Standard Deviation on a Calculator

Hey y'all --

So in 5th period we looked at how to calculate standard deviation on a calculator. This video is really helpful and walks you through the process step by step.

Incidentally, you end up finding Std Dev, Variance, Q1, Med, Q3, Mean, Min, and the Max so this is REALLY helpful.

https://www.youtube.com/watch?v=DMOXzwC2vzg

Enjoy!

Madison

Bad Surveying in The Fourth Grade

At the Friends School, where I attended pre, elementary, and middle school, there were annual science fairs. When I was in the 4^th grade I did an experiment to find out if organic flowers smelt better then non-organic flowers. I bought some flowers that were not organic and then took some organic flowers that had been sitting on the windowsill. I blindfolded the people who I surveyed, and let them smell each. My hypothesis was that the organic ones would smell better, and it was confirmed.

I remember surveying my dad first. After I gave him the non-organic ones and then gave him the organic flowers I introduced the organic flowers with a great amount of lavish: “now smell this one!” After that my mom told me that if I introduced either flower differently I might influence the answers of the people being surveyed. In other words, my asking the question in such a way that implicitly favored one of the answers introduced bias into the survey.

There were also several other problems with the survey, some of which I knew at the time, others I didn’t. One problem, which my mom had also mentioned to me at the time (she said that if I included this in my final project my teachers would be impressed) was that the sample size was relatively small and—she didn’t word it like this—that my results were therefore not statistically significant.

Another problem with my survey is that there may have been confounding variables as the organic flower had been grown at home and I didn’t know much about the store-bought non-organic flowers.

Unit 3 Test Review Sheet Chapters 23, 5, and 6

Disclaimer:  This review sheet does not cover everything you should know.  It's just a helpful guide of some of the problems you might see.  To ensure complete preparation you should be reviewing your in class and out of class notes, as well as, your previous quizzes and tests.

Chapter 23

1.A report by MM Shaheen, a member of the Parliament of the Peoples' Republic of Bangladesh, reported the population in 2002 to be approximately 110 million with a 1.8% annual growth rate. What is the anticipated population in 2006?

2. In the U.S. Department of Energy's (DOE) Energy Information Administration's (EIA) International Energy Outlook 2002, it was estimated that the United States had a 60-year supply of recoverable natural gas. Approximately how long will the supply last if the total demand for natural gas increases at an average rate of 1.8% ? 

3. Attorney Gianetti retired with $2 million in a non interest-bearing savings account. The attorney figured that it would cost him $80,000 per year to live at his current standard of living. Assuming a constant 3.5% per year inflation rate, how long will his savings last?

4.  Name a few nonrenewable resources.

Chapter 5

5.  A Fast Food Company was interested in knowing whether their customers were satisfied with the overall service and cleanliness of the Company's franchises. In an effort to obtain this information, The Fast Food Company randomly selected 75 of the 325 customers from one of their 25 franchise stores to fill out a survey.  What is the sample in this situation?

6. On the final episode of the popular "Dancing with the Stars" show, viewers were asked to call in and vote for their favorite star. This is an example of what type of sampling?

7.  In an effort to determine why contract negations broke down resulting in a devastating long term strike, management formed a task force to randomly select and interview 50 of the 825 employees. The three-digit employee ID and Table 7.1 from your text was used to identify which of the employees were interviewed. Lines 106-109 of Table 7.1 are reproduced below. What would be the ID numbers of the first 15 employees selected?



8.  What do random samples seek to eliminate?

9.  A researcher administers a new migraine headache medication to a group of volunteers in order to observe whether the medication abated the intensity of headache. This is an example of what type of survey?

10.  Suppose 65% of all college students find studying for final exams a waste of time. The population proportion is p = 0.65. Suppose many different simple random samples of 3,000 college students were taken. What would be the mean of the sampling distribution?

11.  The CDC took a random sample of 530 people that lived near high voltage towers. Of these people, they found that 345 developed some form of cancer. Give a 95% confidence statement for the proportion p of all people who live near high voltage towers and develop cancer.

Chapter 6

Thanks to Marc K.

1. What are individuals? What are variables? How are they related?
2. What is distribution and how is it shown in a histogram?
3. What can be used to describe the overall pattern of a histogram?
4. What is an outlier and how does it differ from deviation?
5. How do you make a stemplot and how is it useful?
6. How do you find the mean of a set of data, and how does it differ from the median? Which might be a more accurate representation of the center of the data and why?
7. What are the 5 numbers of a 5 number summary?
8. How is a boxplot made? Why is it useful?
9. What do histograms show that boxplots do not?
10. What is the explanatory variable? What is the response variable?
11. What is a scatterplot? Why are these used?
12. How do you describe the overall pattern of a scatterplot?
13. What are outliers and how do they effect the line of best fit, median, mean, and quartiles?
14. What is a regression line? Why do outliers effect it?
15. What is correlation? What causes a lower correlation? A higher correlation? What is the highest possible correlation?
16. What is a least squares regression line?

