assment math betoi

8/9/2019 Assment Math Betoi...

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BASIC MATHEMATICSSmart Statistics

NO. MEMBERS IC NUMBERS

1. Muhammad Afiq Bin Ameri 910921-08-6199

2. Muhammad Aslam Bin Che Junaidi 910413-02-5525

3. Mohamad Ridzuan Bin Mohamad Razali 910105-08-5059

4. Mohamad Amirruddin bin Zulkafly

INSTITUT PERGURUAN PERLIS01000 KANGAR PERLIS

PREPARED BY:

GROUP: KPLSPM-PENDIDIKAN BAHASA MELAYU/ PENDIDIKANJASMANI/ KAJIAN SOSIAL (SEMESTER 3)

LECTURER: EN SHUHAIRI BIN

DATE OF SUBMISSION: 9 AUGUST 2010


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CONTENTS

Items Page

Declaration Form

Acknowledgement

1.0 Gathering Information

2.0 Collecting Data

3.0 Managing Data

3.1 Frequency distribution table

3.2 Relative frequency

3.3 Cumulative relative frequency

4.0 Central Tendencies

Mean, Median and Mode

5.0 Visual Representation of Data

Reflection

References

Appendices

Collaboration Form


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DECLARATION FORM

We hereby declare that this KKP is original piece of work prepared by our group in

own words and we did not copy or plagiaries any part of the paper that we have

submitted.

We hereby acknowledge, that we:

Please check

I.

Have acknowledge all work and ideas in our

assignment taken from printed and electronically

published resources;

/

II. Did not copy from any other resources or another

student;/

III

.

Did not allow another student to copy our

assignment, and/

IV

.

Have faithfully represented the views of authors cited

in our paper./

Therefore, we understand that if any of the above is found to be untrue,

EN SHUHAIRI BIN has the full right to take any disciplinary action on us.

ACKNOWLEDGEMENT


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In the name of Allah, The most gracious and most merciful.

First of all, A special thanks to our respected Mathematics lecturer, En.Shuhairi , who

had helped us, give us advise and also train us in completing this assignment.

We also like to thank to our group members for their cooperation in the preparation of

this assignment. Not forgotten to our family for their moral support and everyone that helping

us in completing our assignment.

Thank you.


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1.0

GATHERING INFORMATION


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STATISTICS

1.1 INTRODUCTION

Statistics is a mathematical science pertaining to the collection, analysis,

interpretation or explanation, and presentation of data. It is applicable to a wide

variety of academic disciplines, from the natural and social sciences to the

humanities, government and business. A statistic is the result of applying a function

to a set of data.

More formally, statistical theory defines a statistic as a function of a sample

where the function itself is independent of the sample's distribution: the term is used

both for the function and for the value of the function on a given sample.

A statistic is distinct from an unknown statistical parameter, which is not

computable from a sample. A key use of statistics is as estimators in statistical

inference, to estimate parameters of a distribution given a sample. For instance, the

sample mean is a statistic, while thepopulation mean is a parameter.

1.2 TYPES OF STATISTICS

a) Descriptive Statistic

This type of statistic consists of methods for organizing, displaying and describing

data by using tables, graphs and summary measures.


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b) Inferential Statistics

This type of statistic consists of methods that use sample result to help make

decisions or predictions about population.

1.3 VARIABLES

A variable is a characteristic under study that assumes different values for different

elements. In contrast to a variable, the value of a constant is fixed.

a) Quantitative Variable- A variable that can be measured numerically. This

variable divide into two which is:

i) Discrete variable: A variable whose values are countable.

ii) Continuous Variable: A variable that can assume any numerical value

over a certain interval or intervals.

a) Qualitative Variable- A variable that cannot assume a numerical value but can

be classified into two or more nonnumeric categories.


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1.4 STATISTICAL METHODS

The basic steps of an experiment are;

1. Planning the research, including determining information sources, research

subject selection, and ethical considerations for the proposed research and

method.

