basic maths(statistics)

8/14/2019 Basic Maths(Statistics)

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INSTITUT PENDIDIKAN GURU MALAYSIA

KAMPUS PERLIS

Basic Mathematics

SMART STATISTICS

MT 3311D

GROUPS MEMBERS:

OOI YET FANG910220-03-5700

LEE JIA JING910404-07-5010

TEOH YI SIAN

910127-07-5214 CHENG JIA EN

910309-08-6280

GROUP : PPISMP MT/BI/BC SEMESTER 3

LECTURERS NAME : EN SHUHAIRI BIN ABDUL RAZAK

DATE OF SUBMISSION : 9 AUGUST 2010


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CONTENT

Pages

Acknowledgement i

Content ii

1.0 Introduction

2.0 Types of Data

2.1 Quantitative variable

2.1.1 Discrete and Continuous Variable

2.2 Qualitative variable

2.3 Different between Quantitative and Qualitative

3.0 Graphical Representations of Data

3.1 Histogram

3.2 Pie Chart

3.3 Ogive

3.4 Bar Chart

3.5 Line Graph

4.0 Frequency Distribution Table

4.1 Frequency Distribution Table for an Ungrouped Data

4.2 Frequency Distribution Table for a Grouped Data

5.0 Central Tendency

5.1 Mean

5.2 Mode

5.3 Median

4.4 When to use Mean, Median, and Mode

6.0 Survey Form

6.1 The mass of the trainees in ppismp semester 3 in ipg kampus perlis

6.2 The sport shoes brand of the trainees in ppismp semester 3 in ipg

kampus perlis


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7.0 Graphical representation data (results)

7.1 Qualitative

7.2 Quantitative

8.0 Central Tendency of Quantitative

9.0 Conclusion

9.1 Conclusion of Quantitative

9.2 Conclusion of Qualitative

10.0 Reflection

11.0 References

12.0Appendices

Collaboration Form


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ACKNOWLEDGEMENT

First of all, we would like to take this opportunity to thank our lecturer, EnShuhairi Bin Abdul Razak for his guidance and advices for us in order to complete

this task. He had tried his best to help us and give advices to us during the time we

do this task without any impatient. We realized that without his guidance, its

impossible for us to complete this task successfully.

Besides that, we also would like to take this opportunity to thank our friends

who had helped us a lot by giving us some information about the format of the

coursework and the contents of this task. They helped us when we faced problems

during the process of completing the coursework.

In addition, a thousand thanks we would like to express to our group

members for the cooperation given by each other in the group. We knew that without

cooperation and tolerance between three of us, we couldnt finish this coursework.

Once again, thanks a lot to those who had helped us and guided us in order to

complete this coursework


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1.0 INTRODUCTION

Statistics is the science of collecting data, organizing, presenting and

interpreting numerical facts. Such facts or data can be arranged and

displayed in the form nor tables, graphs or charts. It is widely used in many

fields such as economics, medicine, meteorology, sports and social sciences.

The purposes of statistics can be summarized as to summarize

findings, to visualize results, to extract information from data and to

communicate the findings. We compute statistics and use them to estimate

parameters. The computation is the first part of the statistics course

(Descriptive Statistics) and the estimation is the second part (Inferential

Statistics) .

Descriptive statistics is a method in organizing, summarizing and

presenting data in an informative way and utilize both numerical and graphical

tools. It is used whenever a researcher wishes to describe to someone else

the findings and relationships that exist within a sample of observation.

Descriptive statistics consists of method that use sample results to help make

decisions or predictions about population. They provide simple summaries

about the sample and the measures.

Inferential statistics is a method by which decisions about a statistical

population are made based on a sample that is observed. For instance, we

use inferential statistics to try to infer from the sample data what the

population might think. Or, we use inferential statistics to make judgments of

the probability that an observed difference between groups is a dependable

one or one that might have happened by chance in this study.


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2.0 TYPES OF DATA

2.1 Quantitative Variable

A quantitative variable is a numerical datum or observation that represents an

amount or quantity. The quantity can be discrete or continuous.

2.1.1 Discrete and Continuous Variable

A discrete variable is a countable number of values. The values are

generally expressed as integers or whole numbers. It has no possible values

between adjacent units on the scale

A continuous variable is a number that can have an infinite number of values

between adjacent units on the scale.

2.2 Qualitative Variable

A qualitative variable is a non-numerical observation that represents a

category of data.

2.3 Different between Quantitative and Qualitative

At the most basic level, data are considered quantitative if they are numbers

and qualitative if they are words. Qualitative data may also include photos,

videos, audio recordings and other non-text data. Those who favour

quantitative data claim that their data are hard, rigorous, credible and

scientific. Those in the qualitative camp counter that their data are sensitive,

detailed, nuanced and contextual. Quantitative data best explain the whyandhowof your program, while qualitative data best explain the what, who and

when.

