HANOVER AND TYKE

Performance Task in
Statistics and Probability

By: Abanilla, Andrei Vaughn C.

and Benolirao, Ken Jairuz B.

FRIDAY BORCELLE
123 ANYWHERE ST.,
19 APRIL 2023 ANY CITY, ST 12345

@reallygreatsite.com www.reallygreatsite.com
 Height of Students
NAME OF STUDENT HEIGHT NAME OF STUDENT Height

ABANILLA, ANDREI VAUGHN C. 168CM ADANTE, SAMANTHA P. 155CM

AGUA, JAY MARK L. 180CM AGUILA, MIKAELAH JOY B. 162CM

AWATIN, VICTOR MERTEL C. 157CM BAUTISTA, LERIESH M. 157CM

BENOLIRAO, KEN JAIRUZ B. 173CM CABLING, ROCHELLE ERRIN A. 160CM

DELA CRUZ, JOHN EXEQUIEL A. 167CM CAPILI, JULIANE MARGILIE A. 152CM

RODILLO, JOHN JOSEPH U. 168CM DE CASTRO, CZEN CLARE R. 152CM

GALLOS, AARON MATTHEW L. 168CM DEGUITO, RACHEL MARIE T. 150CM

HERNANDEZ, BLISS SEBASTIAN G. 168CM KASILAG, NEL ANGELA I. 149CM

HORNILLA, LEMUEL JAN PIO P. 170CM LEYNES, JULIENNE NICOLE Q. 149CM

LAJARA, CLARENCE JUDIEL B. 175CM LIPA, JEANELLE ANTONIA N. 163CM

MACATANGAY, GINO SANTINO M. 167CM MACASAET, AYEISHA JILLIEN L. 164CM

MAKALINTAL, MAVERICK A. 172CM MACASAET, MARIANNE PRINCESS V. 163CM

OCAMPO, JACOB A. 165CM MACASAET, MARY ANNE P. 154CM

ORIBIANA, TRAVIS MARTY V. 170CM MOJICA, GABRIELLE ZOE R. 162CM

RODILLO, JOHN JOSEPH U. 171CM PINTOR, KLYVE CARMHEZ R. 160CM

SALVADOR, IAN HENRY V. 174CM REGLOS, MARY ANN ALTHEA A. 157CM

SANTANA, CHRISTON LEI S. 173CM SALAZAR, KHRIXIA DANICA S. 163CM

TARGA, JARED ROLAND MARK P. 167CM SALVACION, RHEIGN YSABELLE N. 168CM

VILLAPANDO, MARI ELIJAH V. 168CM SAROL, ERICA ASHLEY D. 159CM

μ=
Σx
n
=
6220
38

σ²=
= 163.68 σ=

Σ(x-m)² 2274.2112
= =
√ √ Σ(x-m)²
n
59.8477
=
2274.2112
38
= 7.7361

n 38
 Simple
Random Sampling
1. Provide the list of names of all the students in the class.
2. Input all names in an online wheel spinner.
3. Spin until you get 15.
NAME OF STUDENT HEIGHT (x) (x-m) (x-m)²

