3 Waja 2010 F4 Student's Copy Statistics

8/6/2019 3 Waja 2010 F4 Student's Copy Statistics

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Program WAJA Negeri Perak Tahun 2010

FORM 4 MATHEMATICS Module 3 : Page 1

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Learning Area 6 : STATISTICS Worksheet 1.1

Learning Objective 6.1 : Understand the concept of class interval.

Learning Outcome : (i) Complete the class interval for a set of data given one of the class intervals.

Activity 1: Completing class interval

1. Complete the following tables using uniform class intervals.(a)

Class interval 1 10 11 20 21

(b)

(c)

2. Complete the class intervals in the following tables.

(a)

Height

(cm)

130 134

135

NOTES

A set of data which consists of many measurements of a certain quantity can beorganised into a suitable number of groups or

Class interval 20 25 26

Class interval 4.5 4.8 4.9

+ 9 + 9 + 9

+ 5 + 5

+ 0.3 + 0.3

(b)

Mass

(kg)

50 55

62 67

(c)

Marks

0 9

10 19

(d)

Distance

(km)

5.1 5.3

5.4 5.6

(e)

Duration

(minutes)

11.0 11.4

11.5 11.9


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Learning Outcome : (ii) Determine

a) the upper limit and lower limit; b) the upper boundary and lower boundaryof a class in a grouped data.

Activity 1: Determining the upper limit and lower limit

1. Determine the lower limit and upper limit of each of the following class intervals.

(a)

Class interval Lower limit Upper limit

31 35 35

36 40

41 45

(b)

Mass (g) Lower limit Upper limit

150 154

155 159

160 164

(c)

Speed (ms1

) Lower limit Upper limit

7.1 7.4

7.5 7.8

7.9 8.2

NOTES

1. . of a class interval is the highest value of the class.2. . of a class interval is the lowest value of the class.

31


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Learning Outcome : (ii) Determine


Activity 1 : Determining the lower boundary and upper boundary

1.

2. Based on the class interval in the table given below, determine the lower boundary and upper

boundary of the class interval 66 70 .

Class interval 61 65 66 70 71 75

20 24

Previous

classNext

class

Lower

limit

Upper

limit

25 29 30 34

Lower boundary of

ClassUpper boundary of

Class

Upper boundary =

=

5.24

2

2524!

5.29

2

3029!

Lower boundary =2

6665

=

2

3029

25 29 25 29


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3. Based on the class interval in the table given below, determine the lower boundary and upperboundary of the class interval 50.5 54.5.

Class interval 45.5 49.5 50.5 54.5 55.5 59.5

NOTES

1. of a class interval

=2

classprevioustheofitlimupperclasstheofitlimlo er

2. of a class interval=

2

classnexttheofitlimlo er classtheofitlimupper

Upper boundary =

=

Lower boundary =

=

2


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Learning Outcome (ii) Determine


Activity 1 : Determining the lower limit, upper limit, lower boundary and upper boundary

1. Based on the following class intervals, determine each of the following for the specific class

intervals.(i) lower limit (ii) upper limit (iii) lower boundary (iv) upper boundary.

Class interval 110 119 120 129 130 139

(a) Class interval 120 129 (b) Class interval 130 139

(i) Lower limit = 120

(ii) Upper limit =

(iii) Lower boundary =

=

(iv) Upper boundary =

(i) Lower limit =

(ii) Upper limit =

(iii) Lower boundary =

(iv) Upper boundary =

2


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2. Determine the lower limit, upper limit, lower boundary and upper boundary of each of thefollowing class interval in the table given below.

Length

(cm)

Lower

limit

Upper

limit

Lower

boundary

Upper

boundary

31 35 31 35

5.30

2

3130

!

5.35

2

3635

!

36 40

41 45

3. Determine the lower limit, upper limit, lower boundary and upper boundary of each of thefollowing class interval in the table given below.

Time

(hours)

Lower

limit

Upper

limit

Lower

boundary

Upper

boundary

2.0 2.9

3.0 3.9

4.0 4.9


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Learning Outcome (iii) Calculate the size of a class interval.