Different techniques are used to collect and analyze quantitative and

qualitative data:


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3.0 GRAPHICAL REPRESENTATIONS OF DATA

The graphical representation of data makes the reading more interesting, less

time-consuming and easily understandable. The disadvantage of graphicalpresentation is that it lacks details and is less accurate. In our study, we have

the graphs such as bar graph, pie charts, frequency polygon and histogram.

3.1 Histogram

Histogram is a representation of frequency distribution through the

four-sided figure whose width represents class intervals and whose areas are

directly proportional to the corresponding frequencies.

Histograms will represent in Two Dimension used to graph continuous

data. The histogram is used in continuous data graphing. This will be plotted

continuously. The histogram is constructed by a frequency table. To construct

the histogram, groups are plotted on the xaxis and their frequencies on the y

axis.

Example/:

Quantitative Techniques Qualitative Techniques

Surveys/Questionnaires Observations

Pre/post Tests Interviews

Existing Databases Focus Groups

Statistical Analysis Non-statistical (methods vary)


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The histogram of the frequency distribution can be converted to a

probability distribution by dividing the tally in each group by the total number

of data points to give the relative frequency.

The shape of the distribution conveys important information such as

the probability distribution of the data. In cases in which the distribution is

known, a histogram that does not fit the distribution may provide clues about a

process and measurement problem. For example, a histogram that shows a

higher than normal frequency in bins near one end and then a sharp drop-off

may indicate that the observer is "helping" the results by classifying extreme

data in the less extreme group.

The histogram provides a graphical summary of the shape of the data's

distribution. It often is used in combination with other statistical summaries

such as thebox plot,which conveys the median, quartiles, and range of the

data.

3.2 Pie Chart

Pie chart relates the quantities of the data size to the size of the angles

of the sectors. It can be used to represent a set of data as well as to obtain

and interpret information. In the pie chart, we can use percentage or fractions

of represent data. Pie charts are mainly suitable for the categoral data. They

are effective means used to show the relative quantities of various items

among the data where exact numbers of the various types of data are not

required.

Example:

A family's weekly expenditure on its house fruits, vegetables, and oils:

Expenses RM

Fruits 250

Vegetables 300

Oil 85
http://www.netmba.com/statistics/plot/box/http://www.netmba.com/statistics/plot/box/


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Solution:

Total weekly expenditure in house = 250 + 300 + 50

= RM 600

Find the percentage of total expenditure of each item

Percentage:

Fruits = (250 / 600)100% = 41.6%

Vegetable = (300 / 600) 100 = 50%

Oils = (50 / 600) 100 = 8.3%

If we draw the pie chart, divide the circle into hundred parts. Allocate the

percentage parts require for each item.

A pie diagram can be used in various applications. For instance, this is

mostly used in government to represent cities and the statistical information

that relates to income, age, gender and race. A pie chart makes the

information more easily and understood as a graphical representation of the

statistics.


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3.3 Ogive

An ogive (a cumulative line graph) is best used when you want to

display the total at any given time. The relative slopes from point to point will

indicate greater or lesser increases; for example, a steeper slope means a

greater increase than a more gradual slope. An ogive, however, is not the

ideal graphic for showing comparisons between categories because it simply

combines the values in each category and thus indicates an accumulation, a

growing or lessening total. If you simply want to keep track of a total and your

individual values are periodically combined, an ogive is an appropriate display.

Cumulative frequency curve or ogive is used to obtain the median,

lower quartiles, upper quartile and inner quartile range from a set of grouped

data.

Before drawing the cumulative frequency curve or ogive, we need to

work out on the cumulative frequencies. This is done by adding the

frequencies in turn.

Example:


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3.4 Bar Chart

A Bar chart is a pictorial representation of numerical data in the form of

rectangles or Bars of equal widths and various heights. These rectangles are

drawn either horizontally or vertically. It should be remembered that bar chart

is of one dimension. The height of bar represents the frequency of the

corresponding observation. The gap between two bars is kept the same.

Example

The attendance at different types if cultural events.

Events Percentage of population

Cinema 56

Plays 22

Art galleries 21

Classical music 12

Ballet 7

Opera 7

Other Dances 5

The bar chart is drawn for the events and the percentage of population.The

event part contains Cinema, plays, art galleries classical music ballet opera

and other dances. Now we are going to plot the bar chart for the given data.


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3.5 Line Graph

Line graph is defined as graphical device show the relationship

between two changing variables with line or a curve that will be connect a

series of successive data points. A grouped line graph compare a one

variable to more other variable and shows the rates of change that is

increasing, decreasing fluctuating, or remaining constant. It is also called as a

line chart.

Example 1:

Draw the line graph for following data.

Score 25 50 60 70 80 90

Matches 1 2 3 4 5 6

Solution:

Mark the matches in x axis and score in y-axis Select the suitable scale for both axis .x axis will be start from 1, 2,

3.up to 6 Similarly in y axis maximum value is 90 so it will be start from 10, 20,

30,..up to 90 Mark the point (1, 25), (2, 50) ..(6, 90) Join the all points using line segment the closed figure is obtained that

is the required line graph for given set of data


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Example: 2

Draw the line graph for different two set of data .It is similar to example one

but we compare the both data with using only one line graph.