2. Design of experiments, concentrating on the system model and the interaction

of independent and dependent variables.

3. Summarizing a collection of observations to feature their commonality by

suppressing details. (Descriptive statistics)

4. Reaching consensus about what the observations tell about the world being

observed. (Statistical inference)

5. Documenting / presenting the results of the study.

1.5 METHODS OF COLLECTING DATA

Statistical methods can be used to summarize or describe a collection of data.

This is called descriptive statistics. In addition, patterns in the data may be modeled

in a way that accounts for randomness and uncertainty in the observations, and then

used to draw inferences about the process or population being studied; this is called

inferential statistics. Both descriptive and inferential statistics comprise applied

statistics. There is also a discipline called mathematical statistics, which is

concerned with the theoretical basis of the subject.

1.6 VISUAL REPRESENTATION OF DATA

1.6.1 Bar Chart

A bar chart is a chart with rectangular bars of lengths proportional to that value

that they represent. Bar charts are used for comparing two or more values. The

bars can be horizontally or vertically oriented.

i. Horizontal

i. Top of Form

Example:

Favorite Cafeteria FoodEach unit represents one student
http://en.wikipedia.org/wiki/Ethicshttp://en.wikipedia.org/wiki/Design_of_experimentshttp://en.wikipedia.org/wiki/Summary_statisticshttp://en.wikipedia.org/wiki/Descriptive_statisticshttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Inferential_statisticshttp://en.wikipedia.org/wiki/Design_of_experimentshttp://en.wikipedia.org/wiki/Summary_statisticshttp://en.wikipedia.org/wiki/Descriptive_statisticshttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Inferential_statisticshttp://en.wikipedia.org/wiki/Ethics


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Hot Dog 27

Hamburger 84

Taco 125

Pizza 143

Spaghetti 65

Meat Loaf 4

ii. Vertical

Vertical Bar Graph

Favorite Cafeteria Food

Each unit represents one student

Hot Dog Hamburger Taco Pizza Spaghetti Meat Loaf

27 84 125 143 65 4

iii.

1.6.2 Histogram

A histogram is a graphical display of tabulated frequencies. It shows what

proportion of cases fall into each of several categories. A histogram differs from a

bar chart in that it is the area of the bar that denotes the value, not the height, a

crucial distinction when the categories are not of uniform width (Lancaster, 1974).

The categories are usually specified as non-overlapping intervals of some variable.

The categories (bars) must be adjacent.

Example:


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1.6.3 Line Graph

In graph theory, the line graph L(G) of an undirected graph G is another graph

L(G) that represents the adjacencies between edges ofG. The line graph is also

sometimes called the edge graph, the adjoint graph, the interchange graph, or

the derived graph ofG.
http://en.wikipedia.org/wiki/Image:Black_cherry_tree_histogram.svg


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Example:


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1.6.4 Pie Chart

A pie chart (or a circle graph) is a circular chart divided into sectors,

illustrating relative magnitudes or frequencies or percents. In a pie chart, the arc

length of each sector (and consequently its central angle and area), is

proportional to the quantity it represents. Together, the sectors create a full disk.

It is named for its resemblance to a pie which has been sliced.

While the pie chart is perhaps the most ubiquitous statistical chart in the business

world and the mass media, it is rarely used in scientific or technical publications.

It is one of the most widely criticized charts, and many statisticians recommend to

avoid its use altogether, pointing out in particular that it is difficult to compare

different sections of a given pie chart, or to compare data across different piecharts. Pie charts can be an effective way of displaying information in some

cases, in particular if

the intent is to

compare the

size of a slice with

the whole pie,

rather than

comparing the

slices among them.

Pie charts work

particularly

well when the

slices represent 25

or 50% of the data,

but in general, other

plots such as the bar chart or the dot plot, or non-graphical methods such as

tables, may be more adapted for representing information.

The earliest known pie chart is generally credited to William Playfair's Statistical

Breviaryof1801.

