Survey Results

Question 7 of Extra Credit II asked students to fill out the survey in section 9.2 of the book. 25 people filled out part of the survey, and 23 completed it entirely. Here is the statistical abstract!




1 Gender
Among respondents: 16 females, 9 males, or 64.0% female vs. 36.0% male.

In the whole class: 45 females and 25, or 64.3% female vs 35.7% male.




2 Weight
Overall: Average: 137.4 lbs,   Standard Deviation: 29.9 lbs
Females: Ave 123.8,   Stdev: 21.6

Males: Ave 161.7,   Stdev: 27.8

3 Height   Note: 60in = 5ft.
Overall: Ave 64.8in,   Stdev 4.15
Females: 62.6,   Stdev 2.4
Males: Ave 68.8,   Stdev 3.6

Among respondents, males on average are 6.2in taller than the females. That's huge.




4 Favorite Body Part

Overall:

It is interesting to see the breakdown by gender on this one.

Females:

Males:

There appears to be more variability among what males consider their favorite body parts.




5 Number of times per month people call home
Overall: Ave: 4.9, Stdev: 2.55
Female: Ave 4.3, Stdev 2.5
Male: Ave: 6, Stdev 2.5

The data reports that males call home more often than females.




6 Number of times per month people do Laundry
Overall: Ave: 6.08, Stdev 2.17
Female: Ave: 5.9, Stdev 2.1
Male: Ave 6.4, Stdev 2.4

The data shows that males do somewhat more washes than females, but the difference may not be statistically significant.




7 How many times per month do you drink alcohol?
Overall: Ave 6.08, Stdev 2.17
Female: Ave 5.87, Stdev 5.07
Male: Ave 6.67, Stdev 4.80

Males drink more frequently on average, but there is a wider range of variability in female drinking.




8 How many dates do you go on per month?
Overall: Ave 3.32, Stdev 2.56
Female: Ave 3.25, Stdev 2.41
Male: Ave 3.44, Stdev 2.96

Males and Females go on approximately the same number of dates, but the variability in the number of male dates is wider.




9 Number of months since you last saw a movie in a theater
Overall: Ave 1.21 months since last theater movie
Females: Ave 1.02 months since last theater movie
Males: Ave 1.56 months since last theater movie

Among respondents, females attend movie theaters more often than males.




10 Number of hours per day spent browsing the internet.
Overall: Ave 3.24, Stdev 0.97
Females: Ave 3.38, Stdev 0.89
Males: Ave 3.00, Stdev 1.12

Among respondents, females use the Internet more often, but among males the usage rate has a wider range of variability. In this case, the data are clearly skewed because the highest allowable number of hours was 4, but some people use the internet more than 4 hours per day.




11 Number of emails received per day
Overall: Ave 15.20, Stdev 4.76
Females: Ave 16.06, Stdev 4.91
Males: Ave 13.67, Stdev 4.33

Females receive more emails on average.




12 Hours per week spent studying
Overall: Ave 21.80, Stdev 11.80  (Wow! That's a HUGE range of variability!)
Females: 21.25, Stdev 10.25
Males: 22.78, Stdev 14.81

Females and males spend about the same number of hours studying, but the variability among males is greater.




13 Number of college courses taken so far
Overall: Ave 16.60, Stdev 6.60
Females: Ave 17.31, Stdev 6.70
Males: Ave 15.33, Stdev 6.61

On average, females have taken more classes.




14 Number of years left before graduation
Overall: Ave 1.92, Stdev 1.10
Females: Ave 1.833, Stdev 1.18
Males: Ave 2.06, Stdev 1.01

On average, females are closer to graduation.




15 Post-Graduation Plans

Overall:

16 How many people in the class do you find attractive?
Overall: Ave 4.22, Stdev 2.75 (Very wide range of variability!)
Females: Ave 4.00, Stdev 3.01
Males: Ave 4.56, Stdev 2.41

On average, the females found fewer people attractive, but the range of variability was significantly higher.

For this one, I was highly curious about the data. Here is a closer look.

Overall:

So the Mode is "at most 2." That's cold, people, cold! What's wrong with kids today?

The averages between females and males are not that different, but just look at how differently the data breaks down:

Females:

Males:

So there we have it. According to this data set, females cluster around not being attracted to many people, but the distribution is wider. Males cluster around the average, but have a tighter distribution.




17 Favorite topic in class

Overall

18 Number of hours of sleep per night
Overall: Ave 6.69, Stdev 1.25  (6.69 seems pretty low to me!)
Females: Ave 6.50, Stdev 1.42
Males: Ave 7, Stdev 0.87

Geeze, ladies, you need to get more sleep at night! Guys, too! You should be getting 8-9 hours!




19 Number of Siblings
Overall: Ave 1.42, Stdev 1.14
Females: Ave 1.27, Stdev 0.96
Males: Ave 1.67, Stdev 1.41

The variability is very large: the standard deviation is larger than the mean.




20 Hours spent doing athletic activities
Overall: Ave 5.65, Stdev 8.46
Females: Ave 2.97,  Stdev 4.06
Males: Ave 10.11, Stdev 11.88

Among respondents, males do far more athletic activities per week. The variability for both males and females is huge.

