INTRODUCTION

Statistics are all around us. In fact it would be difficult to go through

a full week without using statistics.

Imagine watching a football game where no one kept score. The

action itself might provide enough excitement to hold your attention for a

while, but think of all the drama that would be lost if winning and losing

weren't at issue.

Without statistics this task would come down to simple guess work.

You could never know for sure if that worthless mutt were getting the best

(cheapest) treats for your dollar.

Without statistics we couldn't plan our budgets, pay our taxes, enjoy

games to their fullest, and evaluate classroom performance. Are you

beginning to get the picture? We need statistics.

Let's take a look at the information from various sources about

types of graph such as pictograph, pie chart, bar graph, line graph, scatter

gram and histogram to represent the statistics. We also conduct a survey

for two groups of students and present our data into suitable graph.

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PICTOGRAPH

Definition

Pictograph is a way of representing statistical data using symbolic

figures to match the frequencies of different kinds of data.

Characteristics

A pictograph or picture graph is a graph that uses symbols or

pictures to show data.

A key is included with the pictograph to explain what each picture

represents.

Advantages

Easy to show a graph for a small data.

The data is clearly shown by a picture.

Disadvantages

Did not suitable for a large data.

Difficult to compare between the two data.

How to create a pictograph

Draw a graph grid with rows and columns that we needed.

Then draw the any picture that we want to represent our work.

Make up a title for the pictograph. Write it above the grid.

Make up a symbol that will represent a specific number of the

picture that we draw.

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Examples:

Sammy sells apples, oranges, peaches and pears at his fruit stand. He

wants to show how much inventory he has of each fruit.

Types of apples Quantity

Red Delicious 30

Golden Delicious 25

Red Rome 40

McIntosh 20

Jonathan 35

PIE CHART

Definition

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A circular chart divided into sectors, illustrating relative magnitudes

or frequencies.

Characteristics

The arc length of each sector (and consequently its central angle

and area), is proportional to the quantity it represent.

The sectors create a full disk.

Advantages

display relative proportions of multiple classes of data

size of the circle can be made proportional to the total quantity it

represents

summarize a large data set in visual form

be visually simpler than other types of graphs

permit a visual check of the reasonableness or accuracy of

calculations

require minimal additional explanation

be easily understood due to widespread use in business and the

media

Disadvantages

A poor method of displaying information.

It is more difficult for comparisons to be made between the sizes of

items in a chart when area is used instead of length.

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It is rarely used in scientific or technical publications.

do not easily reveal exact values

Many pie charts may be needed to show changes over time

fail to reveal key assumptions, causes, effects, or patterns

be easily manipulated to yield false impressions

How to create a pie chart

First, make a full circle.

Then, draw the each sector according to the data that we already

get.

Make a key for each sector.

Write the title above the pie chart.

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Examples:

The table below is the mode of travel that has been chooses by 30

students to go to school.

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MODE OF TRAVEL FREQUENCY

BUS 13

CAR 6

BICYCLE 8

WALK 3

TOTAL 30

BAR GRAPH

Definition

A bar chart or bar graph is a chart with rectangular bars with

lengths proportional to the values that they represent.

The bars can be horizontally oriented (also called bar chart) or

vertically oriented (also called column chart).

Characteristic:

A bar chart is marked off with a series of lines called grid lines.

These lines typically mark off a numerical point in the series of

numbers on the axis or line.

Graph Title--The graph title gives an overview of the information

being presented in the graph. The title is given at the top of the

graph.

Axes and their labels--Each graph has two axes. The axes labels

tell us what information is presented on each axis. One axis

represents data groups, the other represents the amounts or

frequency of data groups.

Grouped Data Axis--The grouped data axis is always at the base of

the bars. This axis displays the type of data being graphed.

Frequency Data Axis--The frequency axis has a scale that is a

measure of the frequency or amounts of the different data groups.

Axes Scale-- Scale is the range of values being presented along

the frequency axis.

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Bars--The bars are rectangular blocks that can have their base at

either vertical axis or horizontal axis (as in this example). Each bar

represents the data for one of the data groups.

Advantages:

Bar charts are used for comparing two or more values that were

taken over time or on different conditions, usually on small data

sets

Sometimes a stretched graphic is used instead of a solid bar.

