Averages: Mean, Median, and Mode

Being able to utilize and be aware of averages can come in handy especially in heated topics such as tests, quizzes scores, etc that we may deal with on a daily basis. According to Epstein’s text, “the average is not the maximum or most likely depth. The average or mean of a collection of numbers is obtained by adding the numbers and then dividing by the number of items” (273).

For example,to retrieve the average or mean of a collection of numbers,
the average of 3,7,10,15,33 is calculated:
Add 3 + 7 + 10 + 15 + 33 = 68
Divide 68 by 5 = 13.6, the average

The median according to our text "is the midway mark: the same number of items above as below" (274). The median is the number in the middle.

For example, a graph could be helpful to show this, however let's just say
there are the numbers 5,10,15,20,25,30,35,40 that are in a line, when I took Algebra, one method we learned was by counting and crossing out the numbers until we got to the center. We would start w the far left and far right at the same time and cross them out. Then work our way until we got to the center. If there were two numbers left next to each other, we would add them and divide them by two.
However, based off our text, it states that "the distribution of marks should be a bell-shape, clustered around the median" (274).

The mode is "the number most often obtained" (274). So the mode is the number that appears the most.

For example,
5, 5, 10, 10, 10, 15, 20,30
The mode in this case would be 10 because it is shown 3 times when the other numbers were shown twice or once.

Second Assignment

I felt both assignments gave me a more clear and concise understanding on different techniques that can be used to evaluate arguments and claims used in articles, advertisements, social organizations.
However, for me personally it was the second assignment that really went into depth on different aspects used in critical thinking. It showed that there are different ways we can evaluate and analyze a group based on what we have learned throughout this course. For example, after completing this assignment, I am now more fully aware of how organizations use fallacies and concealed claims and especially appeal to emotion, pity to really capture the audience's attention. It never really occured to me prior to this assignment what the term was called when a social organization used certain terms and pictures to make the people watching and looking through their site to feel bad/pity for their cause;thus leading to the individuals giving in to what they see (what they are shown). Now I know that can be appeal to emotion,pity, spite, etc. Now and for the future, when I am watching commercials or see ads or sites for organizations that help give back to the community, I will be able to identify what concealed claim they used, or what their fallacies were, or how appeal to emotion, and/or pity was shown.

Misleading Claims with Numbers

Numbers in general can be tricky, especially when using them in describing a claim, fact, or opinion. In different math subjects, I personally have found it to be easier using numbers alone and not with words (word problems were always a challenge for me) because handling numbers alone was enough as a challenge already however when words were added, I felt the questions and story proposed in that problem became misleading. There were times I felt there was a "numerical comparison" that nothing being compared made sense; in accordance to Epstein's text means "comparing apples and oranges" (268).

Some other "numerical comparison" I have seen, is for example:

Attendance at San Jose Sharks games have increased by 45 % over the past two years.
That is great for the San Jose Sharks, that means on one hand, they must be winning a lot more(which these past two years is a fact; based on their statistics) and/or the popularity of the sport has increased. However, this claim exemplifies what the text also mentions, "two times zero is still zero when someone gives a numerical comparison that makes something look impressive but the base of the comparison is not stated" (268). The claim does not mention what the attendance was for each year, and how about for each month? Were there a total 5,000, or 10,000 people for a total of at least 3 games that caused the increase by 45% or was it the whole season overall?

Judging Analogies

I found section C: Judging Analogies in Chapter 12, very interesting and fascinating because whenever analogies are discussed or mentioned in an argument, they may not always be stated in a clear and cohesive matter. In order to show the analogy makes sense and that it can be used as the premise, as Epstein's text states, "We have to survey the simliarities and guess the important ones in order to find a general principle that applies to both sides. Then we have to survey the differences to see if there isn't some reason that the general principle might not apply to one side" (257). In other words, we have to test and look at both sides of the analogy and see which one relates (is most relevant) to the topic being discussed at hand. As well as making sure the main "principle" would apply to both sides and not just one.