RODILLO, JOHN JOSEPH U. 171CM 5.07 25.7049

DUMDUMAYA, JOHN CLARK A. 168CM 2.07 4.2849

DE CASTRO, CZEN CLARE R. 152CM -13.93 194.0449

VILLAPANDO, MARI ELIJAH V. 168CM 2.07 4.2849

PINTOR, KLYVE CARMHEZ R. 160CM -5.93 35.1649

MACASAET, MARIANNE PRINCESS V. 163CM -2.93 8.5849

SANTANA, CHRISTON LEI S. 173CM 7.07 49.9849

BAUTISTA, LERIESH M. 157CM -8.93 79.7449

LAJARA, CLARENCE JUDIEL B. 175CM 9.07 82.2649

SALAZAR, KHRIXIA DANICA S. 163CM -2.93 8.5849

OCAMPO, JACOB A. 165CM -0.93 0.8649

HORNILLA, LEMUEL JAN PIO P. 170CM 4.07 16.5649

CABLING, ROCHELLE ERRIN A. 160CM -5.93 35.1649

AGUA, JAY MARK L. 180CM 14.07 197.9649

MACASAET, AYEISHA JILLIEN L. 164CM -1.93 3.7249

μ=
Σx
n
=
2489
15

σ²=
= 165.93 σ=

Σ(x-m)² 746.9335
= =
√ √Σ(x-m)²
n-1
53.3524
=
746.9335
14
= 7.3043

n-1 14
 Systematic
Random Sampling
1. List the names of the students in random using simple random sampling.
2. Calculate for interval using K = population size / sample size. (K = 38/15 = 2.53 or 3)
3. Determine the random start by randomly picking between 0-4 (K+1).
4. Pick students based on a certain amount of interval.
N NAME OF STUDENT N NAME OF STUDENT

