“Paper Dispenser in Every Building in TUP-T”A PROJECT PROPOSAL: DATA AND ANALYSIS

BY GROUP 6

Introduction Paper is vital thing for our college life. It might not be an exaggeration to say that your whole college life is written in a piece of paper.

For sure, some time in your daily college life, you were given a vital activity or exam, and you noticed that you don’t have your “gun”; you don’t have a paper. Now you’ll need to excuse yourself to buy some in the Business Center. The problem is, it’s a couple of minutes’ walk from your current position. Now, you have already lost some of your valuable time which you should’ve spent doing the activity rather than walking with face full of anxiety.

This project, the Paper Dispenser in Every Building in TUP-T, aims to reduce the hassle of going to the Business Center every time they need a paper in the middle of the class. Because not every building is close to the business center, this project will save the students some time, giving them more time for their class, thus making them more efficient and more productive.

Research Background Type of Data: Primary Data – By Interview

Sampling Technique Used: Probability Sampling – Cluster Sampling ◦ 33 students per year, excluding 4th year and Ladderized students.◦ Total of 99 respondents

The questionnaire we distributed consisted of questions about the frequency of their use of paper, whether it is convenient to rush down to the business center for papers or not, and whether the idea of paper dispenser will be a benefit to the students or not.

We also have a supporting question which was not included in the questionnaire:

*Supporting Question (Not included in the actual questionnaire):

How many Yellow Paper and Bond Paper do you consume weekly?

Data and AnalysisNOMINAL DATA

Data and Analysis – Nominal Data  First Year Second Year Third Year Total

How often do you use paper in school?

ALWAYS 25 20 26 71

SOMETIMES 8 13 7 28

TOTAL 33 33 33 99

 

Is it convenient to rush down to the business for paper?

YES 10 11 17 38

NO 19 17 11 47

NEUTRAL 4 5 5 14

TOTAL 33 33 33 99

 

Will the students of TUP-T benefit in a Paper Dispenser?

YES 29 26 20 75

MAYBE 4 5 12 21

NO 0 2 1 3

TOTAL 33 33 33 99

Data and Analysis When asked the frequency of their paper consumption, 71 (25 first years, 20 second years, 26 third years) answered ALWAYS (72%), 28 (8 first years, 13 second years, 7 third years) answered SOMETIMES (28%).

Always Sometimes0

10

20

30

40

50

60

70

80

How often do you use paper in school?

First Year Second Year Third Year

Data and Analysis With regards to whether they consider going down the business center for papers as convenient, 38 students (10 first years, 11 second years, 17 third years) said “Yes” (38%), 47 students (19 first years, 17 second years, 11 third years) said “No” (47%), 14 students (4 first years, 5 second years, 5 third years) said “It, doesn’t matter” (14%).

Yes No Neutral0

5

10

15

20

25

30

35

40

45

50

Is it convenient to rush down to the business for paper?

First Years Second Years Third Years

Data and Analysis When we asked them their favor for the idea of a Paper Dispenser, 75 students (29 first years, 26 second years, 20 third years) gave a positive response (76%), 21 (4 first years, 5 second years, 12 third years) gave a neutral response (21%), 3 students (0 first years, 2 second years, 1 third year) gave a negative response (3%).

Yes Maybe No0

10

20

30

40

50

60

70

80

Will the students of TUP-T benefit in a Paper Dispenser?

First Year Second Year Third Year

Data and AnalysisNUMERICAL DATA

Data and Analysis- Numerical Data

Still having the same number of respondents, we obtained the following results:

   I. First Year

Bond Paper

LIMIT BOUNDARY FREQUENCY (No. of Students)

R.F. PERCENTAGE

0 – 5  0 – 5.5 11 0.333 33.3%

6 – 11  5.5 – 11.5 11 0.333 33.3%

12 – 17  11.5 – 17.5 2 0.060 6%

18 – 23  17.5 – 23.5 1 0.031 3.1%

24 – 29  23.5 – 29.5 1 0.031 3.1%

30 – 35  29.5 – 35.5 7 0.212 21.2%

TOTAL 33 1 100%

Data and Analysis- Numerical Data

I. First Year

Yellow Paper

LIMIT BOUNDARY FREQUENCY (No. of Students)

