Statistic

September 17, 2007 [BASIC MATHEMATICS] 1.0

ACQUISITION OF KNOWLEDGE

1.1

Statistic

Statistics, the scientific discipline that deals with the collection, classification, analysis, and interpretation of numerical facts or data, was invented primarily in the nineteenth and twentieth centuries in Western Europe and North America. In the eighteenth century, when the term came into use, "statistics" referred to a descriptive analysis of the situation of a political state-its people, resources, and social life. In the early nineteenth century, the term came to carry the specific connotation of a quantitative description and analysis of the various aspects of a state or other social or natural phenomenon.

Professionalization of Statistics The professionalization of the discipline began in the late nineteenth century. An International Statistical Congress, made up of government representatives from many states, met for the first time in 1853 and set about the impossible task of standardizing statistical categories across nations. In 1885, a new, more academic organization was created, the International Statistical Institute. Statistical work grew in the new federal agencies such as the Departments of Agriculture and Education in the 1860s and 1870s. The annual Statistical Abstract of the United States first appeared in 1878. The states began to create bureaus of labor statistics to collect data on wages, prices, strikes, and working conditions in industry, the first in Massachusetts in 1869; the federal Bureau of Labor, now the Bureau of Labor Statistics, was created in 1884. Statistical 1

September 17, 2007 [BASIC MATHEMATICS] analysis became a university subject in the United States with Richmond Mayo Smith's text and course at Columbia University in the 1880s. Governments created formal posts for "statisticians" in government service, and research organizations devoted to the development of the field emerged. The initial claims of the field were descriptive, but soon, leaders also claimed the capacity to draw inferences from data. Throughout the nineteenth century, a strong statistical ethic favored complete enumerations whenever possible; to avoid what seemed the speculative excess of early modern "political arithmetic." In the first decades of the twentieth century, there were increasingly influential efforts to define formal procedures of sampling. Statistics as a field embraces the scientific ideal. That ideal, which replaces personal judgment with impersonal law, resonates with an American political tradition reaching back to the eighteenth century. The place of science, and especially statistics, as a source of such authority grew enormously in the twentieth century, as a greatly expanded state was increasingly compelled to make decisions in public, and to defend them against challenges.

1.2

Graph

A diagram (as a series of one or more points, lines, line segments, curves or areas) that represents the variation of variable in comparison with that of one or more other variables.

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September 17, 2007 [BASIC MATHEMATICS] 1.2.1 Bar graph A bar graph displays discrete data in separate columns. A double bar graph can be used to compare two data sets. Categories are considered unordered and can be rearranged alphabetically, by size, etc. Advantages •

Visually strong

•

Can easily compare two or three data sets

Disadvantages •

Graph categories can be reordered to emphasize certain effects

•

Use only with discrete data

Bar graphs are an excellent way to show results that are one time, that is not continuous - especially samplings such as surveys, inventories, etc. Below is a typical survey asking students about their favorite after school activity. Notice that in this graph each column is labeled - it is also possible to label the category to the left of the bar. In this case, the numbers for each category are across the bottom of the chart. 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. In this case, each grid line going up and down marks a multiple of 20 as the graph is divided such. 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. Notice that for data that does not fall evenly on a multiple of 20, the bar is in between two grid lines. Bar graphs are useful to get an overall idea of trends in 3

September 17, 2007 [BASIC MATHEMATICS] responses - which categories get many versus few responses). Below, we make a bar graph of the same data that we used for our pie chart in the last section:

The main difference is that instead of using labels to set the labels, we use names instead. (Also note that we have explicitly converted the abbreviations into character data, since they would otherwise be treated as factors for analysis and therefore displayed as numbers.) From this bar graph, the scales that are used in this histogram are not suitable because the data are big. It is because the data are not showing the difference form the others. It must write in a small scale. From 0 - 200 – 400, we must label it by 0 – 100 – 200.

1.2.2 Pictograph A pictograph takes the form of a bar graph. The key for a pictograph tells the number that each picture or symbol represents. Advantages •

Easy to read 4

September 17, 2007 [BASIC MATHEMATICS] •

Visually appealing

•

Handles large data sets easily using keyed icons

Disadvantages •

Hard to quantify partial icons

•

Icons must be of consistent size

•

Best for only 2-6 categories

•

Very simplistic

We can compare the numbers of snowiest cities in Albany, NY, Boston, MA, Juneau, AK and Omaha, NE in snowiest Cities. These below snowiest Cities show that Juneau, AK has more snow from the others. From the pictograph above, whole of the number of objects are not shown. So, we confused how to calculate all the data.

