MAM Day 20: Graphs, charts & visual math

Some of us are visual learners, but most students are able to read and extract information from charts and graphs by the time they reach middle school. Charts and graphs are visual representations of data "represented by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart". I'm sure most, if not all of you, have seen a chart at some point this past week, or even earlier today. Charts are everywhere! On the internet, magazines, newspapers, in school textbooks, on billboards, in all kinds of advertising, on TV, on the bus, and all points in between.


The results of CNN's online poll today

One of my favorite websites with funny charts and graphs where I got quite a few of my graphs for today. The main charts that we see the most in everyday life are pie charts, bar graphs, line graphs, and sometimes venn diagrams. I'll just briefly talk about each one and why they're used.


Pie charts represent a percentages in relation to each other. Usually pie charts are used in tallying 100% of a quantity. See my Billboard pie chart for a better example. The pie chart shows the proportion of pop music that was on the top charts vs. gangsta rap. Pie charts are often used to show a very quick picture of the selections. Out of the listed charts, I would have to say pie charts are the most simple, easy to glimpse at, but limited in what kinds of information they can show.


Well labeled bar graphs can show an amazing amount of information in a single graph. Most often, bar graphs are used to compare frequencies, or how many, of a category of data. Bar graphs can even show multiple sources of the same data, for example the graph below:
Shows the number of students over a period of time and breaks the data down into the number of boys in comparison to the number of girls.


Line graphs show a continuous source of data, someone's budget over the course of a month for example. At the beginning of the month, I posted a line graph of the number of people who visited my blog. This one is a line graph of the same thing, only a different time period. As you can see, the first day was a big increase over the previous number of hits and significantly more than my following days. The line graph shows progression of visitors over time and lets me know which of my posts are more interesting than others. Line graphs are only line graphs if the data has a progression usually over time.


Venn diagrams show an intersection of commonalities. Although venn diagrams aren't often used, they show groups of people, objects, or ideas and then show where other groups of people, objects, or ideas have common links. A proportion of Set A will not have shared characteristics of Set B, but there is a certain area where they do match up. I find venn diagrams don't show hard data, but illustrate concepts quite well.




.

MAM Day 16: US Census 2010

Friday April 16 is the deadline for the United States Census! If you haven't filled it out yet, please do so. Although I was troubled by the race questions, I still believe it's very important for everyone to participate, it's our civic duty! The United States Census is a decennial (once every 10 years) census mandated by the United States Constitution., but funding, services, and politics all depend on the Census.

Not only is it our civic duty to fill out the US Census, the taxpayers of the US will save money - This year, if every household mailed back its census form, taxpayers would save $1.5 billion in costs from sending census takers door-to-door to collect the same information.


Although I don't know very much about the Census, I read up on the Census website and found some cool math related links further down on this blog post. On the surface, the Census is merely counting and getting the most accurate demographic data on the US. The Census is less involved with math directly, but statistical analysis after the Census has been returned is where the math makes the Census so important.

Quotes:

• From the US Census: When you fill out your 2010 census form, you help determine how more than $400 billion a year is distributed in communities like yours.
  
• From the Director, U.S. Census Bureau: Census results are used to decide the number of representatives each state has in the U.S. Congress. The amount of government money your neighborhood receives also depends on these answers. That money is used for services for children and the elderly, roads, and many other local needs.
  
• From C.N. Le, Sociology Professor at University of Massachusetts, Amherst: "For many sociologists and other scholars like me, the census data that is compiled every 10 years is flat-out the most reliable, comprehensive, and best source of data on the American population."
  

My roommate and I questioned the "race" questions on the Census, so I looked it up and tried to make sense of the weirdness on the form.

This webpage explains why they ask race questions:
Asked since 1790. Race is key to implementing many federal laws and is needed to monitor compliane with the Voting Rights Act and the Civil Rights Act. State governments use the data to determine congressional, state and local voting districts. Race data are also used to assess fairness of employment practices, to monitor racial disparities in characteristics such as health and education and to plan and obtain funders for public services.

