Baseball Salary Word Problem

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redsoxnation

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Mar 27, 2011
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I'm hoping that Word Problems go in this "Odds & Ends" spot....

The problem states: Was the difference between the mean and median salaries for all MLB players greater or smaller in 2002 than it was in 2009? 2002 mean = $2,400,000 median = $900,00. 2009 mean = $2,700,000 median = $500,000.

This may just be semantics, but how do you interpret the word "difference" in this case? Is it the mathematical difference? Or the fact that the figures are dissimilar? I've emailed my Professor, but I doubt he's going to answer back on a weekend.

Thanks for all opinions!
 
redsoxnation said:
I'm hoping that Word Problems go in this "Odds & Ends" spot....

The problem states: Was the difference between the mean and median salaries for all MLB players greater or smaller in 2002 than it was in 2009? 2002 mean = $2,400,000 median = $900,00. 2009 mean = $2,700,000 median = $500,000.

This may just be semantics, but how do you interpret the word "difference" in this case? Is it the mathematical difference? Or the fact that the figures are dissimilar? I've emailed my Professor, but I doubt he's going to answer back on a weekend.

Thanks for all opinions!
Click to expand...

tkhunny gave you the short answer.

The long answer is this. You are correct that "difference" has at least two different meanings: a zebra is "different" from a giraffe because they are placed in different zoological sets. But that is qualitative reasoning. You are taking a course in quantitative reasoning, and in quantitative reasoning the most common (perhaps the only) meaning of "difference" involves subtraction. Even in a math course, parsing language according to context is a good strategy. A further clue is that you are being asked about "greater or smaller"? The following two propositions are logically equivalent: a > b and (a - b) > 0. Although I cannot say that "greater or lesser" ALWAYS represent a quantitative difference that can be represented in terms of subtraction, I do say that statements like "Napoleon was a greater general than Haig" are metaphors that rhetorically try to impute mathematical exactness to purely qualitative judgments (which may of course be reasonable) such as "Napoleon was a better general than Haig." (See: you get an answer from tkhunny who is a mathmatician that is short and to the point. From me, however, who studied history, you get a long, convoluted answer that means the same thing.)
 
redsoxnation said:
The problem states:
Was the difference between the mean and median salaries for all MLB players greater or smaller in 2002 than it was in 2009?
2002 mean = $2,400,000 median = $900,00. 2009 mean = $2,700,000 median = $500,000.
Click to expand...
2002: 2,400,000 - 900,000 = 1,500,000
2009: 2,700,000 - 500,000 = 2,200,000
Is the 2002 difference greater or smaller than the 2009 difference?
That's what you're being asked...now, WHY ask such a simple question is beyond me...

Btw, my grandson Tyler plays for the Orleans Red Sox (Little league);
made it to the World Series (Juniors, 2005):
http://www.littleleague.org/series/2005 ... series.htm

Won 2 games...about the best we hockey players usually do!!
 
tkhunny: thank you for your brevity.

jeffm: thank you for your metaphorical grandeur. and your answer.

denis: thank you validating my internal monologue ("this question seems simple. too simple...."). And congratulations to your grandson; I guess if you're going to lose to anyone, it's probably going to be Latin America. We'll keep an eye out for him when he gets to Fenway! (funny how things change; I was one of the first girls to play in a "girls ice hockey" league many years ago, now my daughter plays hockey AND little league!)

thank you all. going back to school as an "older" undergraduate has its challenges. you guys are a huge help!
 
By the way, if I were your math instructor, I would be DELIGHTED that you would ask such a question. Actually thinking about what you are doing, requiring the removal of ambiguity. Excellent. It warms my heart.
 
Redsoxnation

Thank you for the encouraging words. I have just started posting here and am still not sure whether I am doing more harm than good.

Generally what seems to happen is: tkhunny gives the right answer, and then I weave arabesques around it. That way he does the hard work, and I get the grandeur.

Jeff
 
Hmmm...OK....so does this mean you're not sticking around as a volunteer tutor,
so you can help struggling students? You'd rather leave that for "suckers" like us? :wink:
 
Denis said:
Hmmm...OK....so does this mean you're not sticking around as a volunteer tutor,
so you can help struggling students? You'd rather leave that for "suckers" like us? :wink:
Click to expand...

Are you kidding?? I have two more semesters, including Statistics! I hope you "suckers" will still be here for the people like me who are still trying to figure out the "new math" from many years back!

(Denis, I'm going to swipe that signature line! Priceless!)

NEXT HOMEWORK: y = mx + b as it applies to a utility bill. Hang on to your chapeaus....
 


redsoxnation said:
y = mx + b as it applies to a utility bill
Click to expand...

EG:

variable x represents the number of gallons of water consumed last month

constant m represents the rate per gallon (i.e., a fixed dollar amount)

constant b represents the base rate last month (i.e., the fixed-amount paid by everyone regardless of consumption)

variable y represents the total water bill for last month in dollars (as a function of x gallons consumed)



Within the City of Seattle proper, the residential water rate is currently 0.004839 dollars per gallon.

The monthly base rate is currently $13.

Hence, we have the following constants:

m = 0.004839

b = 13

The water meter indicates that I used 2,099.5 gallons of water last month.

x = 2099.5

My water bill for last month is y dollars, calculated by the formula mx + b.

y = $23.16

I hope that my example does not spoil any fun. 8-)

 
Thank you all for the baseball homework help; I scored a "100%" for the first time in this semester's math class.

Big exam this morning; open book, open note, open internet....stand by! mmm4444bot, your information will most definitely come in handy today! Many thanks!
 
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