Example:
http://en.wikipedia.org/wiki/Image:English_dialects1997.svghttp://en.wikipedia.org/wiki/Image:English_dialects1997.svghttp://en.wikipedia.org/wiki/Image:English_dialects1997.svghttp://en.wikipedia.org/wiki/Image:English_dialects1997.svghttp://en.wikipedia.org/wiki/Image:English_dialects1997.svghttp://en.wikipedia.org/wiki/Image:English_dialects1997.svghttp://en.wikipedia.org/wiki/Image:English_dialects1997.svghttp://en.wikipedia.org/wiki/Image:English_dialects1997.svg


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1.6.5 Pictograph

Pictograph is a way of representing statistical data using symbolic figures to match

the frequencies of different kinds of data.

Example

The pictograph shows the number of varieties of apples stored at a supermarket.


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1.7 HOW TO CALCULATE DATA

1.7.1 Mean

The mean is just the average of the numbers.

i) For ungrouped data, use this formula:

x = xN

ii) For grouped data, use this formula:

x = fxf

1.7.1 Median

The median is the value in the middle position of a data set.

i) For ungrouped data, use this formula:

When N is an odd number:

=

When N is an even number:

= mean of th data and th data

i) For grouped data, use this formula:

m = L +

L= lower boundary of the median class

)c

N)(2

N

( )N

The summation of the

values of the dataThe total

number of

The class

midpointFrequency

( )N+1

2

2(

F

fm

+122


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N= total frequency

F=cumulative frequency before the median class

fm= frequency of the median class

c=size of the class interval

1.7.1 Mode:

The mode is a value that occurs with the greatest frequency in a population or a

sample. It could be considered as the single value most typical of all the values.


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2.0

COLLECTING DATA


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3.0

MANAGING DATA

3.0 MANAGING DATA

3.1 Introduction

Knowing a distance from one place to place is very important to us especially for a

driver. From here we can determine how much we spend the money, how long we

take times to arrive at our destination, average of fuel we had used and so on. So,

for our project we had decided to study regarding the distance of IP Perlis student

hometown to the institute.

3.2 Objective

When we know the distance, we can determine how long we take the time to arrive

at IP Perlis from hometown. Besides that, we can plan our budget, time and also the


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6.05 12.30 6.30 12.30 5.30 6.30 7.00 7.31 6.30 6.30 5.00 6.30

6.50 6.00 6.30 6.30 10.30 8.15 6.00 10.30 6.45 7.00 9.00 6.30

6.30 9.30 8.30 8.30 6.00 16.30 6.30 11.45 6.50 5.55 5.45 5.45

9.00 6.30 6.30 13.00 9.00 10.30 13.30 12.30 7.00 10.15 7.00 10.15

14.00 10.00 17.00 5.00 5.00 5.00 4.00 13.00 6.30 6.10 6.30 8.10

most important is money. We also can save our time if we can find another

alternative which is using short-cut road.

3.3 Methodology

We had used two methods to collect the data which are:

Questionnaire form

Face to face interview.

3.4 Survey Analysis

Collected Data:

TIME INTERVEL FREQUENCY

4 - 5 9

6 7 27

8 9 8

10 11 7


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Class Size = RangeNumber of Class

12 13 6

14 15 1

16 17 2

Determine the range for the set of data:

To determine the range, use this formula:

In this case,

Determine the class size:

To determine the class size, use this formula:

So,

Hi hest Data Lowest Data

The lowest data : 4The highest data : 17

17 4 = 13

We know that:

Range = 13

Number of Class = 7

=

= 1.86 2


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Tally Chart:

Time (hour) Tally Frequency (f)

4 - 5 //// //// 9

6 7 //// //// //// //// //// // 27

8 9 //// //// 8

10 11 //// // 7

12 13 //// / 6

14 15 / 1

16 17 // 2

Frequency Distribution Table:

Time (hour) Frequency (f) Boundary Midpoint

(x)Lower Upper

4 - 5 9 3.5 5.5 4.5

6 7 27 5.5 7.5 6.5

8 9 8 7.5 9.5 8.5

10 11 7 9.5 11.5 10.5

12 13 6 11.5 13.5 12.5

14 15 1 13.5 15.5 14.5

683

713

7


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16 17 2 15.5 17.5 16.5

Relative Frequency Table:

Time (hour) Frequency (f) Relative Frequency (ff)

4 - 5 9 9 / 60 = 0.15

6 7 27 27 / 60 = 0.45

8 9 8 8 / 60 = 0.13

10 11 7 7 / 60 = 0.12

12 13 6 6 / 60 = 0.10

14 15 1 1 / 60 = 0.02

16 17 2 2 / 60 = 0.03

Cumulative Frequency Distribution Table:

Time (hour) Frequency (f) Cumulative Frequency Upper

Boundary

4 - 5 9 9 5.5

6 7 27 36 7.5

8 9 8 44 9.5

10 11 7 51 11.5

12 13 6 57 13.514 15 1 58 15.5

16 17 2 60 17.5

Central Tendency:

Time (hour) Frequency (f) Midpoint (x) fx

4 - 5 9 3.5 31.5


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6 7 27 6.5 175.5

8 9 8 8.5 68.0

10 11 7 10.5 73.5

12 13 6 12.5 75.0

14 15 1 14.5 14.5

16 17 2 16.5 33.0

Mean:

x = fxf

Mean = S um of (midpoint frequency)Sum of frequency

= 9(4 .5) + 27 (6.5) + 8(8.5) + 7(10.5) + 6(12.5) + 1(14 .5) + 2(16.5)

60

= 48060

= 8

Median:

Time (hour) Frequency (f)

4 - 5 9

6 7 27

8 9 8

10 11 7


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12 13 6

14 15 1

16 17 2

Median Class is 6 - 7

m = L +

m = 5.5 +

= 5.5 + ( 0.78 ) 2

= 5.5 + 1.56

FN

)c

60

2fm

(

2

(- 9

27

)

2


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= 7.06

Mode:

Time (hour) Frequency (f)

4 - 5 9

6 7 27

8 9 8

10 11 7

12 13 6

14 15 1

16 17 2

Mode for this data also 12 - 13 in hours

REPRESENTING DATAQuantitative

1) Pie Chart

TIME

INTERVAL

FREQUENCY Percentage (%)

4 - 5 9 15

6 7 27 45

8 9 8 13

10 11 7 12

12 13 6 10

14 15 1 2

16 17 2 3


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2) Bar Chart

TIME INTERVEL FREQUENCY

4 - 5 9

6 7 27

8 9 8

10 11 7

12 13 6

14 15 1

16 17 2

3) Line Graph

Time Frequency (f)