1 MACASAET, AYEISHA JILLIEN L. 20 SANTANA, CHRISTON LEI S.

2 OCAMPO, JACOB A. 21 MAKALINTAL, MAVERICK A.

3 LIPA, JEANELLE ANTONIA N. 22 SALAZAR, KHRIXIA DANICA S.

4 TARGA, JARED ROLAND MARK P. 23 SALVADOR, IAN HENRY V.

5 ORIBIANA, TRAVIS MARTY V. 24 ADANTE, SAMANTHA P.

6 HERNANDEZ, BLISS SEBASTIAN G. 25 LAJARA, CLARENCE JUDIEL B.

7 SALVACION, RHEIGN YSABELLE N. 26 RODILLO, JOHN JOSEPH U.

8 BAUTISTA, LERIESH M. 27 KASILAG, NEL ANGELA I.

9 MOJICA, GABRIELLE ZOE R. 28 AGUA, JAY MARK L.

10 BENOLIRAO, KEN JAIRUZ B. 29 DUMDUMAYA, JOHN CLARK A.

11 LEYNES, JULIENNE NICOLE Q. 30 MACASAET, MARIANNE PRINCESS V.

12 REGLOS, MARY ANN ALTHEA A. 31 GALLOS, AARON MATTHEW L.

13 CAPILI, JULIANE MARGILIE A. 32 AGUILA, MIKAELAH JOY B.

14 VILLAPANDO, MARI ELIJAH V. 33 HORNILLA, LEMUEL JAN PIO P.

15 PINTOR, KLYVE CARMHEZ R. 34 DE CASTRO, CZEN CLARE R.

16 ABANILLA, ANDREI VAUGHN C. 35 DELA CRUZ, JOHN EXEQUIEL A.

17 SAROL, ERICA ASHLEY D. 36 DEGUITO, RACHEL MARIE T.

18 MACATANGAY, GINO SANTINO M. 37 AWATIN, VICTOR MERTEL C.

19 CABLING, ROCHELLE ERRIN A. 38 MACASAET, MARY ANNE P.

 Systematic
Random Sampling
NAME OF STUDENT HEIGHT (x) (x-m) (x-m)²

MACASAET, AYEISHA JILLIEN L. 164CM 1.67 2.7889

LIPA, JEANELLE ANTONIA N. 163CM 0.67 0.4489

TARGA, JARED ROLAND MARK P. 167CM 4.67 21.8089

HERNANDEZ, BLISS SEBASTIAN G. 168CM 5.67 32.1489

SALVACION, RHEIGN YSABELLE N. 168CM 5.67 32.1489

MOJICA, GABRIELLE ZOE R. 162CM -0.33 0.1089

REGLOS, MARY ANN ALTHEA A. 157CM -5.33 28.4089

PINTOR, KLYVE CARMHEZ R. 160CM -2.33 5.4289

MACATANGAY, GINO SANTINO M. 167CM 4.67 21.8089

MAKALINTAL, MAVERICK A. 172CM 9.67 93.5089

ADANTE, SAMANTHA P. 155CM -7.33 53.7289

KASILAG, NEL ANGELA I. 149CM -13.33 177.6889

MACASAET, MARIANNE PRINCESS V. 163CM 0.67 0.4489

HORNILLA, LEMUEL JAN PIO P. 170CM 7.67 58.8289

DEGUITO, RACHEL MARIE T. 150CM -12.33 152.0289

μ=
Σx
n
=
2435
15

σ²=
= 162.33

Σ(x-m)²
=
681.3335
σ=

=
√ √
Σ(x-m)²
n-1
48.6667
=
681.3335
14
= 6.9762

n-1 14
 Stratified
Random Sampling
1. Divide the class in 2 stratums (boys and girls).
2. Calculate for the 2 stratums’ sample size by dividing the population size of the
stratum and the class’ whole population.
3. Pick out the students using simple random sampling.
POPULTAION Number of students per Stratum Sample

BOYS 19 8

GIRLS 19 7

TOTAL 38 15

Boys
Boys: K = 19/38 = 7.5 or 8
Girls: K = 19/38 = 7.5 or 7
NAME OF STUDENT HEIGHT (x) (x-m) (x-m)²

ABANILLA, ANDREI VAUGHN C. 168CM -0.38 0.1444

AWATIN, VICTOR MERTEL C. 157CM -11.38 129.5044

DELA CRUZ, JOHN EXEQUIEL A. 167CM -1.38 1.9044

BENOLIRAO, KEN JAIRUZ B. 173CM 4.62 21.3444

HERNANDEZ, BLISS SEBASTIAN G. 168CM -0.38 0.1444

MACATANGAY, GINO SANTINO M. 167CM -1.38 1.9044

LAJARA, CLARENCE JUDIEL B. 175CM 6.62 43.8244

MAKALINTAL, MAVERICK A. 172CM 3.62 13.1044

μ=
Σx
n
=
1347
8

σ²=
= 168.38

Σ(x-m)²
=
σ=

211.8752
=
√ √
Σ(x-m)²
n-1
30.2679
=
211.8752
7
= 5.5016

n-1 7
 Stratified
Random Sampling
1. Divide the class in 2 stratums (boys and girls).
2. Calculate for the 2 stratums’ sample size by dividing the population size of the
stratum and the class’ whole population.
3. Pick out the students using simple random sampling.
POPULTAION Number of students per Stratum Sample

BOYS 19 8

GIRLS 19 7

TOTAL 38 15

Girls
Boys: K = 19/38 = 7.5 or 8
Girls: K = 19/38 = 7.5 or 7
NAME OF STUDENT HEIGHT (x) (x-m) (x-m)²