Important Terms to Know Review:

Chapter 23

Nonrenewable resources
Renewable resources
Static reserve*
Exponential reserve
Population
Growth rate
Maximum sustainable yield **
Reproduction curve

Chapter 5
--Producing data--

Population
Sample
Simple random sample
Types of samples
-Bad samples
-Good samples
Margin of error
Experiments
Observational studies

Chapter 6

Histograms
5-number summary
Mean
Median
Correlation
Association
Box plot
Stem plot
Scatter plot
Standard deviation
Variance
Smoothing
Outliers and their impact on Mean, Median, and Regressions
Regression
Least Squares Line

Kenan Scribe - Box Plots

A box plot by definition is a graphical way of depicting numerical values through their five number summaries. So what does this mean? Let's say for example that I were to hand you 9 balls, each with a random number written on the sides. A box plot would be an easy way to show a bit about the numbers you have received in a neat graphical form.

Five number summaries: Every box plot consists of five unique points, the minimum, the first quartile, the median (or second quartile), the third quartile, and the maximum. After arranging the numbers you receive from smallest to largest you can then begin to decide which numbers are what.

The minimum is simply the smallest number in the data set.

The median is the number directly in the middle of the series. If there are an odd number of numbers then you will not be able to select one single number in the middle. You will take the middle two, add them together and divide the sum by 2, thus finding this average (or the median). This will be the median of your data set.

The maximum is the largest number in your data set, the opposite of the minimum.

The two quartiles are slightly more tricky, but still very simple to find. For the first quartile, look to all the numbers to the left of the median. Find the median of this new data set and you will have your first quartile for all of your numbers. This works inversely with the third quartile. Look to the right of the median, find the median of these numbers and you will have your third quartile. But why do you go from the first directly to third quartile you ask You want to know where the second quartile is? Well, if the data set is to be broken into quarters, there will be four parts of it. A quarter is a fourth. The second quartile will be the number directly in the middle, so we have already found it. The second quartile is the median!

REMEMBER! Box plots must always be drawn along a number line!

Let's look at a box plot, shall we?

These are three very simple horizontal box plots. As you can see, there appears to be lines coming from the box shape we had all assumed would be the graph. These are known as whiskers. At the far left end lies the minimum of the data, at the far right, the maximum. The box starts on the left on the first quartile. The box ends on the third quartile and the whisker that leads to the maximum begins. The median is the line down the middle of the box plot.

Here is a data set of 7 random numbers I just thought of. I have put them in order for you already.

2, 4, 5, 9, 13, 16, 17.

What is the minimum?

What is Q1? (first quartile)

What is the median?

What is Q3? (third quartile)

What is the maximum?

Minimum: 2

Q1: 4

Median: 9

Q3: 16

Maximum: 17

If you were to make this into a box plot, what would it look like?

Sadly, I can't draw a box plot in computer speak so I'm going to tell you what it would look like. The box plot would be set on a number line from 0 to 20, just because that would look nice and encompass all the numbers in our data set. The left whisker would begin at 2 and then continue until the side of the box began at 4. The box would end at 16. There will be a line through the box at 9 to denote the median. The right whisker will begin from the side of the box and go until 17. This is a fairly jacked up box plot but that's what happens when I make up a bunch of random numbers. Box plots are an easy and informative way to collect vital data on an otherwise overwhelming set of numbers.

Madison Scribe Post 11/14

Histograms and Stemplots

Yesterday in class we started discussing Histograms and Stemplots.

Histograms

Histograms display the frequency of a variable.

The x-axis of a histogram displays the amount of variables. Histograms use bins to group data on an x-axis.

In this case, our individuals (or objects that are being described in a data set) are the black cherry trees. This histogram is looking at the height of the cherry trees, otherwise known as a variable, or

a characteristic of an individual.

Instead of having a bar graph, where each individual gets a bar like the graph below, histograms

group the individuals into categories. For example, black cherry trees with heights of 61ft, 62ft and 64ft would be grouped in the "60-64.9ft" bin on the graph.

EXAMPLE OF A BAR GRAPH:

We use bins because we can fit more data onto a histogram that way. If we created a bar graph of the heights of cherry trees it would need an enormous x-axis to fit all of our data.

The y-axis of a histogram represents the frequency of the variables.

So back to our cherry tree example, if you look at the graph, there were 10 cherry trees that were between 75-79.9 feet tall. It's pretty straightforward.

We then looked at the shape of a histogram.

If the histogram has a symmetric "hill" (5th period whaddup) the data is awesome, and nothing

seems to be wrong with it.

If the histogram has a

longer tail of information to the right, then the data is skewed to the right.

If the histogram has a longer tail of information to the left, the data is skewed to the left.

and finally...Outliers are distinct measurements that are separated from the rest of the data.

I found a website that lets you practice creating a histogram, for those of you still confused. Enjoy!

http://www.mathsisfun.com/definitions/frequency-histogram.html

Stemplots

- make data easily presentable

- make plotting decimals easier

- you can display the exact measurement of each individual

A stemplot has two sections called the stem and leaves instead of a y-axis and x-axis.

To read this graph you would read 3|9 as 39 points were scored in a game.