4 - 5 12

6 7 24

8 9 9

10 11 6

12 13 7

14 15 0

16 17 2


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4) Histogram


(x)Lower Upper 4 - 5 9 3.5 5.5 4.5

6 7 27 5.5 7.5 6.5

8 9 8 7.5 9.5 8.5

10 11 7 9.5 11.5 10.5

12 13 6 11.5 13.5 12.5

14 15 1 13.5 15.5 14.5

16 17 2 15.5 17.5 16.5

5) Frequency Polygon


(x)Lower Upper

4 - 5 9 3.5 5.5 4.5

6 7 27 5.5 7.5 6.5

8 9

8 7.5 9.5 8.510 11 7 9.5 11.5 10.5

12 13 6 11.5 13.5 12.5

14 15 1 13.5 15.5 14.5

16 17 2 15.5 17.5 16.5

23

24

3.5 19.5


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6) Ogive

Time (hour) Frequency (f) Cumulative Frequency UpperBoundary

4 - 5 9 9 5.5

6 7 27 36 7.5

8 9 8 44 9.5

10 11 7 51 11.5

12 13 6 57 13.5

14 15 1 58 15.5

16 17 2 60 17.5

25


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Qualitative

Distribution Table

ROMANTIC WAR ACTION ACTION ROMANTIC ACTION ACTION

ROMANTIC ACTION ROMANTIC COMEDY ROMANTIC ROMANTIC

HORROR ROMANTIC COMEDY EPIC MOVIE ACTION WAR WAR

WAR COMEDY COMEDY HORROR HORROR EPIC MOVIE EPIC MOVIE

ROMANTIC WAR ROMANTIC EPIC MOVIE EPIC MOVIE HORROR

ROMANTIC HORROR WAR ACTION ROMANTIC COMEDY EPIC MOVIE

COMEDY WAR ROMANTIC ACTION COMEDY WAR ROMANTIC

ACTION HORROR ROMANTIC WAR EPIC MOVIE HORROR COMEDY

ACTION EPIC MOVIE WAR ROMANTIC ROMANTIC HORROR

TYPE OF MOVIE FREQUENCY

Action 10

Comedy 8

Horror 8

Romantic 16

Epic Movie 8

War 10

1. Pie Chart


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TYPE OF MOVIE FREQUENCY PERCENTAGE (%)

Action 10 17

Comedy 8 13

Horror 8 13

Romantic 16 27

Epic Movie 8 13

War 10 17

2. Bar Chart

TYPE OF MOVIE FREQUENCY

Action 10

Comedy 8

Horror 8

Romantic 16

Epic Movie 8

War 10

COMMENT ON SYMMETRY OR SKEWNESS IN THE HISTOGRAM


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From the histogram we can see that the histogram has longer tail. This histogram is

not symmetric because the tail in the positive direction extends further than the tail in

the negative direction.A histogram with the longer tail in the positive direction said

has to have a positive skew.

This skewness happen because the frequency that we collect from the data

decrease from first class to next classes.

4.0 REFLECTION

Alhamdulillah, we feel thankful to God because bless our group so that we

can finished this Basic Mathematics assignment. For this smart statistics survey, we

had done a survey about the distance from house to institute among of the students

of IPP Perlis.

First of all, we had done this assignment by gathering the information and

studies about the definition of statistics, types of statistics, statistical methods,

method of collecting data, visual representing data and how to calculate data. Then,

after we conducted the survey, we had written about managing data in frequency

distribution table, relative frequency, cumulative relative frequency, central

tendencies, mean, median, mode and visual representation of data.

From there, we knew about how long distance and time students spent from

house to institute. Besides that, we also know the strategies on how to conduct a

survey and write the survey statistics report well than before. This assignment had

Skew to the left


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improved our group skills in analyzing the data approval, showed the data with using

suitable visual representing of the data and managing the data. At the same time,

this assignment had given us some confident to try using correct grammar and

vocabulary. It encouraged us to improve our English Language. We had given all of

our commitment and focus for this assignment.

Nevertheless, the most important thing, in order to finish successfully this

assignment, cooperation among group members is very important. Since, Basic

Mathematics assignment is a group work assignment. Alhamdulillah, during finishing

this assignment, we can improve our good relationship between us. Our group

members had worked together to find the information, did collaboration with our

lecturer to give briefing, advice about how to conduct the survey, discuss about the

collected data and finally, how to manage the data.

Finally, we hope that this task can fulfill the requirement of a good

assignment. Thank you.

REFERENCES

Tan Poo Chang, Halimah Awang. (2001) Pengenalan Statistik. Penerbitan FajarBakti;Kuala Lumpur

Cheang Chooi Yoong, Kamaruzaman Moidunny, K.H. Eng, Y. K. Cheng, 2005 ,

Mathematics Form 4, Shah Alam Selangor Darul Ehsan, Cerdik Publication

Sdn.Bhd.

Statistics, http://onlinestatbook.com/chapter1/variables.html , access on 18 August

2008.

Quick MBA (2007). Central Tendency- Mean, Median, Mode.

www.quickmba.com/stats/centralten/. Accessed on 14 August 2008.
http://onlinestatbook.com/chapter1/variables.htmlhttp://onlinestatbook.com/chapter1/variables.htmlhttp://onlinestatbook.com/chapter1/variables.html

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