SALAZAR, KHRIXIA DANICA S. 163CM 5.86 34.3396

CAPILI, JULIANE MARGILIE A. 152CM -5.14 26.4196

MACASAET, MARY ANNE P. 154CM -3.14 9.8596

BAUTISTA, LERIESH M. 157CM -0.14 0.0196

MACASAET, MARIANNE PRINCESS V. 163CM 5.86 34.3396

AGUILA, MIKAELAH JOY B. 162CM 4.86 23.6196

KASILAG, NEL ANGELA I. 149CM -8.14 66.2596

μ=
Σx
n
=
1100
7

σ²=
= 157.14

Σ(x-m)²
=
σ=

194.8572
=
√ √
Σ(x-m)²
n-1
32.4762
=
194.8572
6
= 5.6988

n-1 6
 Stratified
Random Sampling
NAME OF STUDENT HEIGHT (x) (x-m) (x-m)²

ABANILLA, ANDREI VAUGHN C. 168CM 4.87 23.7169

AWATIN, VICTOR MERTEL C. 157CM -6.13 37.5769

DELA CRUZ, JOHN EXEQUIEL A. 167CM 3.87 14.9769

BENOLIRAO, KEN JAIRUZ B. 173CM 9.87 97.4169

HERNANDEZ, BLISS SEBASTIAN G. 168CM 4.87 23.7169

MACATANGAY, GINO SANTINO M. 167CM 3.87 14.9769

LAJARA, CLARENCE JUDIEL B. 175CM 11.87 140.8969

MAKALINTAL, MAVERICK A. 172CM 8.87 78.6769

SALAZAR - 163 163CM -0.13 0.0169

CAPILI - 152 152CM -11.13 123.8769

MARY ANNE - 154 154CM -9.13 83.3569

BAUTISTA - 157 157CM -6.13 37.5769

MARIANNE - 163 163CM -0.13 0.0169

AGUILA - 162 162CM -1.13 1.2769

KASILAG - 149 149CM -14.13 199.6569

μ=
Σx
n
=
2447
15

σ²=
= 163.13 σ=

Σ(x-m)² 877.7335
= =
√ √
Σ(x-m)²
n-1
62.6953
=
877.7335
14
= 7.9180

n-1 14
 Cluster
Random Sampling
1. Use the groups decided by the class officers of St. John Paul II at the start of the
school year
2. Randomly select 2 groups with the use of simple random sampling
3. List the names of the chosen students
NAME OF STUDENT HEIGHT (x) (x-m) (x-m)²

KASILAG, NEL ANGELA I. 149CM -14.13 199.6569

ABANILLA, ANDREI VAUGHN C. 168CM 4.87 23.7169

LIPA, JEANELLE ANTONIA N. 163CM -0.13 0.0169

MACASAET, MARY ANNE P. 154CM -9.13 83.3569

OCAMPO, JACOB A. 165CM 1.87 3.4969

SALVADOR, IAN HENRY V. 174CM 10.87 118.1569

VILLAPANDO, MARI ELIJAH V. 168CM 4.87 23.7169

SALVACION, RHEIGN YSABELLE N. 168CM 4.87 23.7169

CAPILI, JULIANE MARGILIE A. 152CM -11.13 123.8769

AGUILA, MIKAELAH JOY B. 162CM -1.13 1.2769

AWATIN, VICTOR MERTEL C. 157CM -6.13 37.5769

DELA CRUZ, JOHN EXEQUIEL A. 167CM 3.87 14.9769

LEYNES, JULIENNE NICOLE Q. 159CM -4.13 17.0569

ORIBIANA, TRAVIS MARTY V. 170CM 6.87 47.1969

RODILLO, JOHN JOSEPH U. 171CM 7.87 61.9369

μ=
Σx
n
=
2447
15

σ²=
= 163.13 σ=

Σ(x-m)² 779.7335
= =
√ √
Σ(x-m)²
n-1
55.6952
=
779.7335
14
= 7.4629

n-1 14
 Analysis for the Height of students of
Grade 11 - St. Pope John Paul II

Population Standard
Population mean (𝝁 )
Deviation (σ)

163.68 7.74

SAMPLING Sample Sample Standard

𝝁 − x̄ σ-s
TECHNIQUE Mean x̄ Deviation s

SIMPLE RANDOM 165.93 7.30 -2.25 0.44

SYSTEMATIC
162.33 6.98 1.35 0.77
RANDOM

STRATIFIED
163.13 7.92 0.55 -0.18
RANDOM

CLUSTER RANDOM 163.13 7.46 0.55 0.28

As seen on the table above, both stratified and cluster random sampling has
the nearest sample mean. However, stratified random sampling is the nearest
when it comes to the sample standard standard deviation. Therefore, the best
or most compatible sampling method used is Stratified Random Sampling.

Stratified and Cluster Random Sampling both have a difference of 0.55 from
sample mean to population mean. Stratified is most compatible howeever
because the difference of population standard deviation to sample standard
deviation is -0.18.
 Confidence Interval for Height
(Stratified Random Sampling)
𝝁 = 163.68 σ = 7.74
x̄ = 163.13 s = 7.92

90% 95% 99%

x̄ ± z s/√n x̄ ± z s/√n x̄ ± z s/√n
163.13 ± 1.645 7.92/√15 163.13 ± 1.96 7.92/√15 163.13 ± 2.575 7.92/√15
163.13 ± 3.69 163.13 ± 4 163.13 ± 4.62
163.13 + 3.69 = 166.82 163.13 + 4 = 167.13 163.13 + 4.62 = 167.75
163.13 - 3.69 = 159.44 163.13 - 4 = 159.13 163.13 - 4.62 = 158.51
159.44 < 𝝁 < 166.82 159.13 < 𝝁 < 167.13 158.51 < 𝝁 < 167.75