4|0 1 5 7 7 7 9 reads as 40, 41 45... etc.

When making a stemplot the stems must be arranged vertically by numerical order from smallest to largest and the leaves must be arranged horizontally in order from smallest to largest in each stem category.

Leaves can ONLY BE ONE DIGIT. So if you wanted to represent a number like 356 you would make you stem 35 and your leaf 6. It would end up looking like this: 35|6

We also discussed finding the mean and median for the stemplots.

To find the mean (or average) all all of the individuals up and divide by the # of individuals.

We used the symbol of x̄ to represent the mean. The Σ (sigma) means "the sum of"

x̄ =(1/n)Σ

or basically: mean= (x1+x2+x3...)/(n)

The median is represented as m=(n+1)/(2) or the total number of individuals plus one, divide by two.

When you're finding the median on a stemplot you take the total number of individuals on a stemplot (if we're using the above stemplot that's 12) and apply it to the formula getting us the number 6.5. That is not our median. To find our actual median, we have to find individuals 6 and 7 on our stemplot. So on our graph above individual six has a value of 47, and individual seven also has a value of 47. Now we take the average of those two numbers, which ends up also being 47, and now you have the actual median.

It's a bit confusing, I know. But here's a link for extra clarification!

http://mathforum.org/library/drmath/view/52813.html

That's the gist of what we learned yesterday. It's a bit long, but hopefully it helps. Can't wait for Kenan's amazing scribe post....

Madison

P.s. I don't know why some of my words hilighted....sorry...!

Histogram Help

For those of you needing help on making histograms in Microsoft Excel I found a really handy website that explains a step by step process on how to make a histogram.

Click Here for the website!

Helpful tips:

You don't need to place your bins next to the values that they represent in your data. I find that confusing. You can place your bins anywhere in the spreadsheet.

When actually selecting your options for the histogram, ignore the output range. You don't need it. Nor do you need the "pareto" option nor the "cumulative percentage" option.

Make sure you check "Chart Output" or else you won't actually get a physical histogram.

Your histogram might pop up in a new page in excel. I freaked out because I thought all of my data had been erased because of that. If it happens to you, just know it's still there.

Finally...

I'm the scribe for tonight but I accidentally left my notes at school. So I'll be getting that up tomorrow. But just to keep this going, tomorrow's scribe is Kenan!!! (YAY)

Happy histograming!

Histograms & Stem Plot Assignment

Do and share on googledocs with your name and the title.

Create a Histogram that explores information that interests you.

Create a Stem Plot that explores information that interests you.

Categorize the data, if its too time consuming to explore it all.

Answer the following questions concerning both your histogram and stem plot.

What is the mean of the data?

What is the median of the data?

For each plot state the distribution (skewed left, skewed right, symmetric)?

Is there a statement you would like to make about your data?  What did you find to be true or common about the data that you have explored?

Sir Ronald A. Fisher

Throughout Sir Ronald’s life he broke many new mathematical frontiers. He invented systematic mathematical theories and improved on the ones that were already in place. Fisher had a happy childhood in East Finchley, London England, the youngest of several brothers and sisters. He avidly studied in school, constantly striving to gain more knowledge of the scientific and mathematical worlds. Fisher possessed special abilities in mathematics due to his poor eyesight that both helped and hindered him. Throughout school, because of his inability to see clearly, Fisher intensely studied math without the use of pen or paper. Fisher never practiced the discipline of writing out his steps or writing proofs, which would hinder his communication with other mathematicians in the future, but learning this way it enabled him to view math and it’s relationship to the physical world in a different way than his peers.
Throughout his academic career Fisher astounded his teachers and classmates with his intelligence and innovation. Fisher was eager to join the army and head into WWI but because of his poor eyesight he was not allowed to join, and forced to stay home where he was able to focus on his studies. Unfortunately, Fisher had a heavy interest in eugenics, which was spurred by his interest in Mendelion theories of genetics. Fisher headed many clubs on the study and though the word has poor connotations, he did not see it as a philosophy to be applied to humans but rather to plant populations. His was interested in the randomness of the genetic make-ups and phenotypic natures of plants grown under different conditions/ factors. Using agricultural studies, Ronald Fisher developed new techniques that won him the title of the “Father of Statistical Math’s”. In relationship to what we will learn in class, Ronald A. Fishers invention of randomized testing techniques are his most important development.