R.F. PERCENTAGE

0 – 6 0 – 6.5 8 0.242 24.2%

7 – 13  6.5 – 13.5 8 0.242 24.2%

14 – 20 13.5 – 20.5 10 0.303 30.3%

20 – 26 19.5 – 26.5 5 0.151 15.1%

27 – 33  26.5 – 33.5 0 0.000 0%

34 – 40  33.5 – 40.5 2 0.061 6.1%

TOTAL 33 1 100%

Data and Analysis- Numerical Data

I. Second Year

Bond Paper

LIMIT BOUNDARY FREQUENCY (No. of Students)

R.F. PERCENTAGE

0 – 5  0 – 5.5 7 0.212 21.2%

6 – 11  5.5 – 11.5 17 0.515 51.5%

12 – 17  11.5 – 17.5 6 0.182 18.2%

18 – 23 17.5 – 23.5 0 0 0%

24 – 29 23.5 – 29.5 0 0 0%

30 – 35 29.5 – 35.5 3 0.091 9.1%

TOTAL 33 1 100%

Data and Analysis- Numerical Data

I. Second Year

Yellow Paper

LIMIT BOUNDARY FREQUENCY (No. of Students)

R.F. PERCENTAGE

0 – 6  0 – 6.5 8 0.242 24.2%

7 – 13  6.5 – 13.5 11 0.333 33.3%

14 – 20  13.5 – 20.5 9 0.273 27.3%

21 – 27 20.5 – 27.5 2 0.061 6.1%

28 – 34 27.5 – 34.5 1 0.030 3.0%

35 – 41 34.5 – 41.5 2 0.061 6.1%

TOTAL 33 1 100%

Data and Analysis- Numerical Data

I. Third Year

Bond Paper

LIMIT BOUNDARY FREQUENCY (No. of Students)

R.F. PERCENTAGE

0 – 2  0 – 2.5 3 0.091 9.1%

3 – 5 2.5 – 5.5 5 0.151 15.1%

6 – 8  5.5 – 8.5 9 0.273 27.3%

9 – 11  8.5 – 11.5 6 0.182 18.2%

12 – 14 11.5 – 14.5 6 0.182 18.2%

15 – 17 14.5 – 17.5 4 0.121 12.1%

TOTAL 33 1 100%

Data and Analysis- Numerical Data

I. Third Year

Yellow Paper

LIMIT BOUNDARY FREQUENCY (No. Of Students)

R.F. PERCENTAGE

0 – 1 0 – 1.5 4 0.121 12.1%

2 – 3 1.5 – 3.5 9 0.273 27.3%

4 – 5  3.5 – 5.5 5 0.151 15.1%

6 – 7 5.5 – 7.5 4 0.121 12.1%

8 – 9  7.5 – 9.5 5 0.151 15.1%

10 – 11 9.5 – 11.5 5 0.151 15.1%

12 – 13 11.5 – 13.5 1 0.030 3.0%

TOTAL 33 1 100%

Data and Analysis- Numerical Data

I. Overall

Bond Paper

LIMIT BOUNDARY FREQUENCY (No. of Students)

R.F. PERCENTAGE

0 – 4 0 – 4.5 13 0.131 13.1%

5 – 9  4.5 – 9.5 40 0.405 40.5%

10 – 14 9.5 – 14.5 24 0.242 24.2%

15 – 19 14.5 – 19.5 10 0.101 10.1%

20 – 24 19.5 – 24.5 2 0.020 2.0%

25 – 29  24.5 – 29.5 0 0.000 0%

30 – 34 29.5 – 34.5 9 0.091 9.1%

35 – 39 34.5 – 39.5 1 0.010 1.0%

TOTAL 99 1 100%

Data and Analysis- Numerical Data

I. Overall

Yellow Paper

LIMIT BOUNDARY FREQUENCY (No. of Students)