The population mean is within the range of all

90%, 95%, 99%.
Weight of the Student
of St. John Paul II
NAME OF STUDENT WEIGHT (x) NAME OF STUDENT WEIGTH (X)

ABANILLA, ANDREI VAUGHN C. 110 lbs ADANTE, SAMANTHA A. 106 lbs

AGUA, JAY MARK L. 152 lbs AGUILA, MIKAELAH JOY B. 94 lbs

AWATIN, VICTOR MERTELC. 102 lbs BAUTISTA, LERIESH M. 88 lbs

BENOLIRAO, KEN JAIRUZ B. 106 lbs CABLING, ROCHELLE ERRIN A. 110 lbs

DELA CRUZ, JOHN EXEQUIEL A. 116 lbs CAPILI, JULIANE MARGILIE A. 95 lbs

DUMDUMAYA, JOHN CLARK A. 110 lbs DE CASTRO, CZEN CLARE R. 115 lbs

GALLOS, AARON MATTHEW L 121 lbs DEGUITO, RACHEL MARIE T. 99 lbs

HERNANDEZ, BLISS SEBASTIAN G. 104 lbs KASILAG, NEL ANGELA I. 115 lbs

HORNILLA, LEMUEL JAN PIO P. 146 lbs LEYNES, JULIENNE NICOLE Q. 84 lbs

LAJARA, CLARENCE JUDIEL B. 148 lbs LIPA, JEANELLE ANTONIA N. 115 lbs

MACATANGAY, GINO SANTINO M. 145 lbs MACASAET, AYEISHA L. 95 lbs

MAKALINTAL, MAVERICK A. 175 lbs MACASAET, MARIANNE V. 99 lbs

OCAMPO, JACOB A. 132 lbs MACASAET, MARY ANNE P. 143 lbs

ORIBIANA, TRAVIS MARTY V. 134 lbs MOJICA, GABRIELLE ZOE R. 132 lbs

RODILLO, JOHN JOSEPH U. 161 lbs PINTOR, KLYVE CARMHEZ R. 129 lbs

SANTANA, CHRISTON LEI S. 134 lbs REGLOS, ALTHEA A. 97 lbs

SALVADOR, IAN HENRY 105 lbs SALAZAR, KHRIXIA S. 105 lbs

TARGA, JARED ROLAND MARK P. 146 lbs SALVACION, RHEIGN N. 168 lbs

VILLAPANDO, MARI ELIJAH V. 137 lbs SAROL, ERICA ASHLEY D. 117 lbs

μ=
Σx
n
= 120.79

σ²=
Σ(x-m)²
σ=

= 521.8504
√ Σ(x-m)²
n
= 22.8440

n
 Simple
Random Sampling
1. Go to Google and search for something that will help you randomly pick a name.
For example is a spinning wheel.
2. Encode all the names of the student from 11 - St. John Paul II in the spinning wheel
3. Spin the wheel until you reach the desired sample size which is 15.
NAME OF STUDENT WEIGHT (x) (x-x) (x-x)²

