1B_Ch12(1)

1
1B_Ch12(1)
2
1B_Ch2(2)
12.2 Collection and Classification of Data
Index
3
1B_Ch2(3)
12.4 Presentation and Analysis of Discrete Data
Index
4
1B_Ch12(4)
12.1 Various Stages of Statistics

• Example

Various Stages of Statistics
Index
5
1B_Ch12(5)
12.1 Various Stages of Statistics
Ryan wants to know what kinds of food are the
classmates favourites. Find the correct order of
the stages of the statistics procedures.
(a) Organize the data collected in a
table. (b) Set a questionnaire about the favorite
food of classmates. (c) Analyze the collected
data and obtain the conclusion by using the
diagram. (d) Use a suitable statistical diagram
to present the data.
b
a
d
c

• Key Concept 12.1.1

Index
6
1B_Ch12(6)
12.2 Collection and Classification of Data
Collection of Data
A)
1. Previous Information ? Search for relevant
information from books, newspapers, magazines,
world wide web, etc. 2. Questionnaire ? Set a
questionnaire and distribute to each member of
the target group to obtain the relevant
information.
Index
7
1B_Ch12(7)
12.2 Collection and Classification of Data

• Example

Collection of Data
A)
3. Observation ? Obtain the required information
through direct observation, measurement or
counting. 4. Experiment ? Obtain the required
information by doing real experiments.
5. Interview ?Through household surveys,
street surveys or telephone interviews to obtain
the required data.
Index

• Index 12.2

8
1B_Ch12(8)
12.2 Collection and Classification of Data

• Suggest a suitable way to collect each of the
  following sets of data
• (a) The weights of 30 students in a certain
  class.
• The amount of pocket money that my sister spends
  each day.
• The number of customers shopping in a store
  between700 a.m. and 1200 p.m.
• The number of births in Hong Kong from 2000 to
  2005.

(a) Questionnaire
(b) Interview
(c) Observation
(d) Previous information

• Key Concept 12.2.1

Index
9
1B_Ch12(9)
12.2 Collection and Classification of Data
Classification of Data
B)
1. Discrete Data
? Discrete data can only take up certain values
and these values are usually obtained by
counting, and so are often positive
integers. E.g. the number of rotten apples in a
box.
Note Discrete data may NOT be numbers. Some
examples are peoples religions and favourite
singers. These data are called nominal data.
Index
10
1B_Ch12(10)
12.2 Collection and Classification of Data

• Example

Classification of Data
B)
2. Continuous Data
? Continuous data can take up any value within a
reasonable interval and these values are usually
obtained from measurements. E.g. the weights of
the apples in a box.
Index

• Index 12.2

11
1B_Ch12(11)
12.2 Collection and Classification of Data
However, the time (measured in hours) spent on
watching TV per day can be any value between 0
and 24, e.g. 2, 3.4, 4.15, etc. Hence the time
spent on watching TV is a kind of continuous data.
Index
12
1B_Ch12(12)
12.2 Collection and Classification of Data
Determine whether each of the following sets of
data is discrete or continuous.
Discrete data
Continuous data
Continuous data
Discrete data

• Key Concept 12.2.2

Index
13
1B_Ch12(13)
12.3 Organization of Discrete Data
Organization of Discrete Data

1. We can use a frequency distribution table to
   organize the data that has been collected.
2. The number of tallies recorded for each value is
   called the frequency of that value.

Index
14
1B_Ch12(14)
12.3 Organization of Discrete Data

• Example

Organization of Discrete Data
? For example, the frequency distribution table
below shows the ages of 40 students in Form 1A
Index
15
1B_Ch12(15)
12.3 Organization of Discrete Data
From the data about the favourite extra-curricula
activities of 40 Form 1 students given on the
left below, we can organize them into a frequency
distribution table on the right.
Index
16
1B_Ch12(16)
12.3 Organization of Discrete Data
Given below are the numbers of mistakes made by
40 students of Form 1A in an English dictation.
1 4 5 11 7 8 13 0 6 17
9 7 3 7 10 22 0 5 18 11
10 8 9 6 3 0 14 7 8 5
20 2 6 7 16 8 6 10 1 3
The teacher arranges the number of mistakes 0 3
into the first group, 4 7 into the second
group, 8 11 into the third group, 12 15 into
the fourth group, 16 19 into the fifth group
and 20 23 into the sixth group. Now try to
organize the given data into a frequency
distribution table.
Index
17
1B_Ch12(17)
12.3 Organization of Discrete Data

• Back to Question

According to the above data and the teachers
arrangement, the following frequency distribution
table can be obtained.