R.F. PERCENTAGE

0 – 4 0 – 4.5 23 0.232 23.2%

5 – 9 4.5 – 9.5 26 0.263 26.3%

10 – 14  9.5 – 14.5 19 0.192 19.2%

15 – 19 14.5 – 19.5 10 0.101 10.1%

20 – 24 19.5 – 24.5 10 0.101 10.1%

25 – 29  24.5 – 29.5 6 0.061 6.1%

30 – 34 29.5 – 34.5 1 0.010 1.0%

35 – 39 34.5 – 39.5 1 0.010 1.0%

40 – 44  39.5 – 44.5 3 0.030 3.0%

TOTAL 99 1 100%

Mean, Median, Mode

FIRST YEARBOND PAPER

LIMIT BOUNDARY Class Midpoint (x) FREQUENCY (No. of Students)

f(x) CF<

0 – 5  0 – 5.5 27.5 11 2.5 11

6 – 11  5.5 – 11.5 93.5 11 8.5 22

12 – 17  11.5 – 17.5 29 2 14.5 24

18 – 23  17.5 – 23.5 20.5 1 20.5 25

24 – 29  23.5 – 29.5 26.5 1 26.5 26

30 – 35  29.5 – 35.5 32.5 7 227.5 33

TOTAL 33 424.5

FIRST YEARMEAN: 

MEDIAN: 

MODE: 

YELLOW PAPER

LIMIT BOUNDARY Class Midpoint (x) FREQUENCY (No. of Students)

f(x) CF<

0 – 6 0 – 6.5 3 8 24 8

7 – 13  6.5 – 13.5 10 8 80 16

14 – 20 13.5 – 20.5 17 10 170 26

20 – 26 19.5 – 26.5 23 5 115 31

27 – 33  26.5 – 33.5 30 0 0 31

34 – 40  33.5 – 40.5 37 2 74 33

TOTAL 33 463

MEAN: 

MEDIAN: 

MODE: 

SECOND YEARBOND PAPER

LIMIT BOUNDARY Class Midpoint (x) FREQUENCY (No. of Students)

f(x) CF<

0 – 5  0 – 5.5 2.5 7 17.5 7

6 – 11  5.5 – 11.5 8.5 17 144.5 24

12 – 17  11.5 – 17.5 14.5 6 87 30

18 – 23 17.5 – 23.5 20.5 0 0 30

24 – 29 23.5 – 29.5 26.5 0 0 30

30 – 35 29.5 – 35.5 32.5 3 97.5 33

TOTAL 33 346.5

MEAN: 

MEDIAN: 

MODE: 

YELLOW PAPER

LIMIT BOUNDARY Class Midpoint (x) FREQUENCY (No. of Students)

f(x) CF<

0 – 6  0 – 6.5 3 8 24 8

7 – 13  6.5 – 13.5 10 11 110 19

14 – 20  13.5 – 20.5 17 9 153 28

21 – 27 20.5 – 27.5 24 2 48 30

28 – 34 27.5 – 34.5 31 1 31 31

35 – 41 34.5 – 41.5 38 2 76 33

TOTAL 33 442

MEAN: 

MEDIAN: 

MODE: 

THIRD YEARBOND PAPER

LIMIT BOUNDARY Class Midpoint (x) FREQUENCY (No. of Students)

f(x) CF<

0 – 2  0 – 2.5 1 3 3 3

3 – 5 2.5 – 5.5 4 5 20 8

6 – 8  5.5 – 8.5 7 9 63 17

9 – 11  8.5 – 11.5 10 6 60 23

12 – 14 11.5 – 14.5 13 6 78 29

15 – 17 14.5 – 17.5 16 4 64 33

TOTAL 33 288

MEAN: 

MEDIAN: 

MODE: 

YELLOW PAPER

LIMIT BOUNDARY Class Midpoint (x) FREQUENCY (No. Of Students)

f(x) CF<

0 – 1 0 – 1.5 0.5 4 2 4

2 – 3 1.5 – 3.5 2.5 9 22.5 13

4 – 5  3.5 – 5.5 4.5 5 22.5 18

6 – 7 5.5 – 7.5 6.5 4 26 22

8 – 9  7.5 – 9.5 8.5 5 42.5 27

10 – 11 9.5 – 11.5 10.5 5 52.5 32

12 – 13 11.5 – 13.5 12.5 1 12.5 33

TOTAL 33 180.5

MEAN: 

MEDIAN: 

MODE: 