DEGUITO, RACHEL MARIE T. 99 -18.47 341.1409

RODILLO, JOHN JOSEPH U. 161 43.53 1894.8609

LAJARA, CLARENCE JUDIEL B. 148 30.53 932.0809

BAUTISTA, LERIESH M. 88 -29.47 868.4809

VILLAPANDO, MARI ELIJAH V. 137 19.53 381.4209

LEYNES, JULIENNE NICOLE Q. 84 -33.47 1120.2409

CABLING, ROCHELLE ERRIN A. 110 -7.47 55.8009

HERNANDEZ, BLISS SEBASTIAN G. 104 -13.47 181.4409

BENOLIRAO, KEN JAIRUZ B. 106 -11.47 131.5609

ABANILLA, ANDREI VAUGHN C. 110 -7.47 55.8009

MACASAET, MARIANNE V. 99 -18.47 341.1409

SALAZAR, KHRIXIA S. 105 -12.47 155.5009

GALLOS, AARON MATTHEW L 121 3.53 12.4609

KASILAG, NEL ANGELA I. 115 -2.47 6.1009

MAKALINTAL, MAVERICK A. 175 57.53 3309.7009

μ=
Σx
n
=
1762
15

σ²=
= 117.47 σ=

Σ(x-m)² 9787.7335
= =
√ √
Σ(x-m)²
n-1

686.8381
=
9787.7335
14
= 26.2075

n-1 14
 Systematic
Random Sampling
1. Create a sample frame.
2. Arrange the Names in no particular order.
3.Determine the sampling interval k. K = population size / sample size. (K = 38/15 =
2.53 or 3)
4. Lastly, pick the students based on the calculated interval.
NAME OF STUDENT WEIGHT (x) NAME OF STUDENT WEIGTH (X)

ABANILLA, ANDREI VAUGHN C. 110 lbs ADANTE, SAMANTHA A. 106 lbs

AGUA, JAY MARK L. 152 lbs AGUILA, MIKAELAH JOY B. 94 lbs

AWATIN, VICTOR MERTELC. 102 lbs BAUTISTA, LERIESH M. 88 lbs

BENOLIRAO, KEN JAIRUZ B. 106 lbs CABLING, ROCHELLE ERRIN A. 110 lbs

DELA CRUZ, JOHN EXEQUIEL A. 116 lbs CAPILI, JULIANE MARGILIE A. 95 lbs

DUMDUMAYA, JOHN CLARK A. 110 lbs DE CASTRO, CZEN CLARE R. 115 lbs

GALLOS, AARON MATTHEW L 121 lbs DEGUITO, RACHEL MARIE T. 99 lbs

HERNANDEZ, BLISS SEBASTIAN G. 104 lbs KASILAG, NEL ANGELA I. 115 lbs

HORNILLA, LEMUEL JAN PIO P. 146 lbs LEYNES, JULIENNE NICOLE Q. 84 lbs

LAJARA, CLARENCE JUDIEL B. 148 lbs LIPA, JEANELLE ANTONIA N. 115 lbs

MACATANGAY, GINO SANTINO M. 145 lbs MACASAET, AYEISHA L. 95 lbs

MAKALINTAL, MAVERICK A. 175 lbs MACASAET, MARIANNE V. 99 lbs

OCAMPO, JACOB A. 132 lbs MACASAET, MARY ANNE P. 143 lbs

ORIBIANA, TRAVIS MARTY V. 134 lbs MOJICA, GABRIELLE ZOE R. 132 lbs

RODILLO, JOHN JOSEPH U. 161 lbs PINTOR, KLYVE CARMHEZ R. 129 lbs

SANTANA, CHRISTON LEI S. 134 lbs REGLOS, ALTHEA A. 97 lbs

SALVADOR, IAN HENRY 105 lbs SALAZAR, KHRIXIA S. 105 lbs

TARGA, JARED ROLAND MARK P. 146 lbs SALVACION, RHEIGN N. 168 lbs

VILLAPANDO, MARI ELIJAH V. 137 lbs SAROL, ERICA ASHLEY D. 117 lbs
 Systematic
Random Sampling
NAME OF STUDENT WEIGHT (x) (x-x) (x-x)²