• Key Concept 12.3.1

Index
18
1B_Ch12(18)
12.4 Presentation and Analysis of Discrete Data
Pie Charts
A)
1. Understanding Pie Charts
i. A pie chart is appropriate to present the
various statistical items as percentages of the
whole.
E.g.
Index
19
1B_Ch12(19)
12.4 Presentation and Analysis of Discrete Data

• Example

Pie Charts
A)
1. Understanding Pie Chart
ii. Each item can be indicated as a percentage of
the whole set of data or as the angle of the
sector.
E.g.
Index
20
1B_Ch12(20)
12.4 Presentation and Analysis of Discrete Data

• Example

Pie Charts
A)

1. Drawing a Pie Chart

1. Express each item as a percentage of the whole,
   then calculate the angle of each sector.
2. Construct a circle of suitable radius, and draw
   the various sectors according to the angles
   obtained in (i).
3. Label clearly the item represented by each sector
   and the corresponding percentage (or angle of the
   sector).
4. Give a title to the pie chart.

Index

• Index 12.4

21
1B_Ch12(21)
12.4 Presentation and Analysis of Discrete Data
The pie chart shows the favourite singers of 120
teenagers.

1. Find the value of x.
2. What percentage of the teenagers are the fans of
   Nick?

• Soln

(a) x 90 225 360
? x 360 90 225
45
Index
22
1B_Ch12(22)
12.4 Presentation and Analysis of Discrete Data

• Back to Question

1. The percentage of the teenagers who are the fans
   of Nick

62.6

• Key Concept 12.4.1

Index
23
1B_Ch12(23)
12.4 Presentation and Analysis of Discrete Data
In a survey, 400 F.1F.3 students were asked what
kind of music they like most.The results are
shown in the following pie chart.
Index
24
1B_Ch12(24)
12.4 Presentation and Analysis of Discrete Data
(a) Find the value of x in the pie
chart. (b) Find the number of students who love
folk music. (c) Among those students who love
folk music, 56 are F.1 students and 49 are F.2
students.

• Soln

• Soln

i. Calculate the number of F.3 students who love
folk music. ii. Draw a pie chart to show, in
percentages, the distribution of students who
love folk music in each form.

• Soln

• Soln

Index
25
1B_Ch12(25)
12.4 Presentation and Analysis of Discrete Data

• Back to Question

• Back to Graph

1. 40 35 5 x 100

20
(b) Number of students who love folk music
400 35 140

• i. Number of F.3 students who love
• folk music

140 56 49 35
Index
26
1B_Ch12(26)
12.4 Presentation and Analysis of Discrete Data

• Back to Question

• Back to Graph

(c) ii. We first construct the following table
Index
27
1B_Ch12(27)
12.4 Presentation and Analysis of Discrete Data

• Back to Question

• Back to Graph

(c) ii. The required pie chart

• Key Concept 12.4.2

Index
28
1B_Ch12(28)
12.4 Presentation and Analysis of Discrete Data

• Example

Broken-line Graphs
B)
1. Understanding Broken-line Graphs
i. A broken-line graph is used to show the
change in the data over a period of time and
their overall tendency.
E.g.
Index
29
1B_Ch12(29)
12.4 Presentation and Analysis of Discrete Data

• Example

Broken-line Graphs
B)
2. Drawing a Broken-line Graph

1. List on the horizontal axis, the time of
   happenings of the statistical item in order of
   magnitude.
2. List the frequencies of the item on the vertical
   axis.
3. All necessary scales, items, values and units
   should be shown clearly on the two axes.
4. Use ? or x to indicate points that represent
   the frequency of the corresponding statistical
   item.
5. Join adjacent points by line segments.
6. Give a title to the broken-line graph.