Consider the first example and we have to draw the another set of data.

Score 20 30 40 60 70 50

Matches 1 2 3 4 5 6

Solution:

Drawing procedures are same .it is very easy to display the differencebetween both set of data.


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4.0 FREQUENCY DISTRIBUTION TABLE

The grouped frequency distribution table is used to tabulate a large

number of scores In this method the scores are grouped or classified into

small groups. These small groups are called class intervals. The lower value

of the class interval is called the lower limit and the upper value of the class

interval is called the upper limit. The size or width of the class interval is

defined from the difference between the upper limit and the lower limit of a

class interval. The average of the upper limit and the lower limit is called the

mid value of that interval.

In general, in a grouped frequency distribution, all class intervals are equal

in size. The number of scores falling under each class interval is recorded by

putting tally marks (l) The number of tally marks in a given class interval

represents the frequency of that class interval.

Example

Class intervals Tally marks Frequency

When we prepare a frequency distribution table we have to follow

some primary rules. It is desirable to have ten class intervals and as far as

possible all the class intervals must be of equal size. After deciding about the

choice of class intervals we should form a table with three headings namely

class intervals, tally marks and frequency. We should read the raw data one

by one and put the tally mark against the appropriate class interval. It should

be clearly defined so that no doubt may be left as to which class interval a

particular score belongs. When there are already four tally marks in a class

interval like and we have to enter the fifth tally mark in the same class

interval it is entered as a cross - line cutting across diagonally all the four tally

marks as shown and it is counted as five. We shall execute the above

procedure in the following example.


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4.1 Frequency Distribution Table for an Ungrouped Data:

Example:

Construct a frequency distribution table for the following data.

5, 1, 3, 4, 2, 1, 3, 5, 4, 2, 1, 5, 1, 3, 2, 1, 5, 3, 3, 2.

Solution:

From the data, we observe that the numbers 1, 2, 3, 4 and 5 are

repeated. Hence under the number column write to the five numbers namely 1,

2, 3, 4 and 5 one below the other.

Now read the numbers one by one and put the tally mark in the tally

mark column against the number. For example, the first number is 5. So put a

tally mark ( | ) against the number S. The next number is 1. So put a tally

mark ( I ) against the number l. Continue the process till all the numbers are

exhausted.

Add the tally marks against the numbers 1, 2, 3, 4 and 5 and write the

total in the corresponding frequency column. Now add all the numbers under

the frequency column and write it against the total.

Number Tally marks Frequency

1 5

2 4

3 5

4 2

5 4

Total 20


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4.2 Frequency Distribution Table for a Grouped Data:

Example:

The following are the marks obtained by 50 students in a mathematics test.

Prepare a frequency distribution table for the data.

45 68 41 87 61 44 67 30 54 8 39 60 37 50 19 86 42 29 32 61 25 77 62 98 47

36 15 40 9 25 34 50 61 75 51 96 20 13 18 35 43 88 25 95 68 81 29 41 45 87

Solution:

To decide the length of the class interval and to take all the scores given in

the problem. We have to in the largest value and the smallest value from the

given scores. This we can do by merely going through all the scores. Here thelargest value is 98 and the smallest value is 8.

The difference = Largest value - Smallest value.

= 98 - 8

= 90.

Since the difference between the largest value and the smallest value is

90, taking class intervals such as 0 - 5, 5 -10 , 10 - 15, ..., 95 - 100, the class

intervals are many in number (20). If we take the class interval such as 0-10,

10 -20, 20- 30, ....., 90- 100. The class intervals are considerably reduced to

10. It is advisable not to over reduce the number of class intervals. There

should be at least 5 class intervals. If the class intervals are mentioned in the

problem then we proceed as given in the problem. For the above problem we

form a frequency tab1e taking class intervals 0- 10 , I0-20 ,20-30 , 30 - 40, 40

- 50 , 50 - 60, 60 - 70, 70 - 80, 80 - 90 and 90 - 100.

The first score is 45. It lies in the class interval 40-50. Therefore put one

tally mark ( vertical bar like ' | ') in the class interval 40 - 50. The next score in

the first row is 68 . It lies in the class interval 60 - 70. Therefore put one tally

mark in the class interval 60 - 70. In the same manner take the scores 41 ,

87 , 61 , 44 , 67 one by one, identify the class intervals in which they lie and

put a tally mark in the corresponding class interval.


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Now the next score 30 is to be entered in a class interval. Here the doubt

arises in which class interval 30 is to be included, either in the class interval

20 - 30 or 30 - 40 since the two class intervals contain the value 30. It is

customary to include the value 30 in the class interval 30 - 40, which is the

lower limit of the class interval. So put the tally mark for the score 30 in the

class interval 30 -40. As we continue the process we come across the score

61 in the second line, which is the 5 thtally mark in the class interval 60 - 70.