AWATIN, VICTOR MERTELC. 102 -18.87 356.0769

DUMDUMAYA, JOHN CLARK A. 110 -10.87 118.1569

HORNILLA, LEMUEL JAN PIO P. 146 25.13 631.5169

MAKALINTAL, MAVERICK A. 175 54.13 2930.0569

RODILLO, JOHN JOSEPH U. 161 40.13 1610.4169

TARGA, JARED ROLAND MARK P. 146 25.13 631.5169

AGUILA, MIKAELAH JOY B. 94 -26.87 721.9969

CAPILI, JULIANE MARGILIE A. 95 -25.87 669.2569

KASILAG, NEL ANGELA I. 115 -5.87 34.4569

MACASAET, AYEISHA L. 95 -25.87 669.2569

MOJICA, GABRIELLE ZOE R. 132 11.13 123.8769

SALAZAR, KHRIXIA S. 105 -15.87 251.8569

ABANILLA, ANDREI VAUGHN C. 110 -10.87 118.1569

BENOLIRAO, KEN JAIRUZ B. 106 -14.87 221.1169

GALLOS, AARON MATTHEW L. 121 0.13 0.0169

μ=
Σx
n
=
1813
15

σ²=
= 120.87 σ=

Σ(x-m)² 9087.7335
= =
√ √
Σ(x-m)²
n-1

649.1238
=
9087.7335
14
= 25.4779

n-1 14
 Stratified
Random Sampling
1. Divide the class in 2 stratums (boys and girls).
2. Calculate for the 2 stratums’ sample size by dividing the population size of the
stratum and the class’ whole population.
3. Pick out the students using simple random sampling.
POPULTAION Number of students per Stratum Sample

BOYS 19 8

GIRLS 19 7

TOTAL 38 15

Boys
Boys: K = 19/38 = 7.5 or 8
Girls: K = 19/38 = 7.5 or 7

NAME WEIGHT (x) (x-x) (x-x)²

AWATIN, VICTOR MERTELC. 102 -33.63 1130.9769

DELA CRUZ, JOHN EXEQUIEL A. 116 -19.63 385.3369

GALLOS, AARON MATTHEW L 121 -14.63 214.0369

HORNILLA, LEMUEL JAN PIO P. 146 10.37 107.5369

MACATANGAY, GINO SANTINO M. 145 9.37 87.7969

MAKALINTAL, MAVERICK A. 175 39.37 1549.9969

ORIBIANA, TRAVIS MARTY V. 134 -1.63 2.6569

TARGA, JARED ROLAND MARK P. 146 10.37 107.5369

μ=
Σx
n
=
1085
8

σ²=
= 135.63

Σ(x-m)² 3585.8752
=
σ=

=
√ √
Σ(x-m)²
n-1

512.2679
=
3585.8752
7
= 22.6333

n-1 7
 Stratified
Random Sampling
1. Divide the class in 2 stratums (boys and girls).
2. Calculate for the 2 stratums’ sample size by dividing the population size of the
stratum and the class’ whole population.
3. Pick out the students using simple random sampling.
POPULTAION Number of students per Stratum Sample