It is a visual display used to compare the amount or frequency of

occurrence of different characteristics of data and it is used to

compare groups of data.

Disadvantages:

More gridlines can make it easier to be exact with the amounts

being shown on the bar graph, but too many can make it confusing.

Cannot compare with large amount.

How to create a bar graph

1. Determine the following elements of the bar graph from the table

Title of the graph.

Label for each axis--Here we must determine which is to be

the frequency axis and which is to be the grouped data axis.

Scale for each axis--Determine the numerical scale for the

frequency axis, then the group names for grouped data axis.

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2. Draw a set of axes that you will use to construct your graph

Determine which axis will be the frequency axis--Determine

whether bars will go horizontally or vertically.

Write in axes labels.

For the frequency axis, determine the scale interval.

3. Use the data from the table to draw in the bars on the graph.

Example:

Price per Bushel (dollar) Quantity demanded (per week)

1 55

2 80

3 20

4 50

5 10

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LINE GRAPH

Definition

Line graphs are more popular than all other graphs combined

because their visual characteristics reveal data trends clearly and

they are easy to create.

Specifically, a line graph is a set of quantitative (numeric) data,

plotted in an x-y coordinate system, that are connected together by

lines. The data used to create a line graph must be composed of

pairs of observations.

Characteristic:

Title- The title of the line graph tells us what the graph is about.

Labels- The horizontal label across the bottom and the vertical

label along the side tells us what kinds of facts are listed.

Scales- The horizontal scale across the bottom and the vertical

scale along the side tell us how much or how many.

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Points- The points or dots on the graph show us the facts.

Lines- The lines connecting the points give estimates of the values

between the points.

Advantages:

They are good at showing specific values of data, meaning that

given one variable the other can easily be determined.

They show trends in data clearly, meaning that they visibly show

how one variable is affected by the other as it increases or

decreases.

They enable the viewer to make predictions about the results of

data not yet recorded.

Disadvantages:

had to change source data on the charts

line graphs only show points with no connecting line

How to create a line graph:

Decide on an appropriate scale for each axis.

The scale refers to the min and max numbers used on each axis.

They may or may not begin at zero.

The min and max numbers used for the scale should be a little

lower than the lowest value and a little higher than the highest

value.

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This allows you to have a smaller range which emphasizes the

comparisons/trends in the data.

Decide on an appropriate interval for the scale you have chosen.

The interval is the amount between one value and the next.

Example:

The table below shows Sam’s weight in kilograms for 5 months.

Sam's Weight

Month Weight in kg

January 49

February 54

March 61

April 69

May 73

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SCATTERGRAM

Definition:

A scattergram is a type of mathematical diagram using Cartesian

coordinates to display values for two variables for a set of data.

A scattergram is also called a scatter chart, scatter diagram and

scatter graph.

Characteristic:

A scattergram only specifies variables or independent variables

when a variable exists that is under the control of the experimenter.

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If a parameter exists that is systematically incremented and/or

decremented by the experimenter, it is called the control parameter

or independent variable and is customarily plotted along the

horizontal axis.

The measured or dependent variable is customarily plotted along

the vertical axis.

A scattergram can suggest various kinds of correlations between

variables with a certain confidence interval

If the pattern of dots slopes from upper left to lower right, it

suggests a negative correlation.

One of the most powerful aspects of a scatter plot, however, is its

ability to show nonlinear relationships between variables

Advantages:

A number of measurement strategies can be used including

frequency counts, duration, or latency recording.

Disadvantages:

The scattergram does not provide a way to document what

antecedents and consequences are observed during the sessions.

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How to create a scattergram:

Draw a grid. First, draw a horizontal line (X Axis). Then, draw a

vertical line (Y Axis) intersecting the center of the horizontal line.

Label each axis. The scale you use depends on the data you need

to plot.

Plot the data points. The first column of data relates to the data

point’s orientation along the X axis. The second column relates to

its orientation along the Y axis

View the results. If the results seem closely grouped along a line

or parabola (U or V shape), there is a strong correlation between

the two sets of data. If they do not seem to be related, the

association between the two sets of data is weak, or there may be

no correlation at all. If they are strongly correlated and form a sharp

slope, then a change in the first variable greatly affects the second

variable. If the slope is nearly flat (horizontal), a large change in the

first variable will only affect the second variable a little.

