FACULTY OF SCIENCE AND TECHNOLOGY

SEMESTER JANUARY 2012

SBST1303

ELEMENTARY STATISTIC

MATRICULATION NO : 800717126061001

IDENTITY CARD NO. : 800717-12-6061

TELEPHONE NO. : 014-3343554

E-MAIL : mdhussainabdullah@gmail.com

LEARNING CENTRE : OUM, Petaling Jaya

SBST1303

1

TABLE OF CONTENTS

Contents

1. a Frequency Distribution Table 2

Page

1. b(i) Histogram of Frequency Distribution Table For The Pulse Rates of Males 3

1. b(ii) Histogram of Frequency Distribution Table For The Pulse Rates of Females 4

1. c(i) Cumulative Frequency For The Pulse Rates of Males 5

1. c(ii) Cumulative Frequency For The Pulse Rates of Females 6

2. a Find Mean, Mode, Median and Standard Deviation 7

2. b Pearson’s Coefficient of Skewness 13

ATTACHMENT 14

SBST1303

2

1.a

Table 1.1: Frequency Distribution Table for the Pulse Rate of Males.

Frequency Distribution Table

Class Frequency (f) Cumulative Frequency

50 – 59 6 6 60 – 69 17 23 70 – 79 8 31 80 – 89 8 39 90 – 99 1 40

Table 1.2: Frequency Distribution Table for the Pulse Rate of Females.

Class Frequency (f) Cumulative Frequency 60 – 69 12 12 70 – 79 13 25 80 – 89 10 35 90 – 99 3 38

100 – 109 2 40

Class

1.b (i)

Freq

uenc

y

Figure 1.1: Histogram Of Frequency Distribution Table For The Pulse Rates Of Males

2

10

12

14

4

18

16

313940

70 - 7980 - 8990 - 99

881

623

50 - 5960 - 69

617

CFFrequencyClass

90 - 990

17

6

8 8

1

50 - 59 60 - 69 70 - 79 80 - 89

8

6

1.b (ii)

Class

Freq

uenc

y

2

10

12

14

4

18

16

353840

Figure 1.2: Histogram Of Frequency Distribution Table For The Pulse Rates Of Females

CFFrequencyClass

100 - 1090

60 - 69 70 - 79 80 - 89 90 - 99

8

6

1225

1213

100 - 109

60 - 6970 - 7980 - 8990 - 99

1032

1213

10

32

44

12

8

4

40

36

32

28

24

Freq

uenc

y

20

16

0

Class

40 - 4950 - 5960 - 6970 - 79

23≤ 59.5≤ 69.5

617

1.c (i)

80 - 8990 - 99

Cumulative FrequencyFrequencyUpper

Boundary00≤ 49.56

Figure 1.3: Cumulative Frequency For The Pulse Rates Of Males

313940

≤ 79.5 881

≤ 89.5≤ 99.5

Upper Boundary (Pulse Rates)

99.549.5 59.5 69.5 79.5 89.5

44

12

8

4

40

36

32

28

24

Freq

uenc

y

20

16

0

Class

50 - 5960 - 6970 - 7980 - 89

1.c (ii)

90 - 99100 - 109

Figure 1.4: Cumulative Frequency For The Pulse Rates Of Females

3538

25≤ 69.5≤ 79.5

1213

12

Cumulative FrequencyFrequencyUpper

Boundary00≤ 59.5

40

≤ 89.5 1032

≤ 99.5≤ 109.5

99.5 109.5

Upper Boundary (Pulse Rates)

59.5 69.5 79.5 89.5

SBST1303

2. a

Find Mean, Mode, Median and Standard Deviation

Table 2.1: Lower Boundary, Class Mid-Point, Upper Boundary for the Pulse Rates of Males

MALES

Class Lower Boundary

Class Mid-Point (x)

Upper Boundary

Frequency (f)

50 – 59 49.5 54.5 59.5 6 60 – 69 59.5 64.5 69.5 17 70 – 79 69.5 74.5 79.5 8 80 – 89 79.5 84.5 89.5 8 90 – 99 89.5 94.5 99.5 1

i. Mean = location or position of data distribution

Formula

𝜇𝜇 = ∑ 𝑓𝑓𝑖𝑖 𝑥𝑥𝑖𝑖∑ 𝑓𝑓𝑖𝑖

= 6(54.5)+17(64.5)+8(74.5)+8(84.5)+1(94.5)6+17+8+8+1

= 69.75 ≈

70

SBST1303 ii. Mode = observation (or the number) which has the largest frequency

Formula

𝓍𝓍 � = 𝐿𝐿𝐵𝐵 + 𝐶𝐶 � ∆𝐵𝐵∆𝐵𝐵 + ∆𝐴𝐴

�

= 59.5 + 10 � 17−6(17−6)+(17−8)

�

= 59.5 + 10 � 1111+9

�

= 59.5 + (110/20)