Mark the tally mark corresponding to 61 as in the class interval 60 - 70. If

we have to put a 6th . This process is carried out till the last score is

entered. The tally marks in each class interval are counted and the counted

number is put against the same class interval under the frequency column. Allthe frequencies are added and the number is written as the total frequency for

the entire class intervals. This must match the total number of data given. The

table is called the frequency distribution table for grouped data. tally mark in

any class interval the tally mark is marked leaving a small gap after the block

as shown.

Class Intervals Tally marks Frequency

0-10 2

10-20 4

20-30 6

30-40 7

40-50 9

50-60 4

60-70 8

70-80 2

80-90 5

90-100 3

Total 50


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5.0 CENTRAL TENDENCY

The term central tendency refers to the "middle" value or perhaps a typical

value of the data When some data is collected, we have certain numbers

which represent the characteristics of the data, around which the data

appears to be concentrated, we call such numbers as the measures of central

tendency. There are three measures of central tendency. (i) Mean (ii) Median

and (iii) Mode

5.1 Mean

The mean is the most commonly-used measure of central tendency.

When we talk about an "average", we usually are referring to the mean. The

mean is simply the sum of the values divided by the total number of items in

the set. The result is referred to as the arithmetic mean. Sometimes it is useful

to give more weighting to certain data points, in which case the result is called

the weighted arithmetic mean.

The notation used to express the mean depends on whether we are

talking about the population mean or the sample mean:

= population mean

= sample mean

The population mean then is defined as:

where

= number of data points in the population

= value of each data point i.


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The mean is valid only for interval data or ratio data. Since it uses the values

of all of the data points in the population or sample, the mean is influenced by

outliers that may be at the extremes of the data set.

5.2 Median

The median is determined by sorting the data set from lowest to

highest values and taking the data point in the middle of the sequence. There

is an equal number of points above and below the median. For example, in

the data set {1,2,3,4,5} the median is 3; there are two data points greater than

this value and two data points less than this value. In this case, the median is

equal to the mean. But consider the data set {1,2,3,4,10}. In this dataset, themedian still is three, but the mean is equal to 4. If there is an even number of

data points in the set, then there is no single point at the middle and the

median is calculated by taking the mean of the two middle points.

The median can be determined for ordinal data as well as interval and

ratio data. Unlike the mean, the median is not influenced by outliers at the

extremes of the data set. For this reason, the median often is used when

there are a few extreme values that could greatly influence the mean and

distort what might be considered typical. This often is the case with home

prices and with income data for a group of people, which often is very skewed.

For such data, the median often is reported instead of the mean. For example,

in a group of people, if the salary of one person is 10 times the mean, the

mean salary of the group will be higher because of the unusually large salary.

In this case, the median may better represent the typical salary level of the

group.

5.3 Mode

The mode is the most frequently occurring value in the data set. For

example, in the data set {1,2,3,4,4}, the mode is equal to 4. A data set can

have more than a single mode, in which case it is multimodal. In the data set

{1,1,2,3,3} there are two modes: 1 and 3.


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The mode can be very useful for dealing with categorical data. For example, if

a sandwich shop sells 10 different types of sandwiches, the mode would

represent the most popular sandwich. The mode also can be used with

ordinal, interval, and ratio data. However, in interval and ratio scales, the data

may be spread thinly with no data points having the same value. In such

cases, the mode may not exist or may not be very meaningful.

5.4 When to use Mean, Median, and Mode

The following table summarizes the appropriate methods of determining the

middle or typical value of a data set based on the measurement scale of the

data.

Measurement Scale Best Measure of the "Middle"

Nominal(Categorical)

Mode

Ordinal Median

Interval Symmetrical data: Mean

Skewed data: Median

Ratio Symmetrical data: MeanSkewed data: Median


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SURVEY FORM ON THE MASS OF THE TRAINEES IN PPISMP

SEMESTER 3 IN IPG KAMPUS PERLIS

NO. NAME CLASS(PPISMP SEM 3) MASS(kg)