Example:

Student Number

1

2

3

4

Hours Slept

8

7

7

8

Test Score

83

86

74

88

15

5

6

7

8

9

10

6

5

7

4

9

7

76

63

90

60

89

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HISTOGRAM

Definition

The histogram is a summary graph showing a count of the data

points failing in various ranges.

The effect is a rough approximation of the frequency distribution of

the data.

Characteristics

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The groups of data are called classes.

The context of a histogram are known as bins because one can

think of them as containers that accumulate data and fill up at a

rate equal to the frequency of that data class.

Advantages

Histograms are useful data summaries that convey the following

information.

-The general shape of the frequency distribution (normal, chi-

square)

-Symmetry of the distribution and whether it is skewed.

-Modality-unimodal, bimodal, or multimodal.

Disadvantages

The shape of the histogram sometimes is particularly sensitive to

the number of bins. If the bins are too wide, important information

might get omitted.

If the bins are too narrow, what may appear to be meaningful

information really may be due to random variations that show up

because of the small number of the data points in a bin.

How to create a histogram

Groups are plotted on the x axis and the frequencies on the y axis.

Examples

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Consider the exam scores of a group of students which is the data of

classes spanning an interval of 10 points and counting the number of

scores in each data class, a frequency table and histogram can be

constructed as the following examples:

REPRESENTATION OF DATA

Below is a table and graph from the data of the survey that we have made entitled ‘The

Favourite Magazine among of IPGM KDRI Student Based on Gender’.

TYPES OF MAGAZINE MALE FEMALE

REMAJA 8 6

UTOPIA 4 2

GALAXY 1 8

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 Group     Count  

0 - 9 1

10 - 19 2

20 - 29 3

30 - 39 4

40 - 49 5

50 - 59 4

60 - 69 3

70 - 79 2

80 - 89 2

90 - 99 1

HYPE 1 1

UJANG 3 2

GEMPAK 3 1

TOTAL 20 20

Table 1

COMMENT

We have conducted a survey the favourite magazine among of

IPGM KDRI student based on gender. The most popular magazine that

have been read by the male student is Remaja while Galaxy for female

student. We can conclude that Hype is the least popular magazine among

the student because only one male and female student from 40 student

who read it.

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From the graph, the number of male students who is reading

Remaja is 8 students. Compare to the female students, 6 students only. It

is because female students maybe prefer other types of magazine to read.

Then, 4 male students read Utopia compare to only two female students

which is reading the same magazine. The reason is male students like to

read magazines which have gossip plus comic in there.

The female students who read Galaxy is 8 students compare to

only one male student read the same magazine. According to the female

students, they love to read the gossip of western artist compare from the

local artist. There is only one male and female student who read Hype. It

is because there is only have an entertainment for their reader.

There is a few student read Ujang and Gempak. For Ujang, only 3

male students and two female students read it and for Gempak, also 3

male students and only one female student read it. Students do not really

like to read a funny comic is the reason why the number of student read

Ujang is very little. Like Ujang, Gempak also did not really chosen by a

student because it’s only have fantasy comic in there. It also does not

suitable for student in IPGM KDRI to read it that will become a teacher

one day.

CONCLUSION

In the nutshell, we can concluded that all the graph have their own

advantages and disadvantages regarding to represent the data. Not all the

graph is suitable to represent the variety of number of the data. So, we

ourselves will choose the correct graph to represent our data or number. It

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is important to show our data clearly and easy to understand it if we want

to get the information from it some other time.

In additional, we can use pictograph, pie chart, bar graph and

histogram to represent the data that have small number. To represent the

large data we can used scattergram. Pictograph use picture to show the

data and it is very suitable for even number. It is not suitable for large

number because it is for us to make a picture as a symbol.

Unlike pictograph, a scattergram can suggest various kinds of

correlations between variables with a certain confidence interval. We also

can compare the two variables in the same graph. The popular graphs

that have been used is bar graph. It is because this graph is easy to make.

So, it is interesting to learn and make a graph because with that we

can compare the data especially in Mathematics.