OVERALLBOND PAPER

LIMIT BOUNDARY Class Midpoint (x) FREQUENCY (No. of Students)

f(x) CF< 

0 – 4 0 – 4.5 2 13 26 13

5 – 9  4.5 – 9.5 7 40 280 53

10 – 14 9.5 – 14.5 12 24 288 77

15 – 19 14.5 – 19.5 17 10 170 87

20 – 24 19.5 – 24.5 22 2 44 89

25 – 29  24.5 – 29.5 27 0 0 89

30 – 34 29.5 – 34.5 32 9 288 98

35 – 39 34.5 – 39.5 37 1 37 99

TOTAL 99 1133

MEAN: 

MEDIAN: 

MODE: 

YELLOW PAPER

LIMIT BOUNDARY Class Midpoint (x) FREQUENCY (No. of Students)

f(x) CF<

0 – 4 0 – 4.5 2 23 46 23

5 – 9 4.5 – 9.5 7 26 182 49

10 – 14  9.5 – 14.5 12 19 228 68

15 – 19 14.5 – 19.5 17 10 170 78

20 – 24 19.5 – 24.5 22 10 220 88

25 – 29  24.5 – 29.5 27 6 162 94

30 – 34 29.5 – 34.5 32 1 32 95

35 – 39 34.5 – 39.5 37 1 37 96

40 – 44  39.5 – 44.5 42 3 126 99

TOTAL 99 1203

MEAN: 

MEDIAN: 

MODE: 

Percentile, Decile, Quartile

FIRST YEARBOND PAPER

PERCENTILE: 

DECILE: 

QUARTIEL: 

YELLOW PAPER

PERCENTILE: 

DECILE: 

QUARTIEL: 

SECOND YEARBOND PAPER

PERCENTILE: 

DECILE: 

QUARTIEL: 

YELLOW PAPER 

PERCENTILE: 

DECILE: 

QUARTIEL: 

Variance, Standard Deviation and Z Score

INTRODUCTIONThe variance is a numerical value used to indicate how widely individuals

in a group vary. If individual observations vary greatly from the group mean, the variance is big; and vice versa. It is important to distinguish between the variance of a population and the variance of a sample. They have different notation, and they are computed differently. The variance of a population is denoted by σ2; and the variance of a sample, by s2.

Continuation

Standard Deviation (SD) is the measure of spread of the numbers in a set of data from its mean value. Also called as SD, Standard Deviations symbol σ (sigma). This can also be said as a measure of variability or volatility in the given set of data.

A Z-Score is a statistical measurement of a score's relationship to the mean in a group of scores. A Z-score of 0 means the score is the same as the mean. A Z-score can also be positive or negative, indicating whether it is above or below the mean and by how many standard deviations.

DATA ANALYSISUsing the data table we made using the Amount of Bond Paper used by a

student in a week and the Amount of Yellow Paper used by the same student, we created a table showing the usage of bond paper and yellow paper.

Class x frequency fx x-x' (x-x')^2 f(x-x')^2 zscore=(x-mean)/sd

0 – 4 2 13 26 -9.44 89.11 1158.43 -1.12

5 – 9 7 40 280 -4.44 19.71 788.4 -.53

10 – 14 12 24 288 0.56 0.31 7.44 .7

15 – 19 17 10 170 5.56 30.91 309.1 .66

20 – 24 22 2 44 10.56 111.51 223.02 1.25

25 – 29 27 0 0 15.56 242.11 0 1.85

30 – 34 32 9 288 20.56 422.71 3804.39 2.44

35 – 39 37 1 37 25.56 653.31 653.31 3.04

Total 99 1133

6944.09 8.29

BONDPAPER

BOND PAPER (continuation)

MEAN 1133/99 11.44

VARIANCE 6944.09/99-1 70.86

SD sqrt of variance 8.42

YELLOW PAPERClass x frequency fx x-x' (x-x')^2 f(x-x')^2 zscore=(x-mean)/sd

0 – 4 2 23 46 -10.15 103.02 2369.46 -1.045 – 9 7 26 182 -5.15 26.52 689.52 -.53

10 – 14  12 19 228 -0.15 0.0225 0.4275 -0.0215 – 19 17 10 170 4.85 23.52 235.2 0.5020 – 24 22 10 220 9.85 97.02 970.2 1.0125 – 29  27 6 162 14.85 220.52 1323.12 1.5330 – 34 32 1 32 19.85 394.02 394.02 2.0435 – 39 37 1 37 24.85 617.52 617.52 2.5540 – 44  42 3 126 29.85 891.02 2673.06 3.07

