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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
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
16 17 2 15.5 17.5 16.5
5) Frequency Polygon
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 8.510 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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