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September 17, 2007 [BASIC MATHEMATICS]

1.2.3 Pie chart A pie chart is commonly used to display the relative proportions of different values in a data set (more technically, the frequency of the levels of a categorical variable). For example, if we wanted to show how many seats the various political parties won in the 2004 European Union Parliament elections, we could display the information in the form of a pie chart. A pie chart displays data as a percentage of the whole. Each pie section should have a label and percentage. A total data number should be included. Advantages •

Visually appealing

•

Shows percent of total for each category

Disadvantages •

No exact numerical data

•

Hard to compare 2 data sets

•

"Other" category can be a problem

•

Total unknown unless specified

•

Best for 3 to 7 categories

•

Use only with discrete data

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September 17, 2007 [BASIC MATHEMATICS]

This pie chart is shows the percentages of composition of revenue contribution. In making a circle graph, the area of a sector is proportional to the fraction or percentages that it represents. The pie chart above is not accompanied by a table. Therefore, we cannot see the absolute amount of the composition of revenue contribution.

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September 17, 2007 [BASIC MATHEMATICS] 1.2.4 Line graph A line graph is like a scatter plot, except that its data points are connected by a line. Since line graphs are commonly used to visualize activity in the stock market, we will show how to produce a line graph of the Dow Jones Industrial Average (DJIA) during a twenty-year period (1985 to 2005). The data is saved as tab-delimited texts file and comes from djindexes.com. A line graph plots continuous data as points and then joins them with a line. Multiple data sets can be graphed together, but a key must be used. Advantages •

Can compare multiple continuous data sets easily

•

Interim data can be inferred from graph line

Disadvantages •

Use only with continuous data

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September 17, 2007 [BASIC MATHEMATICS] This graph can be used to trends and comparisons simultaneously. This graph shows the low and the higher in the graph. From this line graph, the graph is suitable to show the data because it is a complete graph which already has their labels of both axis of line graph and the data shown clearly by the graph.

1.2.5 Histogram A bar graph such that the area over each class interval is proportional to the relative frequency of data within this interval in plotting a histogram, one starts y dividing the range of all values into non-overlapping intervals, called class intervals, in such a way that every piece of data is contained in some class interval. A histogram displays continuous data in ordered columns. Categories are of continuous measure such as time, inches, temperature, etc.

Advantages •

Visually strong

•

Can compare to normal curve

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September 17, 2007 [BASIC MATHEMATICS] •

Usually vertical axis is a frequency count of items falling into each category

Disadvantages •

Cannot read exact values because data is grouped into categories

•

More difficult to compare two data sets

•

Use only with continuous data

We determine the height of each rectangular bar of the histogram shows the midpoints of the intervals. Bars are centered above the midpoints of the intervals. The vertical axis of the histogram shows the frequency of the scores in each of the intervals on the horizontal axis. In 20 to 29, it shows an extremely high or low score. From this histogram, we did not found the title of this histogram. The scales that are used in this histogram are suitable because the data are small. However, the raw data is not shown.

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September 17, 2007 [BASIC MATHEMATICS]

2.0

MASTERY OF KNOWLEDGE AND SKILLS

2.1

Introduction

Suicide (to kill oneself) is the act of intentionally terminating one's own life. Suicide occurs for a number of reasons such as depression, substance abuse, shame, avoiding pain or other undesirable fates, and financial difficulties. Views on suicide have been influenced by cultural views on existential themes such as religion, honor, and the meaning of life. Medically assisted suicide (euthanasia, or the right to die) is a controversial ethical issue involving people who are terminally ill, in extreme pain, and/or have minimal quality of life through illness. Self-sacrifice for others is not usually considered suicide, as the goal is not to kill one but to save another. In this survey we chose to look at this controversial topic of suicide. We constantly hear statistics about teenagers and suicide so we wanted to see how much truth they hold. We felt it was important to find out if suicide really did affect teenagers and to what extent it affected them. We also wanted to find out exactly how much teenagers knew about suicide and if the amount of knowledge was gender dependent.

