Transcript Absolute vs. Relative - William & Mary Mathematics

Math162 Presentation
This Presentation
We are going to cover the following:
Example 1: The Math162 grading scheme
Example 2: The First Class Honor
Example 3: HKUST’s world ranking
Example 4: Toy Story 3’s box office in Hong Kong
Example 5: The 2010 Hong Kong by-election
Example 6: Minimum wage in Hong Kong
Example 7: The United States presidential election of 2000
Mickey & Yung, Absolute vs. Relative: 7 Examples of Number Manipulation in Daily Life by Elementary Arithmetic (+, -, ×, ÷)
1173 Hours Ago…
Professor Li invited us to think about this comment:
 “In daily life, we only need to use the four basic arithmetic operations - addition, subtraction,
multiplication, division. So, these are all we need for mathematical training.”
What can (+, -, ×, ÷) do?
When Truth Lies
Mickey & Yung, Absolute vs. Relative: 7 Examples of Number Manipulation in Daily Life by Elementary Arithmetic (+, -, ×, ÷)
Example 1: Math162 grades
The grading is based on the presentation 1 performance.
13 of 21 students are listed below.
The score of the Samson/SuenWai group is fictional.
Name
Samson SuenWai
Alan
Justina
Gloria
Mickey
Yung
Kary
Loretta
Vivian
Leo
Kelvin
Roy
Score
10
10
8.88
8.88
8.88
8.5
8.5
7.91
7.91
7.91
7.82
7.82
7.82
Normal
A+
A+
A-
A-
A-
B+
B+
B
B
B
B-
B-
B-
Math162
A+
A+
B+
B+
B+
B
B
C+
C+
C+
C+
C+
C+
Normal is what most other courses do:
18% A range; 36% B range; 42% C range; 4% D and F
Mickey & Yung, Absolute vs. Relative: 7 Examples of Number Manipulation in Daily Life by Elementary Arithmetic (+, -, ×, ÷)
Example 1: Math162 grades
The unit of the y axis matters.
Mickey & Yung, Absolute vs. Relative: 7 Examples of Number Manipulation in Daily Life by Elementary Arithmetic (+, -, ×, ÷)
Example 2: How many First Class students?
Just like the birthday paradox. Since we have 18% of students getting A’s in every course, some
might intuitively think we have 18% of students getting First Class each year.
Grade
A+
A
A-
B+
B
B-
C+
C
C-
D
F
Score
12
11
10
9
8
7
6
5
4
2
0
Percent
6
6
6
12
12
12
14
14
14
4
Rule: Those with CGA no less than 9.5 get First Class
Assumption: Every course has the same credit
Taking one course: 6 + 6 + 6 = 18%
Taking two courses: A+, and at least B-; A, and at least B; A-, and at least B+.
( (6*54) + (12*42) + (18*30) ) / (100*100) = 13.68%
What about more?
Mickey & Yung, Absolute vs. Relative: 7 Examples of Number Manipulation in Daily Life by Elementary Arithmetic (+, -, ×, ÷)
Example 3: HKUST ranks 41st in the world
And how it does not matter to you.
19.5 + 5.25 + 4.5 + 0.75 +
32.5 + 2.5 +
6 + 2.25 =
At least 73.25% irrelevancy
Mickey & Yung, Absolute vs. Relative: 7 Examples of Number Manipulation in Daily Life by Elementary Arithmetic (+, -, ×, ÷)
Example 4: Toy Story 3 is HUGE in Hong Kong…
Top 10 films with the biggest box office in Hong Kong:
Rank
Title
Year
Box Office (HKD)
1
James Cameron’s Avatar
2009
$176,984,565
2
James Cameron’s Titanic
1997
$104,615,934
3
Pixar’s Toy Story 3
2010
$89.36 Million
4
周星馳《功夫》
2004
$61,278,697
5
周星馳《少林足球》
2001
$60,739,847
6
Steven Spielberg’s Jurassic Park 2
1997
$58,505,480
7
Christopher Nolan’s The Dark Knight
2008
$58,440,488
8
Christopher Nolan’s Inception
2010
$58.38 Million
9
Steven Spielberg’s Jurassic Park
1993
$58,360,645
10
唐季禮《警察故事4之簡單任務》
1996
$57,518,795
Mickey & Yung, Absolute vs. Relative: 7 Examples of Number Manipulation in Daily Life by Elementary Arithmetic (+, -, ×, ÷)
Example 4: Toy Story 3 is HUGE in Hong Kong…
First revelation
Average ticket price for normal films: 60 HKD
Average ticket price for Inception (surchage for the long length and some IMAX): 70 HKD
Average ticket price for Toy Story 3 (surchage for the 3D and some IMAX format): 90 HKD
How many people went to see Inception? And TS3?