1 Ainur PJ/BI/BM 45

2 Nanthini PJ/BI/BM 55

3 Narermon Qetkeaw PS/BI/BM 70

4 Fatimah bt. Zainal Abidin PS/BI/BM 52

5 Farhanim Noduwan PS/BI/BM 40

6 Tan Yu Yan MT/BI/BC 40

7 Foo Lichen MT/BI/BC 40

8 Soh Jing Yih MT/BI/BC 459 Chong Sin Yee MT/BI/BC 49

10 Maxmillion PS/BI/BM 67

11 Ashaari bin Selamat PS/BI/BM 64

12 Philip Lahm KDC 63

13 Mesut Ozil KDC 71

14 Amir Farid KDC 65

15 Chee Mee Poh MT/BI/BC 60

16 Sheril Mieza Yushima PS/BI/BM 4117 Mohd Ubdidillah PS/BI/BM 60

18 Mohd Haziem PS/BI/BM 55

19 Tan Wei Jian MT/BI/BC 61

20 Loh Qi Xiang MT/BI/BC 57

21 Hani bt. Rani PS/BI/BM 45

22 Loh Jia Wei MT/BI/BC 47

23 Tee Sha Ney MT/BI/BC 48

24 Koay Ai Hooi MT/BI/BC 5525 Tan Hui Yen MT/BI/BC 50

26 Wong Siok Shim MT/BI/BC 40

27 Mah Shen Jian MT/BI/BC 73

28 Chan Mun Kit MT/BI/BC 64

29 Choong Chee Lun MT/BI/BC 68

30 Ooi Yet Fang MT/BI/BC 46


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31 Chiang Kok Yoong BC/PJ/KS(B) 42

32 Teoh Yi Sian MT/BI/BC 52

33 Tan Qiu Yan BC/PJ/KS(B) 64

34 Lim Kwee Lian BC/PJ/KS(B) 61

35 Cheng Jia En MT/BI/BC 71

36 Yee Hui Zin BC/PJ/KS(A) 73

37 Ling Siew Jie BC/PJ/KS(A) 46

38 Tan Li Min BC/PJ/KS(A) 74

39 Ee Li Li BC/PJ/KS(A) 51

40 Chai Qin Wen BC/PJ/KS(B) 54

41 Yap Jiunn Jye BC/PJ/KS(B) 53

42 Jeff Siew Kun Xiong BC/PJ/KS(B) 51

43 Chong Shin Mun BC/PJ/KS(B) 52

44 Lai Hui Ping BC/PJ/KS(B) 56

45 Fong Yean Mun BC/PJ/KS(B) 54

46 Mok Jin Yee BC/PJ/KS(A) 53

47 Wee Wen Yee BC/PJ/KS(A) 57

48 Loh Hui Min BC/PJ/KS(A) 54

49 Liew Min Tong BC/PJ/KS(A) 54

50 Hoong Yie Ping BC/PJ/KS(A) 53

51 Wong Xin Jian BC/PJ/KS(A) 50

52 Chia Chong Lin BC/PJ/KS(A) 57

53 Teh Hui Min BC/PJ/KS(A) 51

54 Chung Chin Kwei BC/PJ/KS(A) 58

55 Alex Wong BC/PJ/KS(A) 52

56 Parimala Kumaran PS/BI/BM 59

57 Zahra bt. Zaudi PS/BI/BM 53

58 Fateen Amirah PS/BI/BM 55

59 Tiong Hua Chiang BC/PJ/KS(B) 50

60 Sow Lei Yin BC/PJ/KS(B) 57


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SURVEY FORM ON THE SPORT SHOES BRAND OF THE TRAINEES IN

PPISMP SEMESTER 3 IN IPG KAMPUS PERLIS

NO. NAME CLASS SPORT SHOE'S BRAND

1 Hafizati Husna bt. Ibrahim KS/BI/BM POWER

2 Ameerah bt. Ramli BM/PJ/KS NIKE

3 Parimala Kumaran PS/BI/BM NIKE

4 Narermon Qetkeaw PS/BI/BM ADIDAS

5 Fatimah bt. Zainal Abidin PS/BI/BM EEPRO

6 Farhanim Roduwan PS/BI/BM NIKE

7 Tan Yu Yan MT/BI/BC NIKE

8 Foo Lichen MT/BI/BC ADIDAS

9 Soh Jing Yih MT/BI/BC NIKE

10 Chong Sin Yee MT/BI/BC PUMA

11 Maxmillion PS/BI/BM LOTTE

12 Ashaari bin Selamat PS/BI/BM ADIDAS

13 Philip Lahm KDC ADIDAS

14 Amir bin Razak PS/BI/BM DIADORA

15 Amir Farid PS/BI/BM ALIPH

16 Lee Jia Jing MT/BI/BC POWER

17 Wong Siok Shim MT/BI/BC POWER

18 Tan Hui Yen MT/BI/BC AMSDEX

19 Koay Ai Hooi MT/BI/BC POWER

20 Tee Sha Ney MT/BI/BC NIKE

21 Loh Jia Wei MT/BI/BC NIKE

22 Hani bt. Rani PS/BI/BM DUNLOP23 Zahra bt. Zaudi PS/BI/BM POLO

24 Fateen Amirah PS/BI/BM POLO

25 Loh Qi Xiang MT/BI/BC REEBOOK

26 Tan Wei Jian MT/BI/BC ADIDAS

27 Mohd Ubdidillah PS/BI/BM ADIDAS

28 Mah Shen Jian MT/BI/BC POWER

29 Chan Mun Kit MT/BI/BC NIKE30 Choong Chee Lun MT/BI/BC POWER


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31 Tan Li Min BC/PJ/KS(A) POWER