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September 17, 2007 [BASIC MATHEMATICS]

2.1.1 Rationale We chose to look at this controversial topic of suicide because we constantly hear statistics about teenagers and suicide so we wanted to see how much truth they hold. This survey is conducted for students Institut Perguruan Bahasa Melayu Malaysia (IPBMM) which from PPISMP and PPRET to know what they have ever thought about committing suicide.

2.1.2 Objectives This survey has many objectives: (i) To determine the number of student that ever wanted to commit suicide, (ii) To determine the main reason for suicide that happen to our teenagers today, (iii) To determine the most common method of committing suicide, (iv) To make students or teenagers realize how to manage their mind and their feeling to avoid from depressed which can be cause them to suicide.

2.1.3 Sampling information 12

September 17, 2007 [BASIC MATHEMATICS] This survey involved 44 students (PPISMP and PPRET) which we selected any person from these batch.

2.1.4 Survey Instrument (Questionnaire)

Suicide Survey Questions Age

:

Gender

: Male / Female

Course

: PPISMP / PPPRET

1.

Have you ever wanted to commit suicide? (a) Yes (b) No

2.

Has anyone of importance in your life ever committed suicide? (a) Yes (b) No

The following questions will test your knowledge on suicide (choose ONE answer per question): 3.

Do you think what gender has a higher suicide rate? (a) Male (b) Female (c) Equal

4.

Do you think what the main reason for suicide is? (a) Family 13

September 17, 2007 [BASIC MATHEMATICS] (b) School (c) Peer Pressure (d) Substance Abuse (e) Other 5.

Do you think at what time do most people commit suicide? (a) Morning (b) Afternoon (c) Evening (d) Night

6.

Do you think where do most people commit suicide? (a) Home (b) School (c) Car (d) Buildings

7.

Do you think what the most common method of committing suicide is? (a) Pills (b) Guns (c) Hanging (d) Poison Gas

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September 17, 2007 [BASIC MATHEMATICS]

2.1.5 Survey Responses

Out of all of the surveys we sent out we received 44 responses from PPISMP Semester 1 and Semester 3 students’. We had many female responses than male responses and most of the responses were from 19 year olds and 20 year olds.

(i)

Gender Gender Male Female

Number of Responses 18 26

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September 17, 2007 [BASIC MATHEMATICS]

Male and Female Responses

30 25 20

Number of 15 Responses 10 5 0

Male

Female Gender

(ii)

Age Age 18 19 20 21

Number 13 15 15 1

16

September 17, 2007 [BASIC MATHEMATICS]

Responses by Age 16

Number of Responses

14 12 10 8 6 4 2 0 18

19

20

21

Age

18 18 18 18 18 18 18 18 18 18 18 18 18 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 21

(i)

Mean, = 13(18) + 15(19) + 15(20) + 1(21) 44

= 840 17

September 17, 2007 [BASIC MATHEMATICS] 44

= 19 year olds

(ii)

Mode = 19, 20

(iii)

Median = 19

2.2

Organization, Analyzing and Evaluation of Data

Survey 1: Have you ever wanted to commit suicide?

Overall Result; Ever wanted to do YES

COMMIT SUICIDE Tally IIII IIII IIII 18

Number of Responses 12

September 17, 2007 [BASIC MATHEMATICS] NO

IIII IIII IIII IIII IIII IIII II

32 44

TOTAL

Percentage of the responses; YES

: 12/44 x 100 = 27.3 %

NO

: 32/44 x 100 = 72.7%

72.7% (32) of the people that answered the survey said that they have never thought about committing suicide. The remaining 27.3% (12) of the people said that they have thought about committing suicide.

Have you ever wanted to commit suicide?

35 30 25 Number or 20 Responses 15 10 5 0

YES

NO

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September 17, 2007 [BASIC MATHEMATICS]

Result based on Gender; From the 12 responses that they ever wanted to commit suicide, we got the different between these two genders. There are more females that said they have thought about committing suicide then males. 5 males answered said they have thought about it compared to 7 females.

Ever wanted to do

COMMIT SUICIDE Tally

(gender) FEMALE MALE

IIII II IIII TOTAL

20

Number of Responses 7 5 12

September 17, 2007 [BASIC MATHEMATICS]

Have you wanted to commit suicide? 8

Number or responses

7 6 5 4 3 2 1 0 Female Yes

Male Yes

Result based on Age; As we knew, the students from batch PPISMP and PPRET, the range of their age are just in area eighteen year olds to twenty year olds. The age group that has thought about it the most is eighteen year olds. 6 of 13 eighteen year olds have thought about committing suicide compared to 5 of 15 nineteen year olds, 1 of 15 twenty year olds, and none of twenty one year olds.