58,380 / 70 = 834,000; 89,360 / 90 = 992,000.
Second revelation
Inception: 142 minutes; TS3: 103 minutes.
How long did Hong Kong people spend on watching Inception totally? And TS3?
834,000*142 = 118 million minutes on watching Inception;
992,000*103 = 102 million minutes on watching TS3.
Mickey & Yung, Absolute vs. Relative: 7 Examples of Number Manipulation in Daily Life by Elementary Arithmetic (+, -, ×, ÷)
Example 5: Is 17.1% that large/small a number?
It’s 17.1%, while it was 45.2% in 2008. But…
香港島
陳淑莊
九龍西
黃毓民
九龍東
梁家傑
新界西
陳偉業
新界東
梁國雄
全港
2008
Election
82,600
37,553
39,274
32,182
44,763
236,372
2010 ByElection
103,564
60,395
82,066
109,609
108,927
464,561
100% increase of supporters.
Not to mention the 36,226 votes won by ”大專2012”.
But, the Pro-Democracy Camp won 869,465 votes in 2008
Still 869,465 - 464,561 - 36,226 = 368,678 potential
supporters not convinced.
Mickey & Yung, Absolute vs. Relative: 7 Examples of Number Manipulation in Daily Life by Elementary Arithmetic (+, -, ×, ÷)
Example 6: The Minimum Wage
$18 - $18X8X26=$3744
$28? Why? - $28X8X26=$5824
-cut working hours
-change back the situation
-case 1
$28X7X26=$5096
Mickey & Yung, Absolute vs. Relative: 7 Examples of Number Manipulation in Daily Life by Elementary Arithmetic (+, -, ×, ÷)
Example 7: George Bush vs. Al Gore
Gore 51 Million vs. Bush 50.5 Million, Bush won!
---Indirect Election
The Electoral College
538 electors
Won by absolute majority - 270
Electors of each state
= no. of Senators + no. of Congressmen
---Separation of Powers
The President (1)
The Congress
Senate (2 seats per state, 100 total)
House of Representatives (by population)
The Supreme Court (9)
--50 states, and D.C. (the capital)
Mickey & Yung, Absolute vs. Relative: 7 Examples of Number Manipulation in Daily Life by Elementary Arithmetic (+, -, ×, ÷)
Example 7: George Bush vs. Al Gore
Total congressmen of the nation: 435; Total senators: 100; D.C.: 3
48 states + DC: winner-take-all; Maine and Nebraska: exceptions
Mickey & Yung, Absolute vs. Relative: 7 Examples of Number Manipulation in Daily Life by Elementary Arithmetic (+, -, ×, ÷)
Homework
1.
Recall the numbers in the 7th example, the total number of electors voted for Bush is 271, Gore 266,
accounting for totally 537. There are, however, as we calculated, 538 electors around the nation.
Please do some research, and find out what’s wrong here?
2.
We are going to establish a House of Representative in China, using Hong Kong’s population as the
base. So, Hong Kong has ONE congressman. How many congressmen do Guangdong, Shanghai,
Sichuan, Macau and Tibet have, respectively? Reference:
http://zh.wikipedia.org/wiki/%E4%B8%AD%E5%8D%8E%E4%BA%BA%E6%B0%91%E5%85%B
1%E5%92%8C%E5%9B%BD%E8%A1%8C%E6%94%BF%E5%8C%BA%E4%BA%BA%E5%8F%A3
%E8%A1%A8
3.
Extra: Calculate the percentage of students getting First Class Honor if they take totally 2 courses in
UST.
Mickey & Yung, Absolute vs. Relative: 7 Examples of Number Manipulation in Daily Life by Elementary Arithmetic (+, -, ×, ÷)
Extra question: Can you help us find x?
x
555
444
Thank you.
Mickey & Yung, Absolute vs. Relative: 7 Examples of Number Manipulation in Daily Life by Elementary Arithmetic (+, -, ×, ÷)