Project in Trigonometry

8/2/2019 Project in Trigonometry

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GRAPHSREPORTERS:

Bernardo Ganotice IV

Federico Iringan

Christian Granel


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GRAPHS

Data presented in tabular form can also bepresented in the form of a graph.

A graph is a visual representation of a setof values in relation to another set.

The important features of a graph are the

title of the graph and the two elements orvariables that are being analyzed.


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There are four kinds of simple graphs.Each of which has its particular use.

1. Line graph 3. Circle or Pie graph2. Bar graph 4. Picture graph or

Pictograph


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THE LINE GRAPH

A line graph is used to show changesthat happen over a period of time. It is madeup of two perpendicular lines labeledaccording to the elements that are beinganalyzed. On the vertical scale are foundthe quantities, while on the horizontal scaleare found the time periods. Points are

plotted based on the relationship of theelements, and those points are connectedby a line.


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0

55

110

165

220

275

330

385 KWh

KWh

Monthly Electric Consumption of a

Local Resident ( 13- month period)


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The graph above indicates the trend ofelectric consumption over a period of 13

months, from January 2001 to January 2002.Important information can be observed

and then gathered from the line graph. Try toanswer the following.

1. What two quantities are beingcompared in the line graph?2. When did the highest consumption

occur? The lowest consumption?

3. Which months show the same amountof electric consumption?

4. Between which two months was theincrease/decrease in consumption greatest?


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5. What is the approximate differencebetween the consumption for January

2001 and January 2002?

6. What conclusion can you draw fromthe trend in electric consumption as

shown by the line graph?

There are cases where multiple linegraph is used. This kind of graph is useful

when showing trends and makingcomparisons simultaneously.


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0

10

20

30

40

50

60

70

80

90

100

1992 1993 1994 1995 1996 1997 1998 1999

PalayCorn

Coconut

Sugarcane

PRODUCTION OF SELECTED AGRICULTURALCROPS: 1992-1999


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The multiple line graph records yearlyproduction of selected agricultural crops in thecountry from years 1992 to 1999. Generally, there

are slight changes in the rise and fall of productionfor palay, corn, coconut and sugarcane, exceptfor a very marked increase in the year 1999.Observe these changes these changes andanswer the following questions.

1. What are being compared in the multipleline graph?

2. What does the vertical axis represent? Thehorizontal axis?

3. What was the approximate production foreach crop in the beginning year?

4. Which two crops followed almost the sametrend of increase in production for several years?


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5. Which crop registered almost noincrease in production for seven years?

6. In what year was the greatestincrease in the production for palay,coconut and corn?

7. Which crop registered a verymarked increase in production?Approximate the production of this crop in1992 and in 1999. how many thousand

metric tons was this increase?8. What do you think contributed to

the very great increase in the productionof palay?


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The BAR GRAPH

A bar graph is used for marking direct

visual comparison of data. The bars in thegraph may be drawn horizontally or verticallyto represent the information.

Population by Region : 2000

024

68

1012

4

NCR 3 6 7 5 1 8 9 2

11

12

10

ARMM

C

ARAGA

CAR

Region

Region


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Study the graph and observe the information given.

1. What information does the graph providethe reader?

2. Give an approximation for the population

of each region.

3. How do the largely populated regions

compare? By how many millions do they differ?

4. Which region comprise Luzon? Visayas?

Mindanao? Add the populations of the regions foreach group. Which region has the greatest number

of people?


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The bars in a bar graph can also be drawnhorizontally. Presented below is a multiple

horizontal bar graph.Study the graph and answer the following.

1. What does the graph tell you?

2. What does each type of barrepresent?

3. Which sector of social services has the

largest support from the government?4. Approximate the number of institutions

or centers from each sector for the five-yearperiod.


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0 5 10 15 20 25 30 35 40

2000

1999

1998

1997

1996

Child Caring

Institution

YouthCenters/Facilities

Facilities for

Disabled/Elderly

Persons

Substitute Home forwomen in Different

Circumstances

Distribution of Social Services: 1996-2000

(Number of Institutions, Centers and Facilitiis)


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The CIRCLE GRAPH

A Circle or pie graph is represented by a

circle divided into parts. It shows the relationshipsamong parts as well as the relationship of a partto a whole. The data are presented in

percentage form and represented in the circlegraph by an equivalent fractional part of awhole.

Illustrative Example:

A college student has totaled his expensesfor the last school year and represented hisfindings in a circle graph.


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A College Student's Budget: 80,000PhP

Tuition/Books

ClothingEntertainment

Savings

Utilities

Food

Rent


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Observe the graph and answer the followingquestions.

1. Which two items account for the greatestexpenses?

2. What percent of the budget is spent for food?

3. What percent of the budget is saved?4. Which three items incur the same expense?

5. If the monthly allowance amounts to 80,000 PhP,

how much is spent for each item?

To construct a circle graph, recall the lessonson measures of angles and arcs.


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In the above example, the percent rate foreach type of expense is given. This rate is multiplied

by 360, the measure of one full circle.

Rent 30% of 360 = 0.30 X 360 = 108

Food 20% of 360 = 0.20 X 360 = 72

Tuition/ 15% of 360 = 0.15 X 360 = 54BooksClothing 10% of 360 = 0.10 X 360 = 36

Entertain- 10% of 360 = 0.10 X 360 = 36

MentUtilities 10% of 360 = 0.10 X 360 = 36

Savings 5% of 360 = 0.05 X 360 = 18


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With a protractor, you are ready todetermine the measure of each sector of

the circle representing each item in terms ofdegrees.

