1. Introduction to Statistics
Form 1 Mathematics
Chapter 12

2. Reminder Lesson requirement Before lessons start
Textbook 1B
Workbook 1B
Notebook
Before lessons start
Desks in good order!
No rubbish around!
No toilets!
Keep your folder at home
Prepare for Final Exam

3. Data presentation and analysis (p.221)
Pictogram (象形圖) – learnt in P6
Bar chart (棒形圖) – learnt in P6
Pie chart (圓形圖)
Broken-line graph (折線圖)
Stem-and-leaf diagram (幹葉圖)
Scatter diagram (散點圖)

4. Pie chart (圓形圖, p.221) Circle = all data (360, 100%)
Sector = a particular item
Angle or %  can be compared

5. Number of times visited Disneyland
Pie chart example
Number of times visited Disneyland
Frequency
Percentage
Angle 12
12/20  100% = 60%
12/20  360 = 216 1 5
5/20  100% = 25%
5/20  360 = 90 2 3
3/20  100% = 15%
3/20  360 = 54
Total 20
100%
360

6. Pie chart example
A university is running a survey to find out the idols of 250 students. A pie chart shows different types of their idols.
(a) What percentage of the students choose famous people as their favourite type of idol?
(b) Find the value of x in the diagram.
Answers:
(a) The required percentage
= (100 – 72 – 6 – 2 – 4)% = 16%
(b) x = 360°  16% = 57.6°

7. Pie chart example
The pie chart shows the favourite ball games of a group of students. It is known 12 love volleyball.
(a) Find x.
(b) Find the total number of students in the group.
(c) Find the number of students whose favourite ball game is basketball.
Answers:
(a) x = 360° – 110° – 85° – 60° – 30° = 75°
(b) Let the total number of students in the group be N, then
 N = 72
∴ Total number of students in the group is 72.
N  = 12
60° 360°

8. Pie chart example
The pie chart shows the favourite ball games of a group of students. It is known 12 love volleyball.
(a) Find x.
(b) Find the total number of students in the group.
(c) Find the number of students whose favourite ball game is basketball.
Answers:
(c) Number of students whose favourite ball game is basketball
x 360°
= 72 
75° 360°
= 72 
= 15

9. Time for Practice Page 224 of Textbook 1B
Class Practice
Pages 228 – 230 of Textbook 1B
Questions 1 – 3, 6 – 9
Pages 104 – 105 of Workbook 1B
Questions 4 – 5

10. Broken-line graph (折線圖, p.225)
Link the points by lines on x-y plane
Can see the changes easily

11. Broken-line graph (p.225) Steps:
Draw x-axis and y-axis on a graph paper
Normally, x-axis is time and y-axis is frequency
Mark “” on the graph paper representing the data and the corresponding time
Use line segments to join neighbouring points
Give a title

12. Broken-line graph example
The broken line graph shows the profit of a company in the last 6 seasons.
(a) The company is making less profit in st season than st season, find out the difference.
(b) Describe the changes in the company’s profit.
Answers:
(a) The profit in st season = 7.2 million dollars
The profit in st season = 5.4 million dollars
∴ The difference
(b) The company’s profit is decreasing since the year 2007, and it becomes stable after the first season of 2008.
= (7.2 – 5.4) million dollars
= 1.8 million dollars

13. Time for Practice Page 227 of Textbook 1B
Class Practice
Pages 229, 231 of Textbook 1B
Questions 4 – 5, 10 – 11
Pages 105 – 106 of Workbook 1B
Questions 6 – 7

14. Stem-and-leaf diagram (幹葉圖, p.232)
Keep the real values and show all data
Can see the distribution easily
Like a horizontal bar chart
Stem ($10)
Leaf ($1) 6 7 8 9 10
3 6
The prices of 12 books

15. Stem-and-leaf diagram

16. Stem-and-leaf diagram (p.232)
Steps:
Example: The prices (in $) of books are shown below:
Draw two columns for stem (left) and leaf (right) and specify the values and units
Put values of the stem in ascending order from top to bottom
Put values of the leaf in ascending order from left to right along the row of same stem
Give a title
The prices of 12 books
Stem ($10)
Leaf ($1) 6
3 6 7 8 9 10

17. Stem-and-leaf diagram example
The stem-and-leaf diagram below shows the monthly salaries of all staff of ABC Company.
(a) What is the lowest monthly salary of that company?
(b) How many staff members of that company are earning more than $25,000 per month?
Answers:
(a) From the diagram, we can see that the lowest monthly salary = $7 000.
(b) From the diagram, we can see that there are 2 staff members in ABC Company earning more than $25,000 per month.

18. Stem-and-leaf diagram example
The living areas (in sq. feet) of students are:
(a) If we use stem-and-leaf diagram to present them, which of the following is more suitable? Why?
(1) Use the hundreds digits and the tens digits as stem and the units digits as leaf.
(2) Use the hundreds digits as stem, the tens and the units digits as leaf.
(b) According to the answer in (a), construct a stem-and-leaf diagram to present the given data.
Answers:
(a) For (1), stem from 31 to 88, too many stem, too few leaves
For (2), stem from 3 to 8, it should be easier.
So, (2) is better.

19. Stem-and-leaf diagram example
The living areas (in sq. feet) of students are:
(b) According to the answer in (a), construct a stem-and-leaf diagram to present the given data.
Answers: (b) The living areas of students

20. Back-to-back stem-and-leaf diagram (背對背幹葉圖, p.234)
Keep the real values and show all data
Can see and compare the distributions

21. Back-to-back stem-and-leaf diagram example
The students of a ‘fitness training course’ has to undergo special fitness tests in their first and last lessons. One of the tests is to ask the students to do as many sit-ups as possible in 1 minute. The tests results are recorded below:
Results of the first lesson:
Results of the last lesson:
Construct a back-to-back stem-and-leaf diagram to present the results of the above two tests.

22. Stem-and-leaf diagram example
Answer
Any improvement?

23. Stem-and-leaf diagram example

24. Stem-and-leaf diagram example

25. Time for Practice Pages 241 – 242 of Textbook 1B
Questions 6, 8
Pages 110 – 111 of Workbook 1B
Questions 5
A Typo in SHW (III) Question 2
Use $1000 as stem

26. HKDSE 2013
Paper 1 Question 10
Hint: Range = Largest – Smallest

27. Reminder Missing HW SHW (III) OBQ CBQ Detention 24th April (Wednesday)
29th April (Monday)

28. Enjoy the world of Mathematics!
Ronald HUI