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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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FORM 4 MATHEMATICS Module 3 : Page 2
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Learning Area 6 : STATISTICS Worksheet 2.1
Learning Objective 6.1 : Understand the concept of class interval.
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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FORM 4 MATHEMATICS Module 3 : Page 3
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Learning Area 6 : STATISTICS Worksheet 2.2
Learning Objective 6.1 : Understand the concept of class interval.
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 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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FORM 4 MATHEMATICS Module 3 : Page 4
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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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FORM 4 MATHEMATICS Module 3 : Page 5
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Learning Area 6 : STATISTICS Worksheet 2.3
Learning Objective 6.1 : Understand the concept of class interval.
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 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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FORM 4 MATHEMATICS Module 3 : Page 7
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Learning Area 6 : STATISTICS Worksheet 3.1
Learning Objective 6.1 : Understand the concept of class interval.
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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FORM 4 MATHEMATICS Module 3 : Page 9
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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 Area 6 : STATISTICS Worksheet 5.1
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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FORM 4 MATHEMATICS Module 3 : Page 11
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Learning Area 6 : STATISTICS Worksheet 6.1
Learning Objective 6.2 : Understand and use the concept of mode and mean of grouped data
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 Area 6 : STATISTICS Worksheet 7.1
Learning Objective 6.2 : Understand and use the concept of mode and mean of grouped data
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 !
= (2 decimal places)
3
markmeanThe !
= (2 decimal places)
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)
Frequency v midpoint(fx)
40 44 8
45 49 11
50 54 9
55 59 15
60 64 8
65 69 5
Total
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FORM 4 MATHEMATICS Module 3 : Page 14
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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)
Frequency v midpoint(fx)
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 Area 6 : STATISTICS Worksheet 9.1
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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FORM 4 MATHEMATICS Module 3 : Page 17
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3
2
1
4
5
7
8
9
0
152
Frequency
Heights (c157
10
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FORM 4 MATHEMATICS Module 3 : Page 18
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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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FORM 4 MATHEMATICS Module 3 : Page 19
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Graph for question 2
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FORM 4 MATHEMATICS Module 3 : Page 20
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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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FORM 4 MATHEMATICS Module 3 : Page 21
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Graph for question 3
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Learning Area 6 : STATISTICS Worksheet 10.1
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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Graph for question 1
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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