Throughout Sir Ronald’s life he broke many new mathematical frontiers. He invented systematic mathematical theories and improved on the ones that were already in place. Fisher had a happy childhood in East Finchley, London England, the youngest of several brothers and sisters. He avidly studied in school, constantly striving to gain more knowledge of the scientific and mathematical worlds. Fisher possessed special abilities in mathematics due to his poor eyesight that both helped and hindered him. Throughout school, because of his inability to see clearly, Fisher intensely studied math without the use of pen or paper. Fisher never practiced the discipline of writing out his steps or writing proofs, which would hinder his communication with other mathematicians in the future, but learning this way it enabled him to view math and it’s relationship to the physical world in a different way than his peers.
In his academic career Fisher astounded his teachers and classmates with his intelligence and innovation. Fisher was eager to join the army and head into WWI but because of his poor eyesight he was not allowed to join, and forced to stay home where he was able to focus on his studies. Unfortunately, Fisher had a heavy interest in eugenics, which was spurred by his interest in Mendelion theories of genetics. Fisher headed many clubs on the study and though the word has poor connotations, he did not see it as a philosophy to be applied to humans but rather to plant populations. His was interested in the randomness of the genetic make-ups and phenotypic natures of plants grown under different conditions/ factors. Using agricultural studies, Ronald Fisher developed new techniques that won him the title of the “Father of Statistical Math’s”. In relationship to what we will learn in class, Ronald A. Fishers invention of randomized testing techniques are his most important development.

Scribe Post 11/9/11 by Carly

Today in class, we went over sections 5.5 Estimation and 5.6 Randomized Comparative Experiments. We learned that experiments study the response to a stimulus, to see how one variable affects another when we change existing conditions.

The two different studies we learned about were observational studies and experiment studies. Observational studies observe individuals and measure variables of interest but do not attempt to influence the

responses. The purpose of observational studies are to describe some group or situation, for example, a sample survey.

Experiment studies deliberately impose treatment on individuals in order to observe

their responses. The purpose of experiments are to study whether the treatment causes a change in the response.

Types of Experiments:

An uncontrolled experiment is an experiment where different variables may impact the experiment. For example, suppose two different groups of people, people who took online SAT classes rather than in-class SAT classes, and the experiment concluded that the people who took the online SAT classes did better on the SAT than those who took the in-class SAT classes. This is an uncontrolled experiment because many factors could impact the outcome of t

his experiment, for example, the people who took

online SAT classes could have been older, more experienced people who may have already taken the SAT, and the people who took the in-class SAT classes could have been younger people in high school. This would be a bias experiment, and not accurate.

A Randomized Comparative Experiment strives to get rid of the bias by randomizing which stimulus to apply to certain groups. For example, say we randomly took all of the people who intended to take the SAT classes (online and in-class) and mixed them up into the two classes, without knowing whether they would have originally taken the online classes or the in-class classes. This would make the experiment more accurate, because there would be no bias to this.

A control group in an experiment is the group that nothing is done to. The control is left alone so that the other variables may be compared to it. The control is the variable that is usually the "normal" result and that which you are testing against. For example, say we were testing whether the temperature has an effect on the breaking point of rubber bands. We took one rubber band and put it in the freezer, another rubber band and heated it, and left another rubber band at room temperature. The room temperature rubber band would be t

he control in the experiment, because it is the one that was not affected by any variables. This is also another example of an uncontrolled experiment, because different factors could have affected the out come of this experiment.

The last experiment we talked about was a Double Blind Experiment. This is an experiment where one does not know the difference between the stimulus and the control. For example, say a double-blind experiment was performed at a barbecue,

and Bob is trying to see how many people prefer Texas Pete over his own home made hot sauce. He gets his friend Billy to randomly put the hot sauces in two different bowls, labeling them A and B. Bob then takes the bowls and asks people which they prefer, and records the results. At the end of the experiment, Billy

tells Bob which hot sauce went in which bowl, and people ended up liking Texas Pete better. Poor Bob. This was a double blind experiment because Bob did not know which hot sauce was his, therefore he could not persuade the people in any way.

A good explanation of a double blind experiment is in the video below which we watched today, called "Scientific Method: How Double Blind Clinical Trials Are Done"

Next scribe is Farlz :) (Madison)

Collecting Data;Bad Sampling

my video

http://www.youtube.com/watch?v=ZmxvRrMcLd8

PRODUCING DATA ASSIGNMENT #1 3rd Period Only

1.)  An opinion poll on the ipad/iphone polled 5,249 persons and asks them, "Will the Occupy Wall Street protests end peacefully?"  In all, 2520 of the 5249 say "yes." What is the sample in this setting?

2.) Describe what a simple random sample means.

3.) You must choose 10 teachers of the total teacher population at Paideia.  How would you label this population in order to use Table 5.1 in your book.  (Note:  You need to figure out how many teachers there are at Paideia)

4.)  Show of Hands Poll asked 501 teenagers whether they approved of legal gambling: 52% said they did. Use the quick method to estimate the margin of error for conclusions about all teenagers. (Note: Discription of this method can be found online or in your book)

Myths About Our Water Supply

For whatever bizarre reason, a large demographic of the world's population seems to think that we are "running out of water." I know several members of this demographic. This misunderstanding is not the fault of the believer, but rather the fault of a few myths in circulation. 

One of these myths is that by using water, you destroy it. While reading that, you'll probably think, "Well, of course that isn't true!" But the fact remains: There are quite a few who don't think about it enough to realize the falsehood. Taking a shower, for example, does not spontaneously split water molecules, nor does the water you used become waste. All the water you use in your plumbing is sent to a filtration plant and spat right back of your tap. So trying to calculate when we will run out of water based on how much you used in your shower just won't work, meaning you can't use the Renewable or the Non-Renewable Resource formulas.