NAME: AMNA BINTI ABDUL AZIZ

IC NUMBER: 891005 – 11 – 5088

First, I feel grateful to Allah for giving me and friends also to a lot of

time to finish this mathematics assignment. Thank you to Madam Norizah

for her teaches. When lecture give us this assignment, me and my friend

search the information about type of graph. With this assignment, I can get

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much knowledge. I can conclude that all graph that I need to learn also

advice me that learning is not easy as I think, so I need to study hard

about my learning.

Among I finish this assignment I have learnt and know many things

about mathematics especially about graph such as pictograph, pie chart,

bar graph, line graph, scattergram and histogram. My friend and I also

discuss together to finish this assignment. When I want to do this

assignment, I confuse how I want to start, I ask my friend and they teach

me and then I can do my job very well.

I also get new experience with my friend to conduct a survey for

two groups of student and we need to present our data into graphs. We

survey about favorite magazine. We divide by two groups, one for male

student and another one is female student. Since we do the survey, all

students give their cooperation.

In conclusion, each graph has own advantages and disadvantages.

We can transfer all data that we have into the graph.I can get many

experiences since doing this assignment. I enjoy doing this assignment. I

am happy to finish this assignment with my group.

Thank you.

NAME: NUR FARAHAIN BINTI ISMAIL

IC NUMBER: 890721-03-5172

I am very thankful that my others two friends and me have

completed this assignment on the time. At first, I think this assignment is

easy because I have to do the six graph altogether and a survey. While

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searching the information about the graph, I think this assignment is quite

tough. It is because my friends and I have to find the completed

information about the graph regarding to its characteristic, advantages,

disadvantages and how to create the graph. Fortunately I found it in the

book and also by internet. More or less it helps me to complete this task.

Not only that, another hard word that my group and I have to do is

doing the survey among the students. We choose magazine as our main

title to do the survey. The magazine that has been chosen is Remaja,

Utopia, Ujang, Galaxy, Hype and Gempak. Luckily, the entire students

give a good cooperation to answer our survey. I must get the accurate

data from the survey to do the graph. The graph that has been chosen to

represent the data from our survey is bar graph. It is the only graph that

will show our data clearly. Based on that graph, I make a comment to

complete it. The thing that I have to do is interpreting and comparing the

data from the graph.

I really hope that my assignment doing in the right way and follow

the right format. It is my group hard work to complete this assignment and

it is worth for us if our lecturer, Madam Norizah will satisfy with our

assignment.

Thank you.

NAME: SITI NURFADHILAH BINTI MD YUNUS

IC NUMBER: 890510-06-5240

Firstly, I was grateful because this assignment can summit on the

time. From this assignment, I got many information about statistics. I also

learn to make graph using computer. Draw the graph using computer very

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interesting for me even it quite difficult. It is also difficult to collect

information from various sources about types of graph such as pictograph,

pie chart, line graph, histogram, bar graph and scattergram. There were

many web not suitable with our topics and sometime it make us confused.

As one might expect , we have problem to make discussion. We

need to summit this assignment after holiday. We just make short

discussion. However, I do not have many problem in conduct a survey.

We were survey about favourite magazines among the student of IPGM

KDRI. All student were given cooperate during we conduct the survey.

I was using bar graph to present the data. Bar graph are used for

comparing two values that were taken on different group like male and

female. It is a visual display used to compare the amount or frequency of

occurrence of different characteristics of data and it is used to compare

groups of data.

To overcome the weaknesses I want to suggest that we must have

enough discussion. This very important to avoid mistakes during do this

assignment. Others, I want to suggest that all student given attention

during briefing. I want to thank to our lecturer Madam Norizah because

her helps along do this assignment.

Thank You.

REFERENCE

Whitney, H. (1932), "Congruent graphs and the connectivity of

graphs", American Journal of Mathematics 54: 150–168,

doi:10.2307/2371086.

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Zhang, Fu Ji; Lin, Guo Ning (1987), "On the de Bruijn-Good

graphs", Acta Math. Sinica 30 (2): 195–205, MR 0891925 .

Pie chart. From Wikipedia, the free encyclopedia take at 12

September 2009

Histogram equalization From Wikipedia, the free encyclopedia take

at 12 September 2009

www.mrsglossers.mathgoodiest.my 17 September 2009

Online ISSN 1755-3245 - Print ISSN 0008-6363

Copyright © 2009 European Society of Cardiology

Oxford Journals Oxford University Press

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