To determine the amount spent for

each item, multiply the correspondingpercent for each item by the total budget.For instance, 30% of 80,000 = 0.30 X 80,000 =

24,000 PhP, the expense for the rent.Do the same for each item.


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The PICTURE GRAPH or PICTOGRAPH

A picture graph uses a picture oran icon to symbolize the quantities

being represented. From this graph, the

change in quantity over time can beobserved. An essential part of a picture

graph, besides the title is the legend.

The legend indicates the number ofeach item in a given data.


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Value of Coconut Production: 1995-1999

1995

1996

1997

1998

1999In Million Pesos

Legend: - 5 million pesos


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Study the picture graph and answerthe following.

1. What does the picture graph tell you?

2. What does each coconut fruit represent?

3. Estimate the amount of production peryear as shown by the graph.

4. Which years are the most productive?

5. How will these yearly increases affect thecountrys economy?


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Frequency Distribution and Graphs

Frequency distributions are usuallypresented graphically in order to seethe significant features of the form of

distribution at a glance.


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Frequency Distribution of the Number of Years

Of Experience of Teachers in Bagong Diwa High School

Experience in Years TallyFrequency

30-32 I 1

27-29 I 1

24-26 II 2

21-23 III 3

18-20 IIII 4

15-17 II/II 5

12-14 II/II I 6

9 -11 II/II III 86 -18 II/II II/II 10

35 II/II 5

02 III 3

n = 48


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A frequency distribution is the distribution ofthe total number of observations or frequencies

over arbitrarily defined classes or categories. Thenumber of observations falling under a class is called

class frequency.

A symbol defining a class, like 049 is called a

class interval. The end numbers, 0 and 49, are calledclass limits. The smaller number, o, is the lower classlimit and the higher number, 49, is the upper class

limit.

Continuous variables are reported to thenearest unit while discrete variables are not. For

example, measures of height or weight are

continuous variables


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while those of population are discretevariables. Individuals standing 156 cm high

would vary from 155.5 cm and 156.5 cm. Aclass interval of 154 155 cm would really be

indicated by 153.5 -155.5 cm. Those two

numbers, 153.5 and 155.5 are called class

boundaries; the smaller number, 153.5 is thelower class boundary or exact lower limit whilethe bigger number, 155.5 is the upper class

boundary or exact upper limit.

The size of a class interval is thedifference


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between the

The class mark or mid-value is the midpoint of

the class interval, and is obtained by taking one-halfof the sum of the lower and upper class limits. Forexample, the class mark of the class 0 49 is 0 +

49/2, or 24.5.

Here are the steps in constructing a frequency

distribution.

1. Determine the range. It is the difference

between the highest and the lowest values inthe list of data.

In our example, the range is 30, that is 31 - 1 = 30.


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2. Determine the number of classes or classintervals desired. The number of classes (usually

between 8 to 16) is arbitrarily selected dependingupon the size of the data and spread of the values

over which frequencies are found.

In our example, there are 11classes or class

intervals.

3. Determine the size of the intervals by dividing therange by the desired number of class intervals. The

class size denoted by i is the number of values thatincluded in each class. The usual class sizes arre 2, 3,5, or 10. In our example, the class size is 3.


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4. Determine the lower and upper limits of the firstclass interval. It should include the smallest valuein the list of data. Class marks are the midpoints

of the classes.

In our example, the first class interval includesthe values 0, 1 and 2. 0 is the lower limit while 2 is theupper limit. 1 is the class mark.

5. Determine the lower and upper class limits of thesucceeding class intervals by adding the size ofthe class interval to the lower and upper limits ofthe preceding class interval until the highest classinterval is obtained.

6. Determine the number of observations bytallying each value into each class interval, thusfinding the class frequencies.


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0

2

4

6

8

10

1 4 7 10 13 16 19 22 25 28 31 34

Frequency

Frequency

The HistogramThe distribution of the data is shown below.

Number of Years of Experience of TeachersIn Bagong Diwa High School

No.ofTeache

rs

Length of Experience (Years)


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This graph is called a histogram.

The histogram is constructed as a sequence

of vertical rectangles, each rectangle is drawnwith its base equal to the class interval and a

height corresponding to the class frequency as

shown in the figure above.

What set of values is found along thehorizontal axis? Along the vertical axis?

What does the length of each base

represent? Where do you find the greatest

number of teachers? What can you say aboutthe profile of teachers in Bagong Diwa High

School?


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The Frequency Polygon

Another way of representing a frequencydistribution is drawing a line graph. With the same dataset and in the coordinate plane, plot the class marks ormidpoints of the class intervals against the classfrequencies. With a line, connect these pointssuccessively from left to right. Connect the first and last

points to the horizontal axis by adding an interval withzero frequency.


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0

2

4

6

8

10

1 4 7 10 13 16 19 22 25 28 31 34

No.ofTeache

rs

Length of Experience (Years)


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This line graph is called a frequencypolygon. Notice that the frequency polygon

is drawn against the histogram illustrating thesame frequency distribution.

What is the highest point in the

frequency polygon?What does it show in relation to the

length of experience of teachers in Bagong

Diwa High School?

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Project in Trigonometry