For example,
Manny Ramirez (LA Dodgers) was caught with taking steroids, and although he dealt with the penalty of being suspended from playing, after the suspension he was able to play again with no other penalties. So high school and college baseball players who take steroids should just get the average suspension and not deal with any other penalties.

This can be somewhat convincing because although a player no matter what rank they are, all are aware of the rules and regulations when playing on their team. However, in college and high school, these players are also students and there are seperate rules they have to deal with if the individual chooses to take steroids. In MLB baseball, if the player gets caught and admits to taking steroids, they get the minimal penalty.

Objective 3: Appeal to Fear

The media uses the "appeal to fear" all the time. Appealing to fear, according to Epstein's text is "a way politicians and advertisers manipulate people" (192).
An example I found that was completely relevant to this was drinking while driving and what the consequences of that are.


In this advertisement, I found this image that shows when an individual drinks any type of alcohol such as beer or wine, then operate a vehicle right or soon after consuming those beverages, the risk factor or "danger" of choosing that sort of action. The caution sign that had "Danger" clearly showed and proved that this advirtisement made a good argument because alcohol(any type) reduces the attention span and slows down our speed to reaction. Just imagine, if alcohol even having one drink of any type, can have that type of reaction on an individual, depending on their body tolerance factor or BAC (Blood Alcohol Content, then getting behind the wheel will definitely pose a factor of possible accidents, which can lead to death(s). This advertisement was meant in a way to mainpulate people however not in a deceiving way rather more to inform people; if you choose to drink then drive, you can be at risk of various types of danger.

Appeals to Emotion

Whenever we make decisions, our reasoning usually(most often) are based off of our emotions. Emotions play a big role in general during our daily lives.Whether it is to make a decision on when to get going on homework, studying for exams, getting to work on time, handling relationships, or even when shopping. Most often, those decisions includes us using the idea according to Epstein's text that, "you should believe or do something because you feel a certain way"(191).

For example, there are many beer commercials out there especially in between baseball and football and basketball games. They are used to help hype up the individuals watching the games, to make people feel it will give them a better experience or enjoyment if they drink that certain beer. There's this one commerical on t.v. advertising the beer "Cereva Dos Equis" that I see often while watching the Giants game. The main guy advertising it says he doesn't drink beer much, but when he does, he chooses this beer. He chooses this beer because he "feels like it and it tastes good to him." Appeal to emotion was appealing to me because it made me think of watching those beer commercials and how if an individual chooses that beer, they won't be sorry, that is also including the fact of drinking responsibly and not drinking while driving.

Vague generalities

Oftentimes when we are discussing a part or all of something we tend not to specify the precise number of that subject being discussed. Most vague generalities don’t tend to fit in good arguments nor do most not even “belong in claims” according to Epstein’s text. However, using a few of the words (which stated below) show to make and can be used in strong arguments.

A few brief examples:

All kids like candy.
Almost all kids like candy.
Most SJSU students are commuters.
Some SJSU students are commuters.

Although when using the words “all” and “some” can be interpreted with different meanings, however at the same time using these words can also help show if an argument is valid.
There are two vague generalities that can be used in strong arguments:

Almost all basketball players are over 5’11.
So the basketball players of the LA Lakers are over 5’11.

Very few athletes are not fit.
Adrian is an athlete.
So Adrian is fit.

Truth-Tables~Representing Claims

Before I get into the subject on representing claims, I want to briefly mention the symbols used to describe words that are shown and used in arguments being made in compound claims.
These are shown on page 360 in our text by Epstein:

-and= ^
-or= v
-not= backwards L
-if…then…= -->

In order for us to utilize truth-tables we have to be able to show ordinary claims and arguments.