Index

• Index 12.4

30
1B_Ch12(30)
12.4 Presentation and Analysis of Discrete Data
The broken-line graph shows the number of
visitors to the park in a particular day.
(a) Which period of time did the number of
visitors increase the most? What was the increase
in visitors?
(b) Find the difference in the number of visitors
between 1400 and 1800 in that particular day.
Index
31
1B_Ch12(31)
12.4 Presentation and Analysis of Discrete Data

• Back to Question

• From 1200 to 1400. The increase in visitors was
  70.
• The difference in the number of visitors between
  1400 and 1800 in that particular day
• 120 80
• 40

• Key Concept 12.4.3

Index
32
1B_Ch12(32)
12.4 Presentation and Analysis of Discrete Data
The given bar chart shows the monthly rainfall of
a certain city last year. Paul lives in that
city. The windows in his home leaked badly in the
four most heavy rainfall months last year. He
intends to fix the leakage before those four
rainy months come again this year.
Index
33
1B_Ch12(33)
12.4 Presentation and Analysis of Discrete Data
(a) With reference to last years data shown
above, before which month should Paul fix the
windows? (b) Draw a broken-line graph to present
themonthly rainfall of that city in last year.

• Soln

• The four most heavy rainfall months last year
  were April, May, June and July.
• ? Paul should fix the windows before April.

Index
34
1B_Ch12(34)
12.4 Presentation and Analysis of Discrete Data

• Back to Question

(b) The broken-line graph showing the monthly
rainfall of that city last year is as follows

• Key Concept 12.4.4

Index
35
1B_Ch12(35)
12.4 Presentation and Analysis of Discrete Data

• Example

Stem-and-leaf Diagrams
C)
1. Understanding Stem-and-leaf Diagrams
i. A stem-and-leaf diagram is used to present
the data in a graphical way and record the values
of all the original data.
E.g.
Index
36
1B_Ch12(36)
12.4 Presentation and Analysis of Discrete Data

• Example

Stem-and-leaf Diagrams
C)
1. Understanding Stem-and-leaf Diagrams
ii. If we want to compare two groups of related
data, we can use back-to-back stem-and-leaf
diagram.
E.g.
Index
37
1B_Ch12(37)
12.4 Presentation and Analysis of Discrete Data

• Example

Stem-and-leaf Diagrams
C)
2. Drawing a Stem-and-leaf Diagram

1. Check the range of the collected data and choose
   the place values for the stems and the
   leaves.
2. Arrange the numbers in the stem from top to
   bottom in an ascending order of magnitude.
3. List each datum to the right of its corresponding
   stem.
4. Arrange the data in the leaves in ascending
   order.

Index

• Index 12.4

38
1B_Ch12(38)
12.4 Presentation and Analysis of Discrete Data
The following stem-and-leaf diagram shows the
amount of daily pocket money of students in Class
A.
Index
39
1B_Ch12(39)
12.4 Presentation and Analysis of Discrete Data

1. How many data are recorded in this stem-and-leaf
   diagram?

(b) It is known that Eric is one of the student
in Class A and he has the largest amount of daily
pocket money. Find the amount of his daily pocket
money.

1. 30 data are recorded in the stem-and-leaf diagram.

(b) The amount of Erics daily pocket money is
55.

• Key Concept 12.4.5

Index
40
1B_Ch12(40)
12.4 Presentation and Analysis of Discrete Data
The areas (in square feet) of the homes of 20
students from F.1A are shown below.
310 430 400 882 790 620 325 622 450
390 730 395 345 560 560 515 481 385 450
390
Using 100 sq. ft. as the stem and 1 sq. ft. as
the leaf, construct astem-and-leaf diagram to
presentthe above data.
Index
41
1B_Ch12(41)
12.4 Presentation and Analysis of Discrete Data

• Back to Question

• Key Concept 12.4.7

Index
42
1B_Ch12(42)
12.4 Presentation and Analysis of Discrete Data
The results of the IQ test for 2 groups of
students A and B are as follows
Group A
Group B
81 103 119 86
117 85 98 115
120 126 121 127
112 121 88 90
100 93 102 113
112 102 100 114
118 114 120 115
101 123 106 107
(a) Construct a back-to-back stem-and-leaf
diagram to present the IQ of these two groups of
students. (b) If the IQ of a student is 120 or
above, then he/she is considered as a gifted
student.Which group, A or B, has more gifted
students?
Index
43
1B_Ch12(43)
12.4 Presentation and Analysis of Discrete Data

• Back to Question

• From the diagram in (a), there are more students
  in group A whose IQ are 120 or above.
• ? Group A has more gifted students.