Another popular myth is that the planet is drying up, and that's simply wrong. Water is the most sustainable resource around, because the act of using it is the beginning of the process that renews it. When water is used in plumbing, as said before, it's just put through filtration and used again for something else. When water is used elsewhere, it either sinks into the ground and evaporates, or flows to a body of water and evaporates, before it all gets dumped right back on your head. The largest source of freshwater is rainfall, and about 3 quadrillion gallons of the stuff falls to Earth every year.

So, the trouble is not a lack of water. The problem is getting all that water to the right places, because rain doesn't fall evenly across the globe. With all that said, though, it is clear that we aren't running out of water by using it, so we can't use the Non-Renewable or the Renewable Resource equations. 

In fact, if we were to put this in mathematical terms, the only thing we could confidently say is that if you use an amount of water a, received from the source of the water b, you've done this:

(b - a) + a = b

MAGIC WATER.

From: Chris

Picture

SCRIBE POST OCTOBER 18

This post covers everything we learned on October 18th on sections 23.3-.4

We started class off by watching this video:

This video relates to the equation for exponential reserve: n=(ln(1+(S/U)r))/(ln(1+r)).

In class we also clarified when to used the static reserve formula and when to use the exponential reserve formula. The difference is that the exponential reserve formula takes into account a growing rate of consumption whereas the static equation does not.

Renewable Resource: "any natural resource (as wood or solar energy) that can be replenished naturally with the passage of time."

Non-Renewable Resource: "any natural resource from Earth that exists in limited supply and cannot be replaced. "

Funny Wolfram Alpha Comic

Enjoy!

#ScribePost Luke 23.1-23.3

Sorry about the lateness of this scribe post; it totally slipped my mind over fall break so my bad.

I’ll be covering the class from Tuesday (10/11) and the class from today (10/17) in this Scribe Post.

Tuesday (10/11)-

We started off today by watching a few YouTube videos, one of which we had already watched at the beginning of the year in class.

1. “7 Billion, National Geographic Magazine” was the first one that we watched. This video is all about modeling human population growth exponentially and the threats of over-population to our planet.

Here is the URL: http://www.youtube.com/watch?v=sc4HxPxNrZ0

2. The next video that we watched, “7 Billion People: Everyone Relax!” was a video response to the previous one which argued that human population growth is in fact best modeled after a linear, not exponential, growth rate and that our populations rapid increase is really not that much of a problem because we will reach a carrying capacity, go down, and then be back at 7 billion in 75 years. So, essentially, everything’s fine, everyone chill out. Here is the URL: http://www.youtube.com/watch?v=iodJ0OOdgRg
3. The third video, “Distilled Demographics: Deciphering Population Pyramids,” dealt with population pyramids, obviously. I think that Jojo just turned the sound down and spoke over this video. I had a little trouble finding the video online because all I had in my notes was “Population Pyramid,” so I’m not certain if this is the right video, but I believe so. Here is the URL: http://www.youtube.com/watch?v=sSoSYm4AOls

We didn’t just watch videos in class, we also started in on chapter 23. Here are my notes from that part of class:

Chapter 23.1-

• This formula is used to model population growth: A = P(1+r)^n
• Population growth is an exponential, as opposed to a linear growth rate
• r=rate of natural increase = birth rate / death rate
• P = population
• M = carrying capacity
• Growth rate = r(1-(P/M))
• When solving A = P(1+r)^n r=growth rate not the r that equals the rate of natural increase

We also did some classwork and here is that:

Page 849 Questions: #3 & 5

3. 1.7% = r = .017 25 = n 3,617,000,000=P

P(r+1)^n = 5,595,104,568

5. 818,000,000 = P n = 24 r = .024

P(r+1)^n = 1,284,497,816

Today, Monday (10/17)-

Today we went further into chapter 23, clarifying some confusion to do with the Growth Rate. To clarify any conclusion:

Growth Rate = r(1-(P/M))

If you’re confused about the variables in this equation, see the notes from 23.1 from the previous section of this Scribe Post.

We spent most of class today dealing with Chapter 23.3, here are my notes:

23.3: Nonrenewable Resources

• Nonrenewable resources are resources that cannot be renewed (I know, shocking, but try to bear with me)
• The usage of non-renewable resources can be modeled through this formula:
• A=d(((1+i)^(n)-1)/i))
• The static reserve is the time the resource will last with a constant rate of use.
• Supply / Use à S/U
• The exponential reserve is the time that resource will last given constant use that increases geometrically with the population.
• S=supply, U=Use, r=rate of usage, n=exponential reserve à n=(ln(1+(S/U)r))/(ln(1+r))

The next scribe is Kenan!

Kenan is out of the country and so if he is not back by tomorrow's class the next scribe will be Sarah!

Open Study

I was pretty bored today and was on stumbleupon which brought me to this site:
http://openstudy.com/
If nobody in the class is online when you need math help, there are a lot of people on this site that have questions and answers. I thought it looked pretty cool.
It also helps with science, writing, history and other things.