Total 99 1203 103.02 9272.528 9.11

YELLOW PAPER (continuation)

MEAN 1203/99 12.15

VARIANCE 9272.528/99-1 94.62

SD sqrt of variance 9.73

GRAPHBOND PAPER

0 – 4 5 – 9 10 – 14 15 – 19 20 – 24 25 – 29 30 – 34 35 – 39

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

-1.04

-0.53

-0.02

0.5

1.01

1.53

2.04

2.55

Series1

GRAPHYELLOW PAPER

0 – 4 5 – 9 10 – 14 15 – 19 20 – 24 25 – 29 30 – 34 35 – 39 40 – 44

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Series1

Regression and Correlation

Introduction

Correlation Regression

CORRELATION-> measure of linear association between two variables-> strength of the relationship->r = -1 (perfectly related in a positive linear sense) to +1 (perfectly

related in a negative linear sense) -> r = 0 (No relationship; independent)

Introduction Regression

-> analysis involves identifying the relationship between a dependent variable and one or more independent variables

-> predicting the unknown value of a variable from the known value of another variable.

In this analysis:-> two sets of data :

Amount of Bond Paper; Amount of Yellow Paper

Scatter Diagram

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

f(x) = − 0.544033325291186 x + 16.7029495860005

SCATTER DIAGRAM OF YELLOW PAPER VS BOND PAPER IN ALL YEARS

BOND PAPER USED PER WEEK

YELL

OW

PAP

ER U

SED

PER

WEE

K

Correlation Analysis Pearson’s correlation coefficient formula

Regression Analysis

Bond Paper used per week -> independent variable Yellow Paper used per week -> dependent variable.

Provided by the trendline in the scatter diagram:◦ y-intercept is 16.703 ( )◦ slope is -0.544 ( )

Scatter Diagram

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

f(x) = − 0.544033325291186 x + 16.7029495860005

SCATTER DIAGRAM OF YELLOW PAPER VS BOND PAPER IN ALL YEARS

BOND PAPER USED PER WEEK

YELL

OW

PAP

ER U

SED

PER

WEE

K

Regression Analysis

Then, we can predict the value of Y or the Yellow Paper usage of a student in a week using the formula:

SSR -  (measure of explained variation) sum of the squared differences between the prediction for each observation and the population mean.

Regression Analysis SSE – (measure of unexplained variation ) A least squares regression selects the line with the lowest total sum of squared prediction errors.

Total Variation

Coefficient of Determination ( ) - The proportion of total variation (SST) that is explained by the regression (SSR)

Standard Error - a measure of its variability.

T – Test and ANOVA

Introduction T – TEST

◦ Comparing the means of two samples◦ Compares the actual difference between two means in relation to the

variation in the data. ◦ A one-sample location test of whether the mean of a population has a value

specified in a null hypothesis.◦ t value formula :

ANOVA◦ a collection of statistical models used to analyze the differences among group means.◦ Statistical test of whether or not the means of several groups are equal.◦ Useful for comparing three or more means for statistical significance.

T-Test Analysis◦ In this analysis:

◦ We have two sets of data : Amount of Bond PaperAmount of Yellow Paper

◦ Our null hypothesis is that most of students in the school use bond paper than yellow paper in whole year.

◦ We have means ;@ Bond Paper : 10.84314 @ Yellow Paper: 10.80392

• Next we have variance;@ Bond Paper : 75.63852 @Yellow Paper : 69.72355

• We must get the variance of the difference between the means by using formula :

The t value by using this formula:

Entering a t-table at 100 degrees of freedom (100 for n1 + 100 for n2) we find a tabulated t value of 1.660 (p = 0.05) going up to a tabulated value of 1.984(p = 0.025).

Analysis of Variance Ideally, for this test we would have the same number of replicates for each treatment, but this is not essential.