Age of Respondents 18 19 20 21 TOTAL

COMMIT SUICIDE Tally IIII I IIII I -

21

Number of Responses 6 5 1 0 12

September 17, 2007 [BASIC MATHEMATICS]

Have you ever wanted to commit suicide? 7

Number of Responses

6 5 4 3 2 1 0 18

19

20 Age

18 18 18 18 18 18 19 19 19 19 19 20

(i)

Mean, = 6(18) + 5(19) + 1(20) + 0(21) 12

= 223 12

= 18.6 = 19

22

21

September 17, 2007 [BASIC MATHEMATICS]

(ii)

Median, = (18 + 19) 2

= 37 2

= 18.5 = 19

(iii)

Mode = 18

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September 17, 2007 [BASIC MATHEMATICS]

Survey 2: Has anyone of importance in your life ever committed suicide?

Overall Result; COMMIT SUICIDE Tally

Ever wanted to do

Number of Responses

(importance person in life) YES NO

IIII IIII III IIII IIII IIII IIII IIII IIII I TOTAL

13 31 44

Percentage of the responses; YES

: 13/44 x 100 = 30%

NO

: 31/44 x 100 = 70%

From the survey, the majority (70%) has never lost anyone of serious significance to suicide. Only 30% of those students surveyed have lost someone important to them.

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September 17, 2007 [BASIC MATHEMATICS]

Has anyone of importance in your life ever commited suicide?

35 30 25 Number of 20 Responses 15 10 5 0

YES

NO

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September 17, 2007 [BASIC MATHEMATICS] Result based on Gender

Ever wanted to do

COMMIT SUICIDE Tally

Number of Responses

(importance person in life)-based on gender Male Female TOTAL

IIII IIII III

5 8 13

The total responses for this question were split male and female to determine which gender generally comes in contact with suicide more. Neither male nor female participants have had much experience with suicide, though. However, of the two, males (5) have dealt with suicide more closely than females (7).

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September 17, 2007 [BASIC MATHEMATICS]

Has anyone of importance in your life ever commited suicide? Yes.

7 6 5 Number of 4 Responses 3 2 1 0

MALE

FEMALE

27

September 17, 2007 [BASIC MATHEMATICS]

Survey 3: Do you think that gender has a higher suicide rate?

COMMIT SUICIDE Tally IIII IIII I IIII IIII IIII IIII IIII II IIII IIII

Answer Male Female Equal Total

Number of Responses 7 27 10 44

As we do surveys, females have a higher suicide rate than males do. When we asked this question, 27 people answered that females had a higher suicide rate. 10 of the people surveyed answered equal between the two genders do suicide. Other these two answers, they said males have a higher suicide than females do.

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September 17, 2007 [BASIC MATHEMATICS]

Do you think what gender has a suicide rate? 30

Number of Responses

25 20 15 10 5 0 MALE

FEMALE Gender

29

EQUAL

September 17, 2007 [BASIC MATHEMATICS] Survey 4: Do you think what that the main reason for suicide is?

COMMIT SUICIDE Tally III IIII IIII IIII IIII IIII IIII IIII I IIII

Answer Family School Peer Pressure Substance Abuse Other Total

Number of Responses 3 0 35 1 5 44

Percentage of the responses; Peer pressure

: 35/44 x 100 = 80%

Most people answered peer pressure for this question. 80% of people believed that the main reason for suicide is peer pressure. Other responses answered family, substance abuse and others are the main reason for suicide.

30

September 17, 2007 [BASIC MATHEMATICS]

Do you think what the main reason for suicide is? 35

35 30 25 Number of 20 Responses 15 10 5 0

5

3

1

0 Family

School

Peer Pressure

Main reason

31

Substance Abuse

Other

September 17, 2007 [BASIC MATHEMATICS] Survey 5: Do you think at what time do most people commit suicide?