Twitter!

Hey Y'all-

Just a reminder to tweet tonight about formulas for the test tomorrow. Jojo was nice enough to give us formulas on our quiz and we can have that same advantage if we tweet and print out our formulas!

If y'all can't remember what to do/you never learned:

-tweet formulas, helpful hints, maybe what the formulas are USED for, etc and use the hashtag #discretemath12 (That way we can find each others tweets easily!)

-Favorite the tweets you want to use by clicking on the star when you highlight the tweets

-You can then print out your tweets by either taking a screenshot or some browsers you can print straight from the web. Either way, I don't think we're allowed to make it more than a page long.

Hope this all helps!! Happy tweeting and good luck on the test tomorrow!

Chapter 22 Test Review Sheet

Link For Solutions
  
Able to edit with link now ...8:54pm  Sorry

1.  Sun National Bank of New Jersey is offering a 4.75% fixed discounted student loan to be repaid in monthly installments over the course of 4 years. You expect that you will need a total of $100,000 for your educational expenses. How much should you borrow (round your answer to the nearest whole dollar)? 

2.  Fred wanted to watch the Super Bowl in style, so he charged a $4,999.99 50-inch widescreen plasma HDTV with a built-in digital video recorder to his Sam's Club credit card. The company charges 0.93% interest per month. If Fred made no payment for one year and just let the balance ride, how much interest would he have accrued in the first year (round your answer to the nearest whole dollar)?

3. An Illinois criminal justice professor found eight times as many gambling addicts among college students as among adults. Ignoring the warnings of this professor, Erik, a college junior, went to the Argosy's Alton Belle Casino. Unfortunately, Erik's personality was such that he became addicted. Within the month, Erik had already borrowed $7,500 to support his habit. A judge gave Erik 4 months to find a job and pay off his debt. Assuming Erik deposited each monthly paycheck into an account that paid 2.65% interest per year, how much would Erik need to deposit each month to comply with the judge's order (round your answer to the nearest whole dollar)?

4. Home Savings and Loan of Ohio offers a 15-year fixed home mortgage rate of 4.15% compounded monthly. You borrow $130,000 to build your dream home. How much interest will you have paid on the loan at the end of 15 years (round your answer to the nearest whole dollar)? 

5. Suppose that you have borrowed $800 from your older brother to purchase textbooks for the new term. Your brother agreed to lend you the money provided that you pay him within 20 weeks at a rate of 1.2% interest per week. How much are your weekly payments?


6. You have decided to purchase a used 2005 Porsche 911 Carrera two door coupe with a gray leather interior and manual transmission from Valley M Motors, Inc., for $63,950. Yahoo! Finance is offering a 36-month loan at 4.12% interest compounded monthly for the state of Ohio. What is your monthly payment (round your answer to the nearest whole dollar)?

7. Which type of rate takes into account monthly compounding?
 
8. Gerard and his fiancée are looking for a $150,000 home. They find a bank that is offering a 30-year 4.03% fixed mortgage rate provided they make a down payment of 20%. Gerard and his fiancée bring home a combined weekly amount, after deductions, of $880.51. Which statement best describes how Gerard and his fiancée can afford to buy this home?
 A. They can make the monthly payments with sufficient money left over for necessities.
 B. They can make the monthly payments but will have little money left for necessities.
 C. Between the two incomes, they cannot meet the monthly payment.

9. Sam and Connie built their home in 1984 for $110,000. At that time, they had a 30-year mortgage at an 8.5% fixed interest rate. Sam and Connie sold their home in 2005 exactly 21 years after it was built. How much equity did they have in the loan?


10.  Let's assume that in question 9, along with paying down their initial loan of $110,000 from the bank, their home's value appreciated to $202,400 by the time they decide to sell in 2005.  How much equity did they have in the home?


11. James, a college professor, is retiring at 65 with $507,845.43 in his STRS life income annuity. The STRS retirement specialist told James that he will receive $15 per month for every $1,000. According to the Social Security Administration, ones life expectancy at age 65 is about 16.6 years. If James lives exactly that long, how much (total) can he expect to receive?

Discrete Math Test -BoB

Blogging on Blogging -Reflections -BoB Chapter 22

There is a BIG difference between learning and just being there. Learning is an interactive sport; not a spectator sport. There has to be a conversation between us, back and forth, as we work through the material. Learning doesn't happen when I talk and you listen; learning happens when you have a conversation -- with me and with each other.

I am going to offer you up to 5 bonus points on your test with completion of a simple assignment.  I would like you to post your reflections on the material covered so far in chapter 22.  Just comment on this post by the start of class tomorrow.  To get that bonus on your test, the kind of post I'd like you to make should have one or more of these characteristics:

• A reflection on a particular class (like the first paragraph above-how did that class enhance your learning?).
• A reflective comment on your progress in the course.
• A comment on something that you've learned that you thought was "cool".
• A comment about something that you found very hard to understand but now you get it! Describe what sparked that "moment of clarity" and what it felt like.
• Have you come across something we discussed in class out there in the "real world" or another class? Describe the connection you made.

