𝑠2
7572.5001
=
89
𝒔𝟐 = 𝟖𝟓. 𝟎𝟖𝟒𝟐𝟕
𝒔=
𝒇 𝒙−𝒙
𝒏−𝟏
𝑠 = 85.08427
𝒔 = 𝟗. 𝟐𝟐
𝟐
𝟐
Second Formula
CLASS
FREQUENCY
(f)
CLASS MARK
(x)
fx
x2
fx2
1-5
14
3
42
9
126
6-10
16
8
128
64
1024
11-15
14
13
182
169
2366
16-20
16
18
288
324
5184
21-25
8
23
184
529
4232
26-30
19
28
532
784
14896
31-35
3
33
99
1089
3267
n=90
𝑓𝑥 = 1455
2
𝑓𝑥 = 31095
𝒔𝟐 =
𝒔=
𝒏
𝒇𝒙𝟐 − ( 𝒇𝒙)𝟐
𝒏 𝒏−𝟏
𝒏
𝒇𝒙𝟐 − ( 𝒇𝒙)𝟐
𝒏 𝒏−𝟏
𝑛 = 90
𝑓𝑥 = 1455
𝑓𝑥 2 = 31095
𝒏
𝒇𝒙𝟐 − ( 𝒇𝒙)𝟐
𝒏 𝒏−𝟏
𝒔𝟐
=
𝑠2
90 31095 − (1455)2
=
90 89
2798550 − 2117025
𝑠 =
8010
681525
2
𝑠 =
8010
𝒔=
𝒏
𝒇𝒙𝟐 − ( 𝒇𝒙)𝟐
𝒏 𝒏−𝟏
𝑠 = 85.08427
2
𝒔𝟐 = 𝟖𝟓. 𝟎𝟖𝟒𝟐𝟕
𝒔 = 𝟗. 𝟐𝟐
𝟑
Third Formula
CLASS
f
d
𝑓. 𝑑
𝑑2
𝑓. 𝑑2
1-5
14
-3
-42
9
126
6-10
16
-2
-32
4
64
11-15
14
-1
-14
1
14
16-20
16
0
0
0
0
21-25
8
1
8
1
8
26-30
19
2
38
4
76
31-35
3
3
9
9
27
TOTAL
90
𝑓. 𝑑= -33
𝑓. 𝑑 2 = 315
𝒔𝟐
=
𝒔=
𝒄𝟐
∗
𝒄𝟐 ∗
𝒏
𝒇. 𝒅𝟐 −
𝒇. 𝒅
𝒏 𝒏−𝟏
𝟐
𝒏
𝒇. 𝒅𝟐 −
𝒇. 𝒅
𝒏 𝒏−𝟏
𝟐
𝒔𝟐 = 𝒄𝟐 ∗
𝑠2
𝑛 = 90
𝑓. 𝑑 = −33
𝑓. 𝑑 2
= 315
=
52
𝒏
𝒇. 𝒅𝟐 −
𝒇. 𝒅
𝒏 𝒏−𝟏
90 315 − (−33)2
∗
90(90 − 1)
28350 − 1089
𝑠 = 25 ∗
8010
𝟐
𝒔=
𝒄𝟐
∗
27261
= 25 ∗
8010
𝑠 2 = 25 ∗ 3.403370787
𝒔𝟐 = 𝟖𝟓. 𝟎𝟖𝟒𝟐𝟕
𝒇. 𝒅𝟐 −
𝒇. 𝒅
𝒏 𝒏−𝟏
𝑠 = 85.08427
2
𝑠2
𝒏
𝒔 = 𝟗. 𝟐𝟐
𝟐
𝒔𝟐 = 𝟖𝟓. 𝟎𝟖𝟒𝟐𝟕
𝒔𝟐 = 𝟖𝟓. 𝟎𝟖𝟒𝟐𝟕
𝒔𝟐 = 𝟖𝟓. 𝟎𝟖𝟒𝟐𝟕
𝒔 = 𝟗. 𝟐𝟐
𝒔 = 𝟗. 𝟐𝟐
𝒔 = 𝟗. 𝟐𝟐
Republic of the Philippines
EULOGIO “Amang” RODRIGUEZ
INSTITUTE OF SCIENCE AND TECHNOLOGY
Nagtahan, Sampaloc, Manila
COLLEGE OF ENGINEERING
SURVEY ON CIVIL ENGINEERING STUDENTS OF EULOGIO AMANG
RODRIGUEZ INSTITUTE OF SCIENCE AND TECHNOLOGY –
MANILA CAMPUS ABOUT THEIR FAVORITE
DATE OF THE MONTH (1-31)
THE GROUP 3 PRESENTERS
CARL LESTER D. MARIÑAS
RICO D. MENDOZA
JOHN MARK R. PEDRANO
JESTER T. MIRASOL
MARK ANTHONY A. SOTTO
PRESENTED TO: MR. MARK RONOELE GONZALVO
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PADAYON!
From our Group, to Everyone: