statistics

STATISTICSGrade IX

SutarmanIndonesian International School Yangon

Release 12006

END

SUBTOPICS :

Table Frequency Aritmetic Mean Mode Median Quartile Data Representation

Consider the following case :

The measurement of height was done on a number of people, then the following measures (in centimetres) were obtained:

170, 165, 165, 172, 155, 157, 172, 172,175, 175, 165, 170, 170, 175, 157, 172, 171, 165, 172, 165, 150, 155,180, 170, 165, 157, 165, 175, 165, 170

Statistics gives us easier way to understand the data.

170, 165, 165, 172, 155, 157, 172, 172,175, 175, 165, 170, 170, 175, 157, 172, 175, 165, 172, 165, 150, 155,180, 170, 165, 157, 165, 175, 165, 170

Table Frequency :We can make a table frequency for the data of heightmentioned :

155157165170172175180

IIIIIIIIIII IIIIIIIIIIIIIIIIIII

150 12385551

30

Height (cm) Tally Frequency

Sum

150 160 170 180140

Graph of Frequency

0190

2

4

6

8

10

Frequency

Height

Arithmetic Mean (1)

Arithmetic mean or mean of the mentioned data is the sum of data divided by the number of data.

Suppose that there are n data as follows : nxxxx ,...,,, 321

nxxxxxMean n ...321

Example :

Determine mean from data : 18, 22, 20, 10, 9, 7, 6, 12, 12, 19, 17, 12, 16, 18, 12

Answer :121816121719121267910202218 x

15

15210

14

Arithmetic Mean (2)Example :Determine mean of thedata :

Answer :

Data f679

1012161718192022

11114112111

Data f Data x f

Sum

6791012161718192022

11114112111

679

1048161736192022

15 210

x

21015 = 14

ModeMode is the data of the highest frequency.

Example :

Answer :a. Mode = 12b. Mode = 2 and 3c. no mode

Find mode from each data :a. 18, 22, 20, 10, 9, 7, 6, 12, 12, 19, 17, 12, 16, 18, 12b. 3, 5, 2, 8, 3, 2, 7, 9, 10c. 4, 3, 7, 9, 2, 1

Median (1)

Median is a data that divides the whole data into two parts of equal numbers.

• To find the median, the data must be ordered.

Ordered data : 6, 7, 9, 10, 12, 12, 12, 12, 16, 17, 18, 18, 19 20, 22

Median (2)

Example :

Find the median of data : 18, 22, 20, 10, 9, 7, 6, 12, 12, 19, 17, 12, 16, 18, 12

Answer :

Quartile (1)

• The quartiles (lower quartile, median, and upper quartile) are the data that divides the whole data into four parts of equal numbers.

– To find the quartiles, the data must be ordered.

3 numbers

Equal Numbers !

7 numbers

Quartile (2)Example :

Find the quartiles of data : 18, 22, 20, 10, 9, 7, 6, 12, 12, 19, 17, 12, 16, 18, 12Answer :Ordered data :

6, 7, 9, 10, 12, 12, 12, 12, 16, 17, 18, 18, 19 20, 22

3 numbersLower quartile =10

3 numbers3 numbers 3 numbers

Upper quartile =18

3 numbers

7 numbers

Quartile (3)Example :

Find the quartiles of data : 18, 22, 20, 10, 9, 7, 6, 12, 19, 17, 12, 16, 18, 12Answer :

3 numbersLower quartile =10

3 numbers3 numbers 3 numbers

Upper quartile = 18Ordered data :

6, 7, 9, 10, 12, 12, 12, 16, 17, 18, 18, 19 20, 22

3 numbers

Equal Numbers !

6 numbers

Quartile (5)Example :

Find the quartiles of data : 10, 10, 20, 25, 27, 32, 40, 45, 56, 60, 70, 80Answer :

Median =366 numbers

3 numbersLower quartile =22.5

3 numbers3 numbers 3 numbersUpper quartile = 58

Data has been ordered :

10, 10, 20, 25, 27, 32, 40, 45, 56, 60, 70, 80

Data Presentation (1)Consider the data in the following frequency table :

Goods Weight (kg) FrequencyABCDE

700710820900930

91845279

Sum 108

We can represent those data using the:

• PIE DIAGRAM• BAR CHART• LINE DIAGRAM• PICTOGRAM (PICTURE DIAGRAM)

Data Presentation (2)(Pie Diagram)

Goods

Weight (kg)

Frequency

ABCDE

700710820900930

91845279

Sum 108

A : weight 700 kg, central angle = 30360.108

9

B : weight 710 kg, central angle =

C : weight 820 kg, central angle =

60360.10818

150360.10845

Data Presentation (3)(Pie Diagram)

A : weight 700 kg, central angle = 30360.108

9

B : weight 710 kg, central angle =

C : weight 820 kg, central angle =

60360.10818

150360.10845

A

B

C

D

E

30O

60O

150O

30O

10

20

30

40

50

Data Presentation (4)(Bar Chart)

Goods Weight (kg) Frequency

ABCDE

700710820900930

91845279

Sum 1080

A B C D EGoods

f

10

20

30

40

50

Data Presentation (5)(Line Diagram)

Goods Weight (kg) Frequency

ABCDE

700710820900930

91845279

Sum 1080

700 750 800 850 900Goods

f

950

Data Presentation (6)Pictogram (Picture Digram)

2001

2002

2003

2004

2005

Phone sold in five years from “You Can” shop :

Remark :

= 100 unit

Bye bye …………

n Thank You