Activity 1: Determine the size of a class interval

1. Calculate the size of each of the following class intervals.

Class interval Size of class interval

(a) 140 149 Upper boundary Lower boundary

=2

140139

2

150149

= 149.5 139.5

=

(b) 61 65

(c) 12 15

(c) 2.0 2.9

(d) 0.3 0.6

NOTES

Size of a class interval =


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3. The following data shows the height distribution, in cm, of a group of 40 workers in a factory.

Complete the following frequency table based on the above data

4. The following data shows the number of books read in a month by a group of 30 students for theNILAM project in a school.

Construct a frequency table for the above data by using a class size of 5 books, beginning from theclass intervals 6 10.

151 163 155 162 167 176 154 164

160 154 158 164 154 169 178 167173 152 168 172 168 166 174 178

159 171 177 174 175 176 168 160171 179 173 153 169 173 156 174

Height (cm) Frequency

150 154

155 159

19 32 25 14 15 2912 21 18 17 19 6

17 23 18 7 16 1420 18 15 18 12 17

22 24 9 11 28 15

Number of books

readFrequency


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Learning Objective 6.2 : Understand and use the concept of mode and mean of grouped data

Learning Outcome (i) Determine the modal class from the frequency table of grouped data

Activity 1: State the modal class from the frequency table

1. State the modal class for each of the following frequency tables.(a)

Modal class = _______________

(b)

Modal class = _______________

(c)

Modal class = _______________

(d)

Modal class = _______________

(e)

Modal class = _______________

Length (cm) 20 29 30 39 40 49 50 59 60 69 70 79

Frequency 3 5 10 8 7 2

Mass (kg) 1 5 6 10 11 15 16 20 21 25 26 30Frequency 2 2 5 11 8 2

Marks 40 44 45 49 50 54 55 59 60 64 65 69

Frequency 8 11 9 15 8 5

Height (cm) 140 144 145 149 150 154 155 159 160 164 165 169

Frequency 4 7 11 12 8 3

Age (years) 20 25 26 31 32 37 38 43 44 49

Frequency 5 8 11 4 4


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Learning Outcome (ii) Calculate the midpoint of a class

Activity 1: Calculate the midpoint of a class

Complete the following tables.

1.

2.

NOTES

2

classaofMidpoint

!

Length (cm) Frequency Midpoint

20 29 324.5

2

2920!

30 39 5!

2

3930

40 49 10!

2

49

50 59 8!

2

50

60 69 7!

2

70 79 2!

Mass (kg) Frequency Midpoint

1 5 2

6 10 2

11 15 5

16 20 11

21 25 8

26 30 2


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Learning Outcome (iv) Calculate the mean from a frequency table of grouped of data

Activity 1: Calculate the mean from a frequency table of grouped data

Complete the following table.

1.

35

lengthmeanThe !

= (2 decimal places)

Length (cm) Frequency

(f)

Midpoint

(x)

Frequency v midpoint

(fx)

1 5 33

2

51!

3 v 3 = 9

6 10 52106 !

5v

= 40

11 15 10

2

15!

10v = 130

16 20 8

2

16!

8 v =

21 25 7

2

!

v =

26 30 2!

v =

Total 35


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2.

massmeanThe !


3

markmeanThe !


NOTES

total

)(ofsumdatagroupedofMean

v!

Height (cm) Frequency(f)

Midpoint(x)

Frequency v midpoint(fx)

130 139 2

140 149 2

150 159 5

160 169 11

170 179 8

180 189 2

Total

Marks Frequency (f) Midpoint(x)


40 44 8

45 49 11

50 54 9

55 59 15

60 64 8

65 69 5

Total


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Worksheet 8.1Activity 1 : Test Yourself

1. The table below shows the frequency distribution of scores of a group of 32 students.

Based on the table above,(i) state the modal class,

Modal class = ___________________

(ii) calculate the mean score.

scoremeanThe !

= ___________(2 decimal places)

Score Frequency Midpoint

10 14 3 12

15 19 7

20 24 8

25 29 6

30 34 3

35 39 5

Score Frequency(f)

Midpoint(x)


10 14 3 12 3 v 12 = 36

15 19 7

20 24 8

25 29 6

30 34 3

35 39 5

Total


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2. The data below shows the marks for a Mathematics monthly test for 42 pupils.

(a) Using the data above and class interval of 5 marks, complete the table below.