32 Choo Soo Chin BC/PJ/KS(A) POWER

33 Liew Min Tong BC/PJ/KS(A) ADIDAS

34 Ee Li Li BC/PJ/KS(A) ADIDAS

35 Wee Wen Yee BC/PJ/KS(A) NIKE

36 Teh Hui Min BC/PJ/KS(A) POWER

37 Ling Siew Jie BC/PJ/KS(A) NIKE

38 Chung Chin Kwei BC/PJ/KS(A) ADIDAS

39 Alex Wong BC/PJ/KS(A) NIKE

40 Chai Qin Wen BC/PJ/KS(B) PUMA

41 Tiong Hua Chiong BC/PJ/KS(B) PUMA

42 Mok Jin Yee BC/PJ/KS(B) NIKE

43 Sow Lei Yin BC/PJ/KS(B) PUMA

44 Christine Ow BC/PJ/KS(B) POWER

45 Lim Kwee Lian BC/PJ/KS(B) ADIDAS

46 Yap Jiunn Jye BC/PJ/KS(B) NIKE

47 Chong Shin Mun BC/PJ/KS(B) PUMA

48 Lai Hui Ping BC/PJ/KS(B) ADIDAS

49 Yee Hui Zin BC/PJ/KS(A) ADIDAS

50 Ng Sue Keen BC/PJ/KS(B) PUMA

51 Wong Sin Jian BC/PJ/KS(A) PUMA

52 Lee Jia Ling MT/BI/BC PUMA

53 Fong Yuen Mun BC/PJ/KS(B) POWER

54 Yap Bee Cheng BC/PJ/KS(A) POWER

55 Teoh Yi Sian MT/BI/BC POWER

56 Cheng Jia En MT/BI/BC ADIDAS

57 Jeff Siew BC/PJ/KS(B) NIKE

58 Tan Qiu Yan BC/PJ/KS(B) NIKE

59 Ooi Yet Fang MT/BI/BC ADIDAS

60 Chiang Kok Yoong BC/PJ/KS(B) POWER


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7.0 GRAPHICAL REPRESENTATION DATA (RESULTS)

7.1 Qualitative

Table 7.The sport shoes brand of the trainees in ppismp semester 3 in ipgkampus perlis

Nike

25%

Adidas

23%Power

23%

Puma

15%

Others

14%

Pie chart of the sport shoe's brand of trainees in PPISMPSEM3 in IPG KAMPUS PERLIS

POWER NIKE NIKE ADIDAS EEPRO

NIKE NIKE ADIDAS NIKE PUMALOTTO ADIDAS ADIDAS DIADORA ALIPH

POWER POWER AMSDEX POWER NIKE

NIKE DUNLOP POLO POLO REEBOK

ADIDAS ADIDAS POWER NIKE POWER

POWER POWER ADIDAS ADIDAS NIKE

POWER NIKE ADIDAS NIKE PUMA

PUMA NIKE PUMA POWER ADIDAS

NIKE PUMA ADIDAS ADIDAS PUMA

PUMA PUMA POWER POWER POWER

ADIDAS NIKE NIKE ADIDAS POWER

Brand of sport shoes Frequency Degree () Percentage (%)

Nike 15 90 25

Adidas 14 84 23.33

Power 14 84 23.33

Puma 9 54 15Others 8 48 13.33


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Brand of sport shoes Tally Frequency

Nike 15

Adidas 14

Power 14

Puma 9

Others 8

0

2

4

6

8

10

12

14

16

Nike Adidas Power Puma Others

Frequency

Brand of sport shoes

Bar chart of the sport shoe's brand of trainees in PPISMP SEM3 inIPG KAMPUS PERLIS


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7.2 Quantitative

45kg 55kg 70kg 52kg 40kg 40kg 40kg 45kg 49kg 67kg






Tavle 8.1 :The mass of the trainees in ppismp semester 3 in ipg kampus perlis

Class interval Tally Frequency

40-44 6

45-49 8

50-54 18

55-59 10

60-64 8

65-69 4

70-74 6


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40-44

10%

45-49

13%

50-54

30%55-59

17%

60-64

13%

65-69

7%

70-74

10%

Pie chart of the mass of trainees SEM 3 IPG

KAMPUS PERLIS

The mass of thetrainees in PPISMP

Sem3 (kg)

Frequency Degree () Percentage (%)

40-44 6 36 10

45-49 8 48 13.33

50-54 18 108 30

55-59 10 60 16.67

60-64 8 48 13.33

65-69 4 24 6.67

70-74 6 36 10


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0

2

4

6

8

10

12

14

16

18

20

Mass (kg)

Frequency

Histogram of the mass of trainees SEM 3 IPGKAMPUS PERLIS

40-44

45-49

50-54

55-59

60-64

65-69

70-74

The mass of thetrainees in

PPISMP Sem3(kg)

Lower boundary Upper boundary Frequency

40-44 39.5 44.5 6

45-49 44.5 49.5 8

50-54 49.5 54.5 18

55-59 54.5 59.5 10

60-64 59.5 64.5 8

65-69 64.5 69.5 4

70-74 69.5 74.5 6


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0

2

4

6

8

10

12

14

16

18

20

44.5 49.5 54.5 59.5 64.5 69.5 74.5

Frequency

Mass (kg)