More answers to these following questions

• Why isn’t there a checkbox for my ethnic group on the form?
  
• Why is the Census Bureau spending money on advertising during these tough economic times?
  For every one percent increase in mail response in 2010, the census will save $85 million that would otherwise have to be spent on door-to-door follow-up with households that didn’t respond.
  
• In this day and age, why is the word “Negro” included as part of the race question on the 2010 Census form?
  

It's incredible the statistics that come from the information after the Census has been completed. These are just a few of the links I found off the Census website. It would take weeks possibly months to browse through all of the data, but it's all necessary to make sure communities get the government funding it deserves.

• Quick facts about the United States, specific states, and major cities
  
• Statistics of my hometown
  
• Student fact page where I found out that only 9% of Massachusetts workers use public transportation. Gotta take into account the huge percentage of Massachusetts that doesn't have public transportation...
  
• Census fact sheet where I learned that almost 20% of Americans speak a language other than English at home.
  
• A wealth of information about the United States
  
• The statistics of Boston by age
  

.

MAM Day 5: Sports and Math

In honor of the official Math Awareness Month theme, today's blog post is about sports and the underlying math that allows us to participate in and keep track of sports.

Being a big nerd, I have very limited experience with sports. Unfortunately, I did not make the basketball team and I was not coordinated enough to do anything else in grade school. I managed to eke through gym class and pass it so I could graduate. I enjoyed dodgeball, but hated volleyball because my wrists were too fragile to bump pass those rock hard white volleyballs.

I do, however, really enjoy watching sports. My dad and I used to watch football and after a while, I knew more about the game than he did. My favorite team was the Broncos, I think just because they were the closest professional team to my hometown. There was a period when they were on a good streak (the John Elway days) when I was especially interested in watching Monday Night Football.

The mechanics of playing sports baffle me, but if I had learned more physics and higher level math, I could've applied science and math to sports. What kind of spin and forces does it take to throw a football with surprising accuracy over 20 yards? I'm sure it takes different forces to pitch a curveball some 75+ miles per hour. Think about the angles and power needed to return a Williams sister's tennis serve back onto the court! Venus's average serve tops out at 130 mph - that's twice the allowed average highway speed!

Other sports involve math in different ways - ice skating and the physics of momentum, basketball and trignometry of shots, even golf (which I denounced as a sport for a long time) requires lots of power and mathematical analysis to hit a ball an average of over 200 yards to a certain area with varying weather conditions. I'm not saying that athletes are pulling out their pad and pencil to calculate what kind of swing they should be hitting or the correct angle to take a three pointer, but they've built up an unstated knowledge base of what angles work best for sinking a shot from certain areas, or what strategy, angle, and position would be best for going up against a Williams' serve. It's internal sports math that atheletes rely on but probably don't consciously think about when they're in the game.


Besides the math and science behind the mechanics of sports, many if not all sports have some sort of statistics: batting averages in baseball, point averages of NBA players, and scoring in many other sports. These are generally calculated by computers now, but back in the day, baseball batting averages were done by hand.

Don't even get me started on fantasy sports. Fantasy sports in a nutshell are sports (and secretly math) nerds who use real players' current and regularly updated statistics to make fantasy teams and play against other fantasy teams. Fantasy baseball, football, basketball, and hockey are the bigger sports that have fantasy players.


At the MAM webpage, there are essays and articles on the mathematics behind some of the bigger sports. Or check out their posters for Math Awareness Month. This website also shows how math is involved with scoring.

------------------

For those of you who work with youth who are also involved with sports, you could try starting up a conversation with them about math and sports. Ask him/her if she realizes there's math involved with the scoring, statistics, and actual mechanics of sports and just talk about sports, even if they don't like math.

If you don't work with youth but enjoy sports, try to think about the math behind the sport, it might surprise you that good athletes are also secretly good mathematicians who don't realize it.



.