### Question #27

Saturday, November 7, 2009
KEY (Legend)
RED - A question
BLUE - A key term (important to know)

HEY GUYS! Guess what? My math post is late .. UH-OH! Well, had a busy weekend, so going to do it right now. Well I got question #27 of Extend. Here is the question.

27. The mean of six rational numbers is -4.3.
a) What is the sum of the rational numbers?
b) If five of the numbers equal -4.5, what is the sixth number?

Since this is in the "Extend" section, it's something we haven't really looked at. Do you guys remember this? Measures of Central Tendency. Well we're looking at the term "mean", which some of you might remember basically means "average". The way to find the mean, would be to add up all of the data, and divide it by how many numbers there are.

a) To find the mean of -4.3, we need to find 6 numbers. Since it means average, wouldn't it be easy to have all the data the same number? We're trying to find 6 numbers with a mean of -4.3, so what if the data all equaled 4.3? Let's see. -4.3 (6) = ? Well simple, it equals -25.8! That's the answer to 27 a), and it will be used in question b).

b) If five of the numbers equal -4.5, what is the sixth number? Well, that's simple, or it should be. You have 5 numbers that equal -4.5, which means.. multiplication! The question would be -4.5 (5). Use a calculator, and you get the number -22.5.

This part is simple, remember the answer to question a) ? Well now, you have 5 numbers, and need 6. And remember, the sum has to equal -25.8 for the mean to be -4.3. Take your two answers from earlier and do simple subtraction. -25.8 -(-22.5) = ? Well you see, as Mr. Harbeck likes to put it, there is an "uh-oh" in the question. "owe 25.8 owe owe 22.5" Anyone rembember that? Anyways, to fix that, you just turn 22.5 into a positive and add it. Since -(- looks like + anyways. The question now turns into -25.8 + 22.5 = ? Simple enough, the answer would be -3.3. And that folks, would be the last number to your data set. Sum it all up and your data will look like this. -4.5, -4.5, -4.5, -4.5, -4.5, -3.3. That data would have a sum of -25.8 and a mean of -4.3.

a) Sum is -25.8
b) The sixth number would be -3.3

Anyways guys, hope you had fun reading my late post. Remember, that uh-oh subtraction thing is only a method to do it. You do not need to do that every time if the question is easy enough. Finish all of your questions 9-05! TEST ON MONDAY!

linda 9-05 said...

Nice post, Dean! I thought it was pretty cool how you had a legend thing there. It really helped simplify your post! Your explanations were easy to understand, and that's a definite plus! Great work!

Lissa 9-05 said...

GOOOOOD JOB DEEAN ! I like your pretty colours and your explanations are very well done. Well, I have nothing else to say, so keep up the good work and finish you work on time! (:

xtian 9-05 said...

Good job dean on putting colors and legends and stuff, keep up the good work!