We have two sets of data : Amount of Bond PaperAmount of Yellow Paper

◦ But we have 3 groups:1st years2nd years3rd years

@ Bond PaperWe have Analysis of variance:

1st Year 2nd Year 3rd Year Row totals

S x 446 360 300 1106(Grand total)n 33 33 33

25.48571 10.58824 8.823529S x 2 10456 5866 3310 19632 (call this A)

6027.758 3927.273 2727.273 12682.3 (call this B)Sd 2 4428.242 1938.727 582.7273 6949.7 (A - B)

s 2 (=Sd 2 /n-1) 139.5615 62.24955 20.08913

D = (Grand total)2 /total observations

= 1106^2/99

= 12355.91919

Total sum of squares (S of S) = A - D = 7276.080808

Between-treatments S of S = B - D = 327.3808

Residual S of S = A - B = 6949.7

Sum of squares  Mean square(S of S) (= S of S 

df)

Between treatments 327.380808 u  - 1 (=2)* 163.690404

Residual 6949.7 u (v -1) (=96)* 72.3927083Total 7276.08081 (uv )-1 (=98)*

Source of variance

Degrees of freedom *

F = Between treatments mean square /Residual mean square

= 163.690404 / 72.3927083

= 2.261145

The tabulated value of F (p = 0.05) where u is df of between treatments mean square (2) and v is df of residual mean square (96) is 3.1

The F do not exceed the value 3.1, it means that there is no significant difference between years using bond paper.

Data Summary and Conclusion As we’ve come across the data that we have gathered with regards to our project, we have seen that:

A.) Most students use paper always and some of them use paper sometimes.

B.) Most students use yellow paper more often than bond paper.

C.) Most students find it inconvenient to rush down to the business center to buy paper. More students say that it is convenient to rush down to the business center and only a few number of students say that it doesn’t really matter to them.

D.) Most students say that the idea of a Paper Dispenser in every building is a good idea. Some said maybe and a few said no.

From those answers, we could prove that paper really is a need in a student’s everyday life and that it is a good idea to establish a Paper Dispenser in every building here in TUP-T.

Data Summary and Conclusion Now from our Numerical Data, we could infer that the all of the students from first year to third year that we have interviewed use yellow paper more than bond paper.

Paper really is a need in a student’s everyday life.Yellow papers, bond papers, and all types of paper like graphing paper, tracing paper, so on and so forth.we’ve inferred that it is a good idea to establish a Paper Dispenser in every building here in TUP-T.

Variance, Standard Deviation & Z-Score:

As stated above, we could infer that the all of the students from first year to third year that we have

interviewed use yellow paper more than bond paper. From all the data that we have gathered, we could

prove that paper really is a need in a student’s everyday life, regardless if it’s a bond paper or a yellow

paper. Nobody knows when are you going to need a paper. There may be times wherein you won’t use a

paper for the entire day, but that happens only once in a while and the probability is really small. So

whatever paper that the students may frequently need or use, we’ve inferred that it is a good idea to

establish a Paper Dispenser in every building here in TUP-T.

Conclusion

Correlation Analysis

-> inversely proportional -> far from -1 = little linear relation

-> we can’t expect that a student who uses large amount of Bond Paper will use the inverse amount of Yellow Paper

Conclusion Regression Analysis

Coefficient of Determination -> 32.11%

The small inaccuracy can be explained by the correlation analysis. Since the two sets of data has low linear correlation, we can’t expect our regression formula to be highly accurate.

T – Test Analysis :◦ We get the value between (p = 0.05) and (p = 0.025)so that we have 90% to 95% confidence level.

◦ These levels tell us the probability of our null hypothesis being correct but , but we still have nearly 5% to 10% chance of being wrong in this hypothesis.

◦ Clearly, that most of the student in the school use bond paper than yellow paper in whole year.

Analyzing of Variance( ANOVA)◦ The F do not exceed the value 3.1, it means that there is no significant

difference between years using bond paper.◦ If you exceed to the tabulated value of F (p=.05) it means that there is

significant difference .◦ This is the best test for comparing means of 3 or more groups, to avoid the

error inherent in performing multiple t-tests.

End.THANK YOU FOR LISTENING!

GOD BLESS