BOYS 19 8

GIRLS 19 7

TOTAL 38 15

Girls
Boys: K = 19/38 = 7.5 or 8
Girls: K = 19/38 = 7.5 or 7

NAME WEIGHT (x) (x-x) (x-x)²

BAUTISTA, LERIESH M. 88 -16 256

CABLING, ROCHELLE ERRIN A. 110 6 36

DEGUITO, RACHEL MARIE T. 99 -5 25

LEYNES, JULIENNE NICOLE Q. 84 -20 400

MACASAET, MARIANNE V. 99 -5 25

MACASAET, MARY ANNE P. 143 39 1521

SALAZAR, KHRIXIA S. 105 1 1

μ=
Σx
n
=
728
7

σ²=
=

Σ(x-m)²
104

=
2264
σ=

=
√ √
Σ(x-m)²
n-1

377.3333
=
2264
6
= 19.4251

n-1 6
 Stratified
Random Sampling
NAME OF STUDENT WEIGHT (x) (x-x) (x-x)²

AWATIN, VICTOR MERTELC. 102 -18.87 356.0769

DELA CRUZ, JOHN EXEQUIEL A. 116 -4.87 23.7169

GALLOS, AARON MATTHEW L 121 0.13 0.0169

HORNILLA, LEMUEL JAN PIO P. 146 25.13 631.5169

MACATANGAY, GINO SANTINO M. 145 24.13 582.2569

MAKALINTAL, MAVERICK A. 175 54.13 2930.0569

ORIBIANA, TRAVIS MARTY V. 134 13.13 172.3969

TARGA, JARED ROLAND MARK P. 146 25.13 631.5169

BAUTISTA, LERIESH M. 88 -32.87 1080.4369

CABLING, ROCHELLE ERRIN A. 110 -10.87 118.1569

DEGUITO, RACHEL MARIE T. 99 -21.87 478.2969

LEYNES, JULIENNE NICOLE Q. 84 -36.87 1359.3969

MACASAET, MARIANNE V. 99 -21.87 478.2969

MACASAET, MARY ANNE P. 143 22.13 489.7369

SALAZAR, KHRIXIA S. 105 -15.87 251.8569

μ=
Σx
n
=
1813
15

σ²=
= 120.87 σ=

Σ(x-m)² 9583.7335
= =
√ √
Σ(x-m)²
n-1

684.5524
=
9583.7335
14
= 26.1640

n-1 14
 Cluster
Random Sampling
1. Use the Houses that the teacher made when the school year started.
2. Randomly choose 2 Houses from the 5 Houses using siple random sampling.
3. List the names of the chosen students.
NAME OF STUDENT WEIGHT (x) (x-x) (x-x)²

LEYNES, JULIENNE NICOLE Q. 84 -31.93 1019.5249

BENOLIRAO, KEN JAIRUZ B. 106 -9.93 98.6049

DEGUITO, RACHEL MARIE T. 99 -16.93 286.6249

MACASAET, MARY ANNE P. 132 16.07 258.2449

VILLAPANDO, MARI ELIJAH V. 137 21.07 443.9449

GALLOS, AARON MATTHEW L 121 5.07 25.7049

ORIBIANA, TRAVIS MARTY V. 134 18.07 326.5249

MACATANGAY, GINO SANTINO M. 145 29.07 845.0649

SALAZAR, KHRIXIA S. 105 -10.93 119.4649

AGUA, JAY MARK L. 152 36.07 1301.0449

MACASAET, AYEISHA L. 95 -20.93 438.0649

SANTANA, CHRISTON LEI S. 134 18.07 326.5249

ABANILLA, ANDREI VAUGHN C. 110 -5.93 35.1649

BAUTISTA, LERIESH M. 88 -27.93 780.0849

REGLOS, ALTHEA A. 97 -18.93 358.3449

μ=
Σx
n
=
1739
15

σ²=
= 117.13 σ=

Σ(x-m)² 6662.9335
= =
√ √
Σ(x-m)²
n-1

475.9238
=
6662.9335
14
= 21.8157

n-1 14
 Analysis for the Weight of students of
Grade 11 - St. Pope John Paul II

Population Standard
Population mean (𝝁 )
Deviation (σ)

120.79 22.84

SAMPLING Sample Sample Standard

𝝁 − x̄ σ-s
TECHNIQUE Mean x̄ Deviation s

SIMPLE RANDOM 117.47 26.21 3.32 -3.37

SYSTEMATIC
120.87 25.48 -0.08 -2.64
RANDOM

STRATIFIED
1̀20.87 26.16 -0.08 -3.32
RANDOM

CLUSTER RANDOM 117.13 21.82 3.66 1.02

Base on the table above, we can see that both Systematic and Stratified
Random Sampling are the closest to the sample mean. But the systematic is
closer than systematic when it comes to sample standard deviation. In
conclusion, Systematic Random sampling is the most compatible to use.

Systematic and Stratified Random Sampling both have a difference of -0.08

from sample mean to population mean. Systematic is most compatible
howeever because the difference of population standard deviation to sample
standard deviation is -2.64.
 Confidence Interval for Weight
(Systematic Random Sampling)
𝝁 = 120.79 σ = 22.84
x̄ = 120.87 s = 25.48

90% 95% 99%

x̄ ± z s/√n x̄ ± z s/√n x̄ ± z s/√n
120.87 ± 1.645 (25.48/√15) 120.87 ± 1.96 (25.48/√15) 120.87 ± 2.575 25.48/√15
120.87 ± 10.82 120.87 ± 12.89 120.87 ± 16.94
120.87 + 10.82 = 131.69 120.87 + 12.89 = 133.76 120.87 + 16.94 = 137.81
120.87 - 10.82 = 110.05 120.87 - 12.89 = 107.98 120.87 - 16.94 = 103.93
110.05 < 𝝁 < 131.69 107.98 < 𝝁 < 133.76 103.93 < 𝝁 < 137.81

The population mean is within the range of all

90%, 95%, 99%.