Introduction to Statistics Form 1 Mathematics Chapter 12

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

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)

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

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

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°

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°

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

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

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

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

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 2008 1st season than 2007 1st season, find out the difference. (b) Describe the changes in the company’s profit. Answers: (a) The profit in 2007 1st season = 7.2 million dollars The profit in 2008 1st 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

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

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 2 5 8 0 5 9 2 5 8 8 The prices of 12 books

Stem-and-leaf diagram

Stem-and-leaf diagram (p.232) Steps: Example: The prices (in $) of books are shown below: 95 78 102 63 108 75 90 99 66 108 105 72 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 2 5 8 8 9 0 5 9 10 2 5 8 8

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.

Stem-and-leaf diagram example The living areas (in sq. feet) of students are: 310 430 400 882 790 620 325 622 450 390 730 395 345 560 560 515 481 385 450 390 (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.

Stem-and-leaf diagram example The living areas (in sq. feet) of students are: 310 430 400 882 790 620 325 622 450 390 730 395 345 560 560 515 481 385 450 390 (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

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

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: 8 23 9 14 21 13 15 20 17 18 22 19 15 21 8 17 32 16 Results of the last lesson: 12 31 15 18 29 16 22 28 26 27 31 27 23 30 14 27 35 26 Construct a back-to-back stem-and-leaf diagram to present the results of the above two tests.

Stem-and-leaf diagram example Answer Any improvement?

Stem-and-leaf diagram example

Stem-and-leaf diagram example

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

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

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

Enjoy the world of Mathematics! Ronald HUI