• Key Concept 12.4.6

Index
44
1B_Ch12(44)
12.4 Presentation and Analysis of Discrete Data
Scatter Diagrams
D)
1. Understanding Scatter Diagrams
i. A scatter diagram is appropriate to show
whether two variables have close relationship
with each other.
E.g.
Index
45
1B_Ch12(45)
12.4 Presentation and Analysis of Discrete Data

• Example

Scatter Diagrams
D)
1. Understanding Scatter Diagrams
ii. In general, the two variables x and y may
relate in different ways.
Index
46
1B_Ch12(46)
12.4 Presentation and Analysis of Discrete Data

• Example

Scatter Diagrams
D)
2. Drawing a Scatter Diagram

1. Indicate clearly on the x-axis and y-axis the
   variable that each axis represents.
2. Scales, values and units should be shown clearly
   on the two axes.
3. Represent the corresponding values of the two
   variables on the rectangular coordinate plane
   using a point ? or x.
4. Give a title to the scatter diagram.

Index

• Index 12.4

47
1B_Ch12(47)
12.4 Presentation and Analysis of Discrete Data
The heights of fathers and their sons are shown
in the scatter diagram.
Do you think there is a relationship between the
heights of fathers and their sons?
Index
48
1B_Ch12(48)
12.4 Presentation and Analysis of Discrete Data

• Back to Question

Yes, there is a correlation between the heights
of fathers and the heights of their sons.
From the scatter diagram, it can be seen
that the taller the father is, the taller his
son will be.

• Key Concept 12.4.8

Index
49
1B_Ch12(49)
12.4 Presentation and Analysis of Discrete Data
A group of 10 students studied last night for
their dictation test today. The table below shows
the time that each student spent on studying and
the number of mistakes that they made in todays
dictation test.
Index
50
1B_Ch12(50)
12.4 Presentation and Analysis of Discrete Data

1. Draw a scatter diagram to show the relationship
   between the time spent on studying by the 10
   students last night and the number of mistakes
   they make in the dictation test today.

(b) According to the scatter diagram obtained in
(a), do you think there is a relationship between
the time that a student spent on studying and the
number of mistakes that he makes in the dictation
test?
Index
51
1B_Ch12(51)
12.4 Presentation and Analysis of Discrete Data

• Back to Question

(a) The required scatter diagram is
(b) From the scatter diagram in (a), it can be
seen that the more time a student spent on
studying for the dictation test, the fewer
mistakes he/she makes.
Index

• Key Concept 12.4.9

52
1B_Ch12(52)
12.4 Presentation and Analysis of Discrete Data

• Example

Choosing Suitable Statistical Graphs to Present
Data
E)
? There are many different types of statistical
graphs. The one that should be chosen to present
the collected data depends on the nature and the
number of data, the purpose of the survey, the
points to be emphasized, etc.
Index

• Index 12.4

53
1B_Ch12(53)
12.4 Presentation and Analysis of Discrete Data
1. There were 5 major spendings for a certain
company last year.We can show the relationship
between each spending and the total spending by
using a pie chart.
Index
54
1B_Ch12(54)
12.4 Presentation and Analysis of Discrete Data
2. We can show the change in number of students
in a certain secondary school over the last 6
years by using a broken-line graph.
Index
55
1B_Ch12(55)
12.4 Presentation and Analysis of Discrete Data
3. We can show the relationship between the time
spent by 30 students in doing their project and
the marks they obtained from the project by using
a scatter diagram.
Index
56
1B_Ch12(56)
12.4 Presentation and Analysis of Discrete Data
4. In one of the Home Ownership Schemes provided
by the government, 10 different sizes of flats
are available. The distribution of the areas of
these flats can be shown in a stem-and-leaf
diagram.
Index
57
1B_Ch12(57)
12.4 Presentation and Analysis of Discrete Data
In September 1999, the Walt Disney Company
decided to build a theme park in Hong Kong.The
admission fee of the theme park would be around
250 to 350. Some citizens were interviewed to
ask their views on the admission fees. The
following results were obtained.
Index
58
1B_Ch12(58)
12.4 Presentation and Analysis of Discrete Data