=

iii. Median = summarise distribution in two equal parts of 50% each

65

Formula

𝑥𝑥� = 𝐿𝐿𝐵𝐵 + 𝐶𝐶�𝑛𝑛 +1

2 − 𝐹𝐹𝐵𝐵 �

𝑓𝑓𝑚𝑚

(a) Where (n + 1)/2 = (40 + 1)/2 = 20.5

(b) The median class is 60 – 69 with the following:

𝑓𝑓𝑚𝑚 = 17, 𝐿𝐿𝐵𝐵 = 59.5, 𝐶𝐶 = 10, 𝐹𝐹𝐵𝐵 = 6

= 59.5 + 10 (𝟐𝟐𝟐𝟐.𝟓𝟓 − 𝟔𝟔)𝟏𝟏𝟏𝟏

= 68.03 ≈ 68

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iv. Standard Deviation

Formula

𝜎𝜎 = �∑ 𝑥𝑥𝑖𝑖

𝑛𝑛

2

− �∑ 𝑥𝑥𝑖𝑖

𝑛𝑛 �2

= �4545

− �405

�2

= √90.8 − 64

=

5.18

SBST1303

Table 2.2: Lower Boundary, Class Mid-Point, Upper Boundary for the Pulse Rates of Females

FEMALES

Class Lower Boundary

Class Mid-Point (x)

Upper Boundary

Frequency (f)

60 – 69 59.5 64.5 69.5 12 70 – 79 69.5 74.5 79.5 13 80 – 89 79.5 84.5 89.5 10 90 – 99 89.5 94.5 99.5 3

100 – 109 99.5 104.5 109.5 2

i. Mean = location or position of data distribution

Formula

𝜇𝜇 = ∑ 𝑓𝑓𝑖𝑖 𝑥𝑥𝑖𝑖∑ 𝑓𝑓𝑖𝑖

= 12(64.5)+13(74.5)+10(84.5)+3(94.5)+2(104.5)12+13+10+3+2

=

77

SBST1303 ii. Mode = observation (or the number) which has the largest frequency

Formula

𝓍𝓍 � = 𝐿𝐿𝐵𝐵 + 𝐶𝐶 � ∆𝐵𝐵∆𝐵𝐵 + ∆𝐴𝐴

�

= 69.5 + 10 � 13−12(13−12)+(13−10)

�

= 69.5 + 10 � 11+3

�

= 69.5 + (10/4)

=

iii. Median = summarise distribution in two equal parts of 50% each

72

Formula

𝑥𝑥� = 𝐿𝐿𝐵𝐵 + 𝐶𝐶�𝑛𝑛 +1

2 − 𝐹𝐹𝐵𝐵 �

𝑓𝑓𝑚𝑚

(c) Where (n + 1)/2 = (40 + 1)/2 = 20.5

(d) The median class is 70 – 79 with the following:

𝑓𝑓𝑚𝑚 = 13, 𝐿𝐿𝐵𝐵 = 69.5, 𝐶𝐶 = 10, 𝐹𝐹𝐵𝐵 = 12

= 69.5 + 10 (20.5 − 12)13

= 76.04 ≈ 76

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iv. Standard Deviation

𝜎𝜎 = �∑ 𝑥𝑥𝑖𝑖

𝑛𝑛

2

− �∑ 𝑥𝑥𝑖𝑖

𝑛𝑛 �2

Formula

= �4265

− �405

�2

= √85.2 − 64

=

4.60

SBST1303

2. b

Pearson’s Coefficient of Skewness

𝑃𝑃𝐶𝐶𝑃𝑃 (1) = (𝑀𝑀𝑀𝑀𝑀𝑀𝑛𝑛 − 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 )𝑃𝑃𝑆𝑆𝑀𝑀𝑛𝑛𝑀𝑀𝑀𝑀𝑆𝑆𝑀𝑀 𝐷𝐷𝑀𝑀𝐷𝐷𝑖𝑖𝑀𝑀𝑆𝑆𝑖𝑖𝑀𝑀𝑛𝑛

= 𝑥𝑥̅ − 𝑥𝑥�𝑠𝑠

MALES

= (70−65)5.18

=

Value obtained show it positively skewed

0.97

𝑃𝑃𝐶𝐶𝑃𝑃 (1) = (𝑀𝑀𝑀𝑀𝑀𝑀𝑛𝑛 − 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 )𝑃𝑃𝑆𝑆𝑀𝑀𝑛𝑛𝑀𝑀𝑀𝑀𝑆𝑆𝑀𝑀 𝐷𝐷𝑀𝑀𝐷𝐷𝑖𝑖𝑀𝑀𝑆𝑆𝑖𝑖𝑀𝑀𝑛𝑛

= 𝑥𝑥̅ − 𝑥𝑥�𝑠𝑠

FEMALES

= (77−72)4.60

=

Value obtained show it positively skewed

1.07

14

ATTACHMENT

REFERENCES

Prof Dr Mohd Kidin Shahran (2011). Module SBST1303 Elementary Statistics. Open

University Malaysia.