Teaching Blog Test Time!

Preparing for a test requires figuring out what you need to know. That involves two things: figuring out what's important, and figuring out what the teacher thinks is important. And what is that? In the broadest perspective, this class has two main themes: learn the skills of mathematical reasoning, and learning about the subject matter of mathematics.

I'll say just a word about the first part, mathematical reasoning. Math isn't numbers. It is the study of formal structures, which are systems of specific, clearly-defined objects along with rules by which the objects relate. Perfect examples include arithmetic in the integers, and the game of Chess. Imperfect examples include the system of traffic laws and the American legal system. Much of what we experience in daily life has nothing to do with formal systems, but in whatever you do in life, having the ability to formulate problems in formal ways, and to use formal reasoning to analyze problems, will be a benefit.

As for the second part, the subject matter itself, I present the following outline.

Proofs you need to know:

• There are infinitely many primes.
• square roots of 2, 3, etc are irrational
• The cardinality of the reals is larger than the cardinality of the natural numbers
• The Pythagorean Theorem
• There are only 5 regular polyhedra (aka Platonic solids)

Chapter 1
No real content. Just some puzzles meant to make a point, for instance that formal reasoning can be used to solve real-world problems.

Chapter 2 - Numbers (Sections: 2.1- 2.4, 2.6)

1. The pigeon hole principle
2. The Fibonacci sequence. Recursive formulas and direct formulae. Ratios of successive numbers in a recursive sequence. Limits. Infinite fractions.
3. Prime numbers. Divisibility (for instance, the exact  meaning of m|n). Unique factorization. The division algorithm. Quotient and remainder. Proof that there are infinitely many primes.
4. Modular arithmetic. Reduction mod n. UPC codes and check-digits.
5. Rational (numbers that are ratios) and irrational numbers (numbers that are not ratios). Proof that square roots of 2, 3, etc are not rational

Chapter 3 - Infinity (Sections: 3.1-3.3)

1. One-to-one correspondence. Something more primitive than counting: Cardinality.
2. The even numbers, the prime numbers, the integers, and the rationals all have the same cardinality as the natural numbers.
3. Countable and uncountable sets. Examples of countable and uncountable sets. The diagonal argument. Proof that the reals are uncountable.

Chapter 4 - Geometry (Sections 4.1-4.3, 4.5, 4.7)

1. The Pythagorean theorem.
2. Triangulation. The art gallery theorem.
3. Definition of the Golden Rectangle. Computation of the value of the Golden Ratio. The Golden Spiral
4. Polygons. Polyhedra. Duals of polyhedra. Stellation and truncation. Regular polygons. Regular polyhedra. Proof that there are only 5 regular polyhedra.
5. Definition of dimension (a degree of freedom, or a mode of measurement). Real-life examples of multi-dimensional problems and data sets. Imagining the 4th dimension. Analogy with 1, 2 and 3 dimensions.

Chapter 5 - Geometry and Topology (Sections 5.1-5.3)

1. Geometry is the study of shape. Topology is more primitive: it is the study of connectedness. Topological changes and geometric changes. How to prove two objects are topological equivalent, and how to prove two objects are topologically different.
2. Gluing patterns. The Torus. The Mobius strip. The Klein bottle.
3. Knots and links. Equivalent and inequivalent knots. The unknot.

Chapter 6 - Graphs (Sections 6.1-6.3)

1. Graphs. Euler Circuits. The Konigsberg bridge problem.
2. The Euler characteristic. Second proof that there are only 5 regular polyhedra.
3. Planar and non-planar graphs. E<3V-6 for planar graphs without multiple edges. The graphs K5 and K3,3. Application of graphs: maps and the 4 color problem.

Chapter 7 - Fractals (Sections 7.1-7.3)

1. Self-similarity. Infinite detail. Fractal-like objects and phenomena in nature.
2. Examples of fractals: simple instructions repeated indefinitely. Sierpinski triangle. Sierpinki carpet. Menger sponge. Koch curve and Koch snowflake.
3. Fractal dimension. Scale and content.

Chapter 8 - Chance and Probability (Sections 8.1-8.3, 8.5)

1. Definition of the probability of an event. Definition of relative frequency. P(not E) = 1-P(E). Yatzhee question. Birthday question. Law of independent events: P(E and F) = P(E)P(F) provided E and F are independent.
2. Streaky-ness and probability.
3. Nash equilibrium. Payoff matrix. Probability strategies (eg. pgs 630-631)

Chapter 9 - Statistics (Sections 9.1-9.3, 9.5)

1. Statistics is the organization of data. Ways statistics can be misused. Coin-flip strategies for poll-taking. Correlation.
2. Histograms. "Center" of a distribution: mean, median, and mode. Skewed and normal distributions. The desert island example. Distributions that are bimodal, trimodal, etc. 
3. The bell curve. Standard deviation. Coin flips.
4. Deeper analysis of data: the hospital example, and the university gender discrimination example.

Chapter 10 - Applications (Portions of Sections 10.1-10.3)

1. Expected value. Weighted standard deviation.
2. Testing for a disease.
3. Interest and compounding.