Millionaire's Son Wins $107 Million Jackpot - Sacramento News Story - KCRA Sacramento

Millionaire's Son Wins $107 Million Jackpot - Sacramento News Story - KCRA Sacramento

Read page 810-811 in your book for an explanation of how annuities work.

Let's assume this guy chose the annuity instead of the lump sum.  Based on the 107 million dollars he was promised, what would be this guy's annual payments (before taxes) be if he were to receive equal  payments for 25 year installments rather than a lump sum?

Based on ordinary annuity principles, what would be the present value of the annuity after one payment was made?

Let's assume the in the annuity situation, instead of the lotto administration buying an annuity, the State buys U.S. securities paying an interest rate 7%.  How much would the winner have received in cash instead of the original $107 million jackpot?

Discrete Math Borrowing Assignment

Please use the following link to complete the assignment.  This assignment should be done on Googledocs with a partner. Just make statements about what you did and found out for each number in the assignment.  Title the borrowing document:  Name Borrowing Assignment

https://docs.google.com/leaf?id=0BzAgKqsf1_OcODg0ODNmYmYtMTQ2My00MzUzLTljYzEtNTYwNDY4OGEwZGY3&hl=en_US

Home Mortgage Assignment

Due 10/3

Visit the link below for questions.  Create your own googledoc titled Name Home Mortgage Assignment and share with paideiamath.  Good Luck.



https://docs.google.com/document/d/1SF_4r8ipqjXlOs-3di8Cy3vNcXhHxNdPR4ldFEG9JF0/edit?hl=en_US

Scribe Post - 22.1-22.4

*This Scribe Post covers everything we learned last week (Sept 16th - 21st)


22.1

Bonds:
- Bonds always pay simple interest! A=P(1-rt)
- The Principal plus Interest is paid at the end of the maturity of the bond
*All risk goes to the buyer
- Inflation? Will the bond issuer be able to pay?

Need help understanding bonds? Check out this video!!




Add-On Loans:
- What is an Add-On loan?
An Add-On loan is a loan in which you, the borrower, pays back the Principal amount plus the Interest over a fixed period of time.
- Always use Simple Interest when working with add on loans!
- Formula for Add on Loans:
d = P(1+rt)/n
d = payment per interval

Discounted Loans:
- What is a Discounted loan?
A Discounted loan is a loan in which you, the borrower, pay interest upfront, and then eventually pay back the principal over time. In other words, I may want to borrow $100 with 6% interest; the lender would only hand me $94, which I would pay back over time ($94 = 6% of $100). Since I paid my interest up front ($6) I only receive the remaining principal ($94).
- Always use Simple Interest when working with Discounted Loans!
- To find the discounted loan:
1) find interest added onto original Principal
2) subtract interest from original Principal
= this will give you how much you are "handed" the day you get the loan
3) then divide this number by the number of payments you will be making


22.2 - 22.3

Credit Card Payments:
- Always use Compound Interest when working with Credit Card Payments
A = (P+i)^n
- Also know Savings Formula when working with Credit Card Payments
A = d[((1+i)^n-1) / n]


22.4

Amortizing:
- Formula:
A = d[ (1-(1+i)^-n) / n]
This formula is used when you need to find out how much to pay at each interval for a house that costs $x with y% interest over z years.

How to find APY:
- APY = i(n)
i = rate per compounding period
n = number of times compounded


Things to know:
- The definition of "bond"
- Simple Interest Formula & how and where to apply it
- Compound Interest formula & how and where to apply it
- The definition of "Add-On loan"
- The definition of "Discounted loan"
- The formula for amortizing (loan on a house)
- How to find APY

How To Solve For d, Payments Per Interval in Loan Amortization

Today in class we worked our way through using of a couple of familiar equations to derive the conventional loan payment equation. 

If we replace (P), the principal, on a loan with (A), the present value of an annuity or amount being amortized, then we know

A(1+i)^n = d [((1+i)^n - 1)/i]      which after algebra reflects   A = d[(1-(1+i)^-n)/i]

If you continue with algebra operations to solve for d using the above equation you get

d = Ai/(1-(1+i)^-n)

Discounted Loan help

this is for anyone who was still a little confused as to what a discounted loan is.

http://www.investorglossary.com/discount-loan.htm

Test Aftermath Instructions

Reflect on your performance mathematically (do not talk about non-math related things like sleep, breakfast, or study skills). Talk about math!


(1 point)
1. Offer specific examples of some areas you did well on the test (use math terms to describe, not numbers of problems from the test.)


(2 point)
2. Offer specific examples of some areas you did poorly on the test (use math terms to describe, not numbers of problems from the test.) Tell specifics about the problem that caught you up...(wording, computation, comprehension, etc.)


(3 points)
3. Select one problem you got wrong. Show me that you understand the problem by doing another problem like it correctly.  This can be one problem from the test, as long as I did not write the answer during corrections.  Please avoid correcting small errors.