Line graph of the mass of trainees SEM 3 IPG

KAMPUS PERLIS


PPISMP Sem3(kg)

Mid-point of classfrequency

Upper boundary Frequency

35-39 37 39.5 0

40-44 42 44.5 6

45-49 47 49.5 8

50-54 52 54.5 18

55-59 57 59.5 10

60-64 62 64.5 8

65-69 67 69.5 4

70-74 72 74.5 6

75-79 77 79.5 0


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0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70 80

CumulativeFrequency

Mass (kg)

Ogive of the mass of trainees SEM 3 IPG

KAMPUS PERLIS


PPISMP Sem3(kg)

Upper boundary Frequency Cumulativefrequency

40-44 44.5 6 645-49 49.5 8 14

50-54 54.5 18 32

55-59 59.5 10 42

60-64 64.5 8 50

65-69 69.5 4 54

70-74 74.5 6 60


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8.0 CENTRE TENDENCY OF QUANTITATIVE

A total of 60 students have been chosen randomly to complete this survey.

From the table, we can find the central tendency of the data such as mode,

median, mean, variance and standard deviation.

Calculation for histogram

(a) Modal class= 50-54

(b) Mean

Mass(kg) Midpoint (x) Frequency (f) fx

40-44 42 6 252

45-49 47 8 376

50-54 52 18 936

55-59 57 10 570

60-64 62 8 496

65-69 67 4 268

70-74 72 6 432

Total f= 60 fx= 3330

= 6(42) + 8(47) + 18(52) + 10(57) + 8(62) + 4(67) + 6(72)60

= 252 + 376 + 936 + 570 + 496 + 268 + 43260

= 55.5

(c) Mode

There are two methods can be used to estimate the mode for grouped data.

f frequency of the data

x midpoints of the mass


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Method 1: Graphical method

The mode can be estimated by using the point of intersection of AC and BD

as shown above where AEFD is the modal class.

Step 1: Mark four points A, B, C and D on the modal class bar as shown

above.

Step 2: Connect with lines from A to C and B to D.

Step 3: Find the point of intersection of the lines AC and BD. That is the

estimated mode of the data.


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Based on our histogram, the mode is 52.25

Mode = 52.25

0

2

4

6

8

10

12

14

16

18

20

Mass (kg)

Frequency

Histogram of the mass of trainees SEM 3 IPGKAMPUS PERLIS

40-44

45-49

50-54

55-59

60-64

65-69

70-74


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Method 2: Calculation method

Mode, Mo =

21

1

fffcL

L = lower boundary of the modal classf 1 =frequency of the modal class minus frequency of the previous classf 2 = frequency of the modal class minus frequency of the next class

C = width of the modal class

Modal class = 50-54

L = 49.5

f 1 = 18-8

= 10

f 2 = 18-10

= 8

C = 54.5-49.5

= 5

Mo =

21

1

ff

fcL

= 49.5+ 5

= 52.28

Mass(kg) frequency Lower boundary Upper boundary

40-44 6 39.5 44.5

45-49 8 44.5 49.5

50-54 18 49.5 54.5

55-59 10 54.5 59.5

60-64 8 59.5 64.5

65-69 4 64.5 69.5

70-74 6 69.5 74.5

Total 60


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(d) MEDIAN

From the graph, the median class is 30th.

1stmethod

Based on the formula, Median , m =

= 49.5 + (0123 ) 5= 49.5+ 4 9= 53.94

2ndmethod

Based on the ogive drawn, the median is 53.75 .

L= lower boundary of the median classN = total number of observationsF = cumulative frequency before the

median classfm = frequency of the median class= size of the median class


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9.0 CONCLUSION

9.1 Conclusion (Quantitative)

In our histogram based on our data collection showed the type of right-

skewed graph.

Analysis:

First of all, we would like to explain why we chose the mass of the

trainees in IPG KAMPUS PERLIS as our survey title. Nowadays, most of the

people are suffered from obesity and even the teenagers are suffered from

obesity. Hence, we have the interest to look into this problem.

As a conclusion, our histogram is a Histogram of right-skewed.

There is less number on the right skew of histogram. The centre part of skew

showed the large observations. This scenery is close to our data collected.

In our survey about the mass of PPISMP trainees in IPGM KAMPUS PERLIS,

we had collected the data from 60 students in our campus.

Among them, there are a few numbers of students whose weight are

between 70-74kg. Due to that, they had obesity. Most of their weights arebetween 50-54kg. So, on the histogram, it showed a large observation on

the left skew.

On the other hands, the right skew showed a small observation

compared to the left skew. Refer back to our Frequency Distribution Table, it

is less than 50%of the above trainees are distributed at the class interval

above 60kg. This is because most of the trainees are well educated and they

know how to maintain their moderate body weight by practicing balanced diet.

