representing data. adaptif hal.: 2 isi dengan judul halaman terkait a. stem diagram representing...

REPRESENTING DATA

REPRESENTING DATA

Hal.: 2 Isi dengan Judul Halaman Terkait Adaptif

a. Stem Diagram Representing data by using picture in

stem or rectangle form and it is called stem diagram. It can be painted vertically or horizontally.

REPRESENTING DATA


Example 1: This table below shows number students who

have problem in a school.

0

2

4

6

8

10

12

14

2001 2002 2003 2004

Year

Num

ber

of S

tuden

ts

REPRESENTING DATA


Determine the number of students who have problem from 2001 to 2004!

Answer: The number of students who have problem from 2001 to

2004 = 6+10+13+10

= 39 students

REPRESENTING DATA


Example 2:

The stem diagram below shows the graduation of an SMK since 1992 until 1996. The total number of students who have job since 1992 until 1995 are…

REPRESENTING DATA


0

50

100

150

200

250

300

1992 1993 1994 1995 1996

Year

Num

ber

of G

raduat

eses

Work

Continuingstudy

Jobless

REPRESENTING DATA


Question:

The number of graduates who have job since 1992 until 1995 are…

Answer: = 200+100+225+100+200+75+250+75 = 1225

REPRESENTING DATA


b. Circle Diagram

Representing data by using picture in circle form is called circle diagram.

The circle area is separated in segments .

REPRESENTING DATA

Example 1:

Next diagram shows the ways of the students

in SMK go to school. If the total number

of students is 480 persons, then the

students who goes to school on foot is…

On foot

Cycling

600

720 By Bus

45 0

By

Motorcycle


Answer : The segment degree of students who goes to

school on foot: 3600 – (600+720+450) = 1830

The number of students who goes to school on foot:

= x 480 students

= 244 students

0

0

360

183

REPRESENTING DATA


Example 2 : The investigation of the graduate of an SMK

represented by this diagram. If the number of graduates who work is 135 persons, then the students who continue the study is……. Entrepreneur

Jobless

10%

Work

45%

Continuing study

REPRESENTING DATA


Answer : The percentage of graduates who continue their study

= 100% - (25%+45%+10%) = 20% The number of graduates who continue study

= x 135 Persons

= 60 persons

%45

%20

REPRESENTING DATA


REPRESENTING DATA

c. Line Diagram

Representing data by using line diagram and it is usually used to show the dynamics in certain period.

Example :

Data of Smk Nusantara graduates who work based on their field study since 2003 until 2007 as follows:

Make the line diagram

Year

Number of students

2003 2004 2005 2006 2007

80 100 160 120 200


REPRESENTING DATA

Answer :

Year

2003 2004 2005 2006 2007

Number who works

80

100

120

160

200

•

•

•

•

•


REPRESENTING DATA

d. Histogram & Frequency Polygon Histogram is as representing data if the data are grouped

in frequency distribution table.

There are several ways to make frequency distribution table, they are:

1.Determine data range ( J )

J = datum maximum - datum minimum

2. Determine interval class ( K )

K = 1 + 3,3 log n and n = number data ; K round no.

3. Determine the length of interval class = KJ


REPRESENTING DATA

Example :Data Result of math test as follows:Make Histogram and its frequency Polygon

Score Frequency Mid Score (xi)

38 - 45

46 - 53

54 - 61

62 - 69

70 - 77

78 - 85

86 - 93

Total

2

8

8

7

5

7

3

40

41,5

49,5

57,5

65,5

73,5

81,5

89,5


REPRESENTING DATA

From the data above, can be explained that: Class lower limit, are 38, 46, 54, 62, 70, 78 and 86 Class upper limit, are 45, 53, 61, 69, 77, 85 and 93

Class mid-score ( xi ) = ½ ( lower limit + upper limit )

Side class lower = lower limit - 0,5

Side class upper = upper limit + 0,5

So side class lower fro the above data, are: 37,5; 45,5; 53,5; 61,5; 69,5

77,5 and 88,5


REPRESENTING DATA

Histogram of data is :

THE MEASURE OF CENTRAL TENDENCYTHE MEASURE OF CENTRAL TENDENCY

Title Part


Central tendency measurement is a single score of data which gives clear and short illustration about where is the central data and represents all data.

x

1. Mean

a. Single data = n

x


Example :

Determine mean of the data: 2,3,4,5,6

Answer =

= 4

x 5

65432


b. Weight Data

=

Example : The weight of package that has been

accepted by a company for a week as in the table beside.

The average weight of the packages in a week is…

f

xf .xWeight

(kg)Frequency

5678

68

124


Answer: Weight

(kg)Frequency

5678

68

124

Total 30

f

xf .

30

194

x =

=

= 6,47

So the average of package weight = 6,47 kg

UKURAN PEMUSATAN DATA

F. XX F

30

48

84

32

194


c. Group Data Step I:

= Example : Find the mean of math test of 20 students

which is represented in the table beside!

f

xf .x

Score Frequency

3 - 45 - 67 - 8

9 - 10

2486

Total 20


x = Mid-point


Score Frequency

3 - 4

5 - 6

7 - 8

9 - 10

2

4

8

6

Total 20

20

146x

Answer:

=

= 7,3


x F . x

3,5

5,5

7,5

9,5

7

22

60

57

146



Step II:

xo = the average is, d = x - xo

Example : If the average of the table is 67, then the average score of the data is...

f

f.dxx 0

Score f x

55-59

60-64

65-69

70-74

75-79

4

10

17

14

5

57

62

67

72

77

Total 50


Score f x

55-59

60-64

65-69

70-74

75-79

4

10

17

14

5

57

62

67

72

77

Total 50

Answer:


d f. d

- 10

- 5

0

5

10

- 40

- 50

0

70

50

30

= 67 +50

30

= 67,6


2. Median

Median of number set is the number in the middle after they have been arranged orderly from the smallest up to the biggest one.

2

)1( n

a. Single Data

b. If n is odd number

Place of Me=data to-

If n is even number

Me = ½ ( Xn/2 + Xn/2 + 1 )



Answer :

Data is arranged : 5,5,6,6,6,6,7,7,8,8,8,9

The number of data ( n ) = 12 ( even )

Place of Me = data to ½ ( X6 + X7 )

= ½ ( 6 + 7 )

= 6,5

Example :

The math score of 12 students are: 6,8,5,7,6,8,5,9,6,6,8,7.

Find the median of that data!



b. Grouped Data

Score of Me = b + p

b = Side below a median class p = Length of interval class F = Number of frequency before Me class f = Frequency of median class n = Data size

f

Fn21



Example :

Determine median of this frequency distribution table below!

Score Frequency

40-44

45-49

50-54

55-59

60-64

65-69

4

8

12

10

9

7



Answer : To determine the median class, is needed ½ .n = ½ x 50 data = 25 data , it means

median located in the 4rd interval class Score of Me = 54,5 + 5

= 54,5 + 0,5 = 55

10

2425



Mode

Mode of number set is a number which often appears or the score which has the most frequency.

a. Single data / weight

Example :

Find the mode of each number sets below:

a. 5,3,5,7,5 c. 2,5,6,3,7,9,8

b. 4,3,3,4,4,7,6,8,7,7 d. 2,2,3,3,5,4,4,6,7



Answer :

a. Mode of the data is 5

b. Mode of data is 4 and 7

c. Mode of data is not exist

d. Mode of data is 2,3,4



b. Groped Data

Mo = b + p

b = side below of mode class p = length of interval class d1 = the difference between mode class frequency and

the previous class frequency d2 = the difference between mode class and the next

class frequency

21

1

dd

d



Example :

The weighs of 30 students of a class are represented in the table below. Mode of data is….

Weigh (kg) f

41 - 4546 - 5051 - 5556 - 6061 - 65

16

1283



Answer :

Mode located in the 3rd interval class,

with b = 50,5; p = 5; d1 = 6; d2 = 4

Mode (Mo) = 50,5 + 5

= 50,5 + 3

= 53,5

46

6



Exercise

1. This table shows the using of tax income in the town. If the total fund that has been used for the school building about

Rp. 440.000.000,00, then the fund for the road construction is…P

roperty

4%

School

22%

Administration

16%

Road

PENYAJIAN DATA


Aswer : The fund used for the road construction is

x Rp 440.000.000,00

= Rp 1.160.000.000,00

%22

%58

PENYAJIAN DATA


2. The mean of the height table below is…

Height (cm).

f

150 -154155 -159160 -164165 -169170 -174

36984

Total 30

x d fd

152157162167172

-10-505

10

-30-300

4040

20


f

dfx

.0x

30

20

=

= 162 +

= 162,7


3. The loan of cooperation as follows :

The Loan(in Rp)

Frequency

55 - 6061 - 6667 - 7273 - 7879 - 84

8141086

The loan which divides grouped data into two part equally is….




Answer : Median located in the 3rd interval class, with b = 66,5 ; p = 6 ; F = 22 ; f = 10 ; n = 46

Value of Me = 66,5 + 6

= 66,5 + 0,6 = 67,1

So the loan = 67,1 x Rp 1000,00

= Rp 67.100,00

10

224621x


4. The total loan of member Tahu “SUMEDANG” Cooperation noted as follow :

Saving account

(in thousands Rp)Frequenc

y

60 - 6263 - 6566 - 6869 - 7172 - 74

31020157

According to the above data, the most member who have the same saving account is….




Answer :

Mode located in the 3rd interval class,

with b = 65,5 ; p = 3 ; d1 = 10 ; d2 = 5;

Mode (Mo) = 65,5 + 3 = 65,5 + 2 = 67,5

So the most member of cooperation have saving account about

67,5 x Rp 10.000,00 = Rp 675.000,00

510

10


5. If mean of this table is equal to 7, then x is….

Score f

56789

68

10x4

Total 28 + x

f.x

3048708x36

184 + 8x


Answer :

7 =

7 ( 28 + x ) = 184 + 8x

196 + 7x = 184 + 8x

7x – 8x = 184 – 196

x = 12

x

x

28

8184

representing data. adaptif hal.: 2 isi dengan judul halaman terkait a. stem diagram representing...

Documents

representing data slide

adaptif hal

data answer

data example

number students

total number of students

number of graduates

motorcycle slide