(3 points)
4.    Select a topic that was NOT covered on the test, but was covered in class or the book. Show me you understand it by working a pr

Gil CPI Review

The Basic CPI (Consumer Price Index) formula is:

(New Price/Old Price)=(CPI New/CPI Old)

That is the simplest form of the equation. Another one is:

New Price=Old Price + (cpi of event A / cpi of event B)
This is useful when trying to find a different part of the equation.

Here is an Example Problem: Let's say that you own a TV, purchased in 2004. You purchase this fine piece of technology for $999.

Lets say that you want to sell it now, and the year is 2011. You want to know how much the tv would be worth now had you bought in 2011. Basically, you want to know how much money you really spent on it, by seeing how much money you spent in constant dollars.

To do this, you do: 999(ww5.922/188.9)= $1,109.87 which is how much you would have spent had you bought that tv this year.

So why not use Compound interest to find this?



The answer is, because compound interest is for constant growth, whereas inflation isn't constant. CPI gives nominal value rather than assuming.







I Choose You, Miranda (next scribe)!!!!

Eli: 21.9 CPI

Inflation fluctuates. It is very unstable, and changes very frequently. The government came up with a system to calculate the changes in value, called the CPI (consumer price index.) This is to figure out the cost of the necessities of living – food, clothes, cars, electronics, etc. This system allows us to compare dollars from one year to another, in a way that shows us the constant dollar. Ten dollars now does not mean the same exact thing as 5 dollars 10 years ago. What we learned in class is to calculate what an item or amount of money is worth in a certain number of years in today’s worth. The CPI allows us to calculate what values were in the past.

Cost Year A/Cost Year B = CPI Year A/CPI Year B. This is long version of the equation. The shorter version that most people use, and is most useful is this:

Recent Dollars = Old Dollars (CPI of recent year/CPI of old year)

The government has calculated the CPI rates for us, and we can see that in the early 1900s, the CPI was in the tens, and the CPI today is about 218. There was a dramatic increase.

The government bureau that created all of these numbers is the Labor Statistics Bureau.

Below is the table showing the CPI that the LSB came up with:

Year Annual Average Annual Percent Change (rate of inflation) 1913 9.9 1914 10.0 1.3% 1915 10.1 0.9% 1916 10.9 7.7% 1917 12.8 17.8% 1918 15.0 17.3% 1919 17.3 15.2% 1920 20.0 15.6% 1921 17.9 -10.9% 1922 16.8 -6.2% 1923 17.1 1.8% 1924 17.1 0.4% 1925 17.5 2.4% 1926 17.7 0.9% 1927 17.4 -1.9% 1928 17.2 -1.2% 1929 17.2 0.0% 1930 16.7 -2.7% 1931 15.2 -8.9% 1932 13.6 -10.3% 1933 12.9 -5.2% 1934 13.4 3.5% 1935 13.7 2.6% 1936 13.9 1.0% 1937 14.4 3.7% 1938 14.1 -2.0% 1939 13.9 -1.3% 1940 14.0 0.7% 1941 14.7 5.1% 1942 16.3 10.9% 1943 17.3 6.0% 1944 17.6 1.6% 1945 18.0 2.3% 1946 19.5 8.5% 1947 22.3 14.4% 1948 24.0 7.7% 1949 23.8 -1.0% 1950 24.1 1.1% 1951 26.0 7.9% 1952 26.6 2.3% 1953 26.8 0.8% 1954 26.9 0.4% 1955 26.8 -0.3% 1956 27.2 1.5% 1957 28.1 3.4% 1958 28.9 2.7% 1959 29.2 0.9% 1960 29.6 1.5% 1961 29.9 1.1% 1962 30.3 1.2% 1963 30.6 1.3% 1964 31.0 1.3% 1965 31.5 1.6% 1966 32.5 3.0% 1967 33.4 2.8% 1968 34.8 4.2% 1969 36.7 5.4% 1970 38.8 5.9% 1971 40.5 4.2% 1972 41.8 3.3% 1973 44.4 6.3% 1974 49.3 11.0% 1975 53.8 9.1% 1976 56.9 5.8% 1977 60.6 6.5% 1978 65.2 7.6% 1979 72.6 11.3% 1980 82.4 13.5% 1981 90.9 10.4% 1982 96.5 6.2% 1983 99.6 3.2% 1984 103.9 4.4% 1985 107.6 3.5% 1986 109.7 1.9% 1987 113.6 3.6% 1988 118.3 4.1% 1989 123.9 4.8% 1990 130.7 5.4% 1991 136.2 4.2% 1992 140.3 3.0% 1993 144.5 3.0% 1994 148.2 2.6% 1995 152.4 2.8% 1996 156.9 2.9% 1997 160.5 2.3% 1998 163.0 1.5% 1999 166.6 2.2% 2000 172.2 3.4% 2001 177.0 2.8% 2002 179.9 1.6% 2003 184.0 2.3% 2004 188.9 2.7% 2005 195.3 3.4% 2006 201.6 3.2% 2007 207.3 2.8% 2008 215.2 3.8% 2009 214.5 -0.3% 2010 218.1 1.6% 2011* 225.4 3.3%

Next scribe is Gil.