For example,

Ice cream can be found at Cold Stone Creamery or Frozen Yogurt can be found at Pinkberry.
When analyzing this, we can represent this using the “exclusive” or.
(Ice cream can be found at Cold Stone Creamery v Frozen yogurt can be found at Pinkberry) ^ backwards L (Ice cream can be found at Cold Stone Creamery ^ Frozen Yogurt can be found at Pinkberry

An example of using a conditional (“ --> - claim is false if the antecedent=true and consequent=false. Otherwise it is true” (361) would be:
(in baseball): Strike me out and I’ll strike you out.
This is an example of a conditional and it can represent as:
You strike me out --> I strike you out

General Claims and their Contradictories

Being able to distinguish, understand, and recognize general claims as well as their contradictories is not only imperative but helpful on a daily basis. We hear and see them all the time, whether it being stated aloud or in writings such as newspapers, online, magazines.

Our text by Epstein in Chapter 8, defines a general claim as "a claim that asserts something in a general way about all or a part of a collection" (159).
The text also defines and exemplifies what all and some mean when making a general claim and contradicting it. "All means 'every single one, no exceptions.' Sometimes all is meant as 'Every single one, and there is at least one."
"Some means 'At least one.' Sometimes some is meant as 'At least one, but not all" (160).

For example, when using all and some in a general claim then their contradictory:
Claim: Contradictory:
All Giants fans hate Dodgers fans Some Giants fans like Dodgers fans
Some Giants fans hate Dodgers fans No Giants fans hate Dodgers fans
No Californian can handle the Some Californians can handle the East Coast
East Coast weather weather

The contradictory of a claim

Often times whether it occurs daily or time to time to time, I have heard family, friends, acquaintances, strangers, doctors, even myself state a claim and then contradict it. So what I found interesting in Chapter 6 in Epstein's text was the contradictory of a claim which "is one that has the opposite truth-value in all possible circumstances. Sometimes a contradictory is called the negation of a claim" (114). So what makes the claim contradictory is based on it having the opposite of true or false value.

For example,

When I was a freshman in college, I lived with seven other girls on campus. Every single day literally I would hear a contradictory of a claim.

*(following names used are not the actual individual's names)

Claim: Contradictory:

"Lexi is being loud" "Lexi isn't being loud"
"Rose backstabbed Jane" "Rose didn't backstab Jane"
"Sarah will go to the football "Sarah won't go to the football
game or she will go to a party." game and she won't go to a party."
"Jessica or Angela will go with "Neither Jessica or Angela will go with Eric to his friend's house." Eric to his friend's house."

Raising Objections

On a daily basis, as part of being human, we deal with raising objections. We deal with “arguments, counterarguments, counter-counterarguments.” According to Epstein’s text, “raising objections is a standard way to show an argument is bad. In doing so, we are making another argument that either calls into question one of the premises, or shows that an unstated premise is dubious, or illustrates why the argument is weak” (147). In other words, raising an objection or objections shows how someone is objecting to the argument being stated because it lacks either cohesiveness, or its premises are weak.

For example, let’s take Sean and Jill. A happy young married couple (for 2 years now) and Jill wants to have a baby. Sean begs to differ. Jill says “Sean, all children are miracles and are so precious.” Sean then chimes in, “But Jill, at first when they are babies, they are not so pleasant and wonderful as you may think.” Jill then argues, “Sean! How can you say that about babies? Yes when they are newborns they require a lot of attention however, then through all that tender, love, and care they grow up to be wonderful human beings.” “They also bring more joy and happiness to you as the parents than if you had no children whatsoever.”

As the text mentioned rather than evaluating this argument, you raise objections.

Sean raises some good points when stating, “Not all couples are meant to have kids, and that is including us.” “Once we have kids, that means we won’t be able to provide attention to our work as much or we’ll have to divide work and the kids (our family). Is that something we both really want and need?”

Jill’s initial argument on all children being miracles and are so precious can absolutely be questioned because children can be precious however they require a lot of work, attention, love, etc.