Answer Morning Afternoon Evening Night

COMMIT SUICIDE Tally I IIII II IIII IIII IIII IIII IIII IIII IIII II Total

Number of Responses 1 4 2 37 44

Percentage of the responses; Night : 37/44 x 100 = 84% Others: 7/44 x 100 = 16%

From the survey we did, the most common time to commit suicide is in the night. Out of all of the people that answered the survey only 16% of the people answered that the most common time to commit suicide was the morning, afternoon, and evening. 84% of the people surveyed felt that the most common time was night.

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September 17, 2007 [BASIC MATHEMATICS]

Do you think at what time do most people commit suicide? 37

40 35 30 25 Number of 20 Responses 15 10 5 0

4

2

1 Morning

Afternoon Time

33

Evening

Night

September 17, 2007 [BASIC MATHEMATICS]

Survey 6: Do you think where do most people commit suicide?

COMMIT SUICIDE Tally IIII III II I IIII IIII IIII IIII IIII IIII III

Answer Home School Car Building Total

Number of Responses 8 2 1 33 44

Percentage of the responses; Building

: 33/44 x 100 = 75%

Others

: 11/44 x 100 = 25%

Another question asked was "Do you think where do most people commit suicide?" 75% of all of the people answered that most people commit suicide at building. 25% of those asked saying that the most common place was home, school, or cars.

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September 17, 2007 [BASIC MATHEMATICS]

Do you think where do most people commit suicide? 33

35 30 25 Number of Responses

20 15 10

8

5

2

1

0 Home

School

Car Place

35

Building

September 17, 2007 [BASIC MATHEMATICS]

Survey 7: Do you think what the most common method of committing suicide is?

COMMIT SUICIDE Tally IIII IIII IIII IIII IIII II I IIII IIII II IIII

Answer Pills Guns Hanging Poison Gas Total

Number of Responses 27 1 12 4 44

Percentage of the responses; Pills

: 27/44 x 100 = 61%

Others

: 39/44 x 100 = 39%

Most people said, the most common method of committing suicide is pills. 61% of those surveyed answered that the most common method was with pills. 39% of the people thought that the most common method was guns, hanging and poison gas.

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September 17, 2007 [BASIC MATHEMATICS]

Do you think what the most common method of committing suicide is?

30

27

25 20 Number of 15 Responses

12

10 4

5 1 0 Pills

Guns

Hanging

Poison gas

Method

Conclusion We received 44 comments in total. The comments were mostly about suicide in general and how it isn't the way out. People said that our survey made them think and that it was well done. After doing this survey, we found there are more females that said they have thought about committing suicide then males. Most people answered peer pressure is the main reason for commit suicide. We thought that some people who end their lives or attempt suicide might be trying to escape feelings of rejection, hurt, or loss. Some people may be worried about disappointing friend 37

September 17, 2007 [BASIC MATHEMATICS] members. And some may feel unwanted, unloved, victimized, or like they’re a burden to others. The most common time to commit suicide is in the night and the most common place is building. Others is the most common method that they use to commit suicide is pills. If you have been thinking about suicide, get help right away. Depression is powerful. You can not wait and hope that your mood might improve. When a person has been feeling down for a long time, it is hard to step back and be objective. Talk to someone you trust as soon as you can if you can not talk to a parent, talk to a coach, a relative, a school counselor, a religious leader, or a teacher.

REFERENCES

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September 17, 2007 [BASIC MATHEMATICS] •

Anderson, Margo. The American Census: A Social History. New Haven, Conn.: Yale University Press, 1988.

•

NC State University (2004). Lab Write Resources. [online] http://www.ncsu.edu/labwrite/res/gh/gh-bargraph.html [August, 30, 2007]

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NC State University (2004). Lab Write Resources. [online] http://www.ncsu.edu/labwrite/res/gh/gh-linegraph.html [August, 30, 2007]

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NC State University (2004). Lab Write Resources. [online] http://www2.ucdsb.on.ca/athens/surveys/index.htm [August, 30, 2007]

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K.M Lee. (2007, July 31). Support Line. Starbiz Times, p. B5.

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Max A. Sobel, Evan M. Malestsky (1970), Teaching Mathematics A Sourcebook of Aids, Activities and Strategies, Second Education, Prentice – Hall

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Rick Billstein, Shlomo Libeskind (2004), A Problem Solving Approach to Mathematics, Pearson Education

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McGraw-Hill (2002), Mathematics Level 9, McGraw-Hill School Division

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McGraw-Hill (2002), Mathematics Level 5, McGraw-Hill School Division

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