• Back to Table

Which statistical graph is most suitable to
present the above data, and at the same time
(a) shows clearly the number of citizens in each
category. (b) shows the number of citizens in
each category as a percentage of the total number.
(a) A bar chart can best present the above data.
(b) A pie chart can best present the above data.

• Key Concept 12.4.10

Index
59
1B_Ch12(59)
12.5 Misuse of Statistical Graphs
Misuse of Statistical Diagrams
? Statistical diagrams are sometimes used
deliberately to exaggerate or conceal the truth,
and to mislead the readers.
Index
60
1B_Ch12(60)
12.5 Misuse of Statistical Graphs

• Example

What should we be careful when we are reading
statistical diagrams?
Index
61
1B_Ch12(61)
12.5 Misuse of Statistical Graphs
The following graph is a bar chart shown in the
advertisement of the Hurryson Telecommunications
Company.
Index
Telecommunications Company
62
1B_Ch12(62)
12.5 Misuse of Statistical Graphs

• Back to Graph

(a) Measure the lengths of the bars of HK United
and Hurryson, express the length of the bar of
Hurryson Telecommunications Company as a fraction
of that of HK United. (b) Now express the actual
charges of Hurryson as a fraction of HK United
and compare this result with that obtained in
(a). Do you agree that this bar chart is
misleading? Explain your answer.
Index
63
1B_Ch12(63)
12.5 Misuse of Statistical Graphs

• Back to Question

• Actual charge per minute of HK United 3.2
• Actual charge per minute of Hurryson 3

Index
64
1B_Ch12(64)
12.5 Misuse of Statistical Graphs
The Money Commercial College used the following
diagram to show the highest monthly salary of
their fresh graduates in the years 2004 and 2005.
Index
65
1B_Ch12(65)
12.5 Misuse of Statistical Graphs
(a) Find the areas of the two triangles A and B
in the statistical diagram shown above. Express
the area of B as a multiple of the area of A.
(b) Find out, from the diagram, the
actualhighest monthly salaries in the twoyears.
Express the one in 2005 as amultiple of that in
2004.

• Soln

• Soln

Index
66
1B_Ch12(66)
12.5 Misuse of Statistical Graphs

• Back to Question

(a) Suppose each small square in the figure has a
side of 1 unit
240 sq. units
60 sq. units
Thus, the area of B is 4 times that of A.
Index
67
1B_Ch12(67)
12.5 Misuse of Statistical Graphs

• Back to Question

(b) From the diagram,
the highest monthly salary in 2005
12 000
the highest monthly salary in 2004
6 000
? The highest monthly salary in 2005 was 2 times
that in 2004.
Index
68
1B_Ch12(68)
12.5 Misuse of Statistical Graphs
Fig. A below shows the profits of ABC company
from 2000 to 2004. In order to show the
shareholders that the companys profit has
increased a lot since 1990. The managing director
of the company added the profit of the company in
1990 to the graph (Fig. B).
Fig. A
Fig. B
Index
69
1B_Ch12(69)
12.5 Misuse of Statistical Graphs
(a) As compared with Fig. A, does Fig. B give
the readers an impression that the companys
profit increases rapidly?
(b) Do you think that the managing director is
misleading the readers in Fig. B? Why?
Index
70
1B_Ch12(70)
12.5 Misuse of Statistical Graphs

• Back to Question

(a) Yes, Fig. B gives the readers an impression
that the companys profit increases rapidly.
(b) Yes, the managing director is misleading the
readers in Fig. B. Because the profits in the
years 1991 to 1999 are not shown, people may be
misled to think that the profit increases rapidly
from 1990 to 2000.

• Key Concept 12.5.1

Index