(b) Based on your table above,(i) State the modal class,

Modal class = ________________

(ii) Calculate the mean mark for the Mathematics monthly test and give your answercorrect to 2 decimal places.

scoremeanThe !

= ___________(2 decimal places)

Score Frequency Midpoint

20 24 5 22

25 29

51 20 45 31 26 40 3025 32 37 41 21 36 38

46 38 28 37 39 23 39

33 35 42 29 38 31 2342 34 26 35 43 28 2225 47 31 48 44 34 54


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Learning Objective 6.3 : Represent and interpret data in histograms with class intervals of the same size

to solve problems.

Learning Outcome : (i) Draw a histogram based on the frequency table of a grouped data.

Activity 1: Drawing histogram by labelling the horizontal axis using midpoints.

1. The following table shows the frequency distribution of the heights, in cm, of a group of 40

soldiers in an army camp.

Heights (cm) Frequency

150 154 3

155 159 9

160 164 10

165 169 7170 174 6

175 179 3

180 184 2

By using a scale of 2 cm to 5 cm on the horizontal axis and 2 cm to 1 soldier on the vertical axis,draw a histogram based on the above data.

Step 1 : Determine the midpoints of each class.

Heights (cm) Frequency Midpoint150 154 3 152

155 159 9

160 164 10

165 169 7

170 174 6

175 179 3

180 184 2

Step 2 : Draw the histogram using the scales given.


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3

2

1

4

5

7

8

9

0

152

Frequency

Heights (c157

10


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2. The following table shows the frequency distribution of the amount of donations (in RM)

collected by 200 students to help the fire victims.

Donations (RM) Frequency

1 5 20

6 10 17

11 15 48

16 20 43

21 25 31

26 30 22

31 35 19

By using a scale of 2 cm to RM5 on the horizontal axis and 2 cm to 5 students on the vertical axis,

draw a histogram based on the above data.

Donations (RM) Frequency Midpoint

1 5 20

6 10 17

11 15 48

16 20 43

21 25 31

26 30 22

31 35 19


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Graph for question 2


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3. The following table shows the frequency distribution of the ages of 70 participants in a seminar.

Age (years) Frequency

10 19 3

20 29 6

30 39 16

40 49 19

50 59 13

60 69 9

70 79 4

By using a scale of 2 cm to 5 years on the horizontal axis and 2 cm to 2 participants on the vertical

axis, draw a histogram for the above data.

Age (years) Frequency Midpoint

10 19 3

20 29 6

30 39 16

40 49 19

50 59 13

60 69 9

70 79 4


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Learning Objective 6.4 : Represent and interpret data in frequency polygons to solve problems.Learning Outcome (i) : Draw the frequency polygons based on;

(b) a frequency table;

Activity 1: Drawing frequency polygon by labeling the horizontal axis using midpoints.

1. The following table shows the frequency distribution of the scores obtained by a group of 70students in a quiz.

Scores Frequency

6 10 14

11 15 8

16 20 20

21 25 10

26 30 631 35 12

By using a scale of 2 cm to 5 scores on the horizontal axis and 2 cm to 2 students on the verticalaxis, draw a histogram based on the above data.

Step 1 : Add another two classes before the first class and after the last class with 0 frequency.

Step 2 : Find the midpoint of each class.

Step 3 : Plot the midpoints.Step 4 : Joint all the points using straight lines.

Scores Frequency Midpoint

1 5 0

6 10 14

11 15 8

16 20 20

21 25 10

26 30 6

31 35 12

36 40 0

3


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6

4

2

8

10

12

14

16

18

Frequency

Scores

20

83


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2. The following table shows the frequency distribution of the height, in cm, a grouped of 30students.

Height (cm) Frequency

140 144 3

145 149 7

150 154 8

155 159 5

160 164 3

165 169 4

By using a scale of 2 cm to 5 cm on the horizontal axis and 2 cm to 1 student on the vertical axis,

draw a histogram based on the above data.

Height (cm) Frequency Midpoint

135 139 0

140 144 3

145 149 7

150 154 8

155 159 5

160 164 3

165 169 4

170 174 0


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FORM 4 MATHEMATICS Module 3 : Page 25Graph for question 2

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3 Waja 2010 F4 Student's Copy Statistics