As a conclusion, it is obviously can be conclude that our histogram is a

Histogramof right-skewed.

Through the research on our survey, we had learnt how to make the

result to be nicer. For the further survey, we should carry out the survey in the

same population. Due to that, the difference in the results will be decreased

and the graph will look better.


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9.2 Conclusion (Qualitative)

In our bar chart based on our data collection showed the type of right-

skewed graph.

Analysis:

We would like to choose to do survey on the sport shoes brand of the

trainees in IPG KAMPUS PERLIS to get our qualitative data. It is because

everyone in this institute has at least a pair of sport shoes as we have to carry

out a lot of sport activities such as pendidikan jasmani and GERKO. A pairs of

sport shoes can said to be a need for a trainee here. Hence, we would like to

know the reason which brand of sport shoes is the most popular in among the

trainees.

As a conclusion, our bar chart is a Bar chart of right-skewed as well.

There is less number on the right skew of histogram. The centre part of skew

showed the large observations. In our survey about the sport shoes brand of

the trainees in IPG KAMPUS PERLIS, we had collected the data from 60

students in our campus.

From the data we collected and bar chart drawn, we can see that Nike is

the most popular among the brands of sport shoes. It is because NIKE is a

very well-known brand among teenagers, comfortable to wear and nice out-

look of the shoes of that brand. Besides, ADIDAS and POWER got the same

number of users in the 60 trainees being surveyed. These two brands are

quite famous and also comfortable to wear.

As a conclusion, it is obviously can be conclude that our bar chart is a

Bar chart of right-skewed.


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10.0 Reflection

First of all, we are feeling glad that we had done this coursework for

Basic Mathematics. We had learnt few things which are useful for us in the

process of doing this coursework.

First and foremost, this coursework helped us in improving our skill on

finding and gathering the information from different sources. Once we got the

question paper from our lecturer, our group which in four started to look for

the information and notes on smart statistic. We tried our best to get ample

and useful information no matter through internet or reference books from

library of our institute. Due to the question, we have to carry out survey and

hence we learned how to collect the data, classify and represent in any

appropriate illustration.

After taking into consideration and discussion, four of us had come to a

decision to choose the SPORT SHOES BRANDS OF TRAINEES in PPISMP

SEM3 in IPG KAMPUS PERLIS as our title for qualitative data and MASS OF

TRAINEES in PPISMP SEM3 in IPG KAMPUS PERLIS as our title for

quantitative data in our survey. We set our target for 60 people in our campus.When we made the survey among the friends, we found that the trainees here

are very good in maintaining their body weight and hence they avoid from

getting obesity. Besides, the brand of shoes which is the most popular among

60 trainees being surveyed is Nike which is a very well-known brand all over

the world. This can be said that most of the trainees are materialistic and

yearning for wearing famous brand rather than other reasons. But the most

important thing in this coursework is that we got to learn and explore the worldof statistic which will be very useful for us in the future teaching field.

This assignment helps us a lot in our understanding about statistic. We

will appreciate and use this advantage in our further survey. Thanks for giving

us the chance to learn more about statistic. We really enjoy the joyful of the

process.


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11.0 REFERENCE

Lim Swee Hock(2005) Chapter 6 MATHEMATICS FORM4 (pg145-

175).Kuala Lumpur DARUL FIKIR

Latifah Mohd. Nor(2005) Chapter 1 STATISTICS Mada Simple Second

Edition (pg1-5) Kuala Lumpur International Islamic University Malaysia

H.L.CHUA( 2005) Chapter 25 NEW VISION MATHEMATICS FORM1.2.3

(pg241-309) Shah Alam SNP PANPAC(M) SDN.BHD

Chin Siew Wui(2003) Chapter 3 STPM MATHEMATICS [Mathematics S

Paper2] (pg 7699)Selangor Penerbitan Pelangi Sdn. Bhd

Quantitative and Qualitative Evaluation Method. Retrieved on 24 July 2010

fromhttp://www.civicpartnerships.org/docs/tools_resources/Quan_Qual%20M

ethods%209.07.htm

Statistics. Retrieved on 24 July 2010 fromhttp://statistics.unl.edu/whatis.shtml

Central Tendency. Retrieved on 24 July 2010 from

http://www.tutorvista.com/search/central-tendency
http://www.civicpartnerships.org/docs/tools_resources/Quan_Qual%20Methods%209.07.htmhttp://www.civicpartnerships.org/docs/tools_resources/Quan_Qual%20Methods%209.07.htmhttp://statistics.unl.edu/whatis.shtmlhttp://www.tutorvista.com/search/central-tendencyhttp://www.tutorvista.com/search/central-tendencyhttp://statistics.unl.edu/whatis.shtmlhttp://www.civicpartnerships.org/docs/tools_resources/Quan_Qual%20Methods%209.07.htmhttp://www.civicpartnerships.org/docs/tools_resources/Quan_Qual%20Methods%209.07.htm


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12.0

APPENDICES

basic maths(statistics)

Documents