Statistics Reflection

This unit on statistics was pretty challenging for me and I’m pretty sure that it was pretty challenging for the rest of the class. I think that I have quite a grasp at what each command does, like the inversenorm, normalcdf, binocdf etc. But I think that for me to fully understand this unit, I would need about an extra week or two more to fully understand it. From our last class I think that I was finally able to talk to my other group members to clarify what I had problems with, and that was VERY helpful for me. In about two hours our math test will take place, and hopefully everyone is prepared! Good luck to everyone!

REFLECTION!

Statistics, well what can I say about statistics. It was a pretty long unit and it was hard to get a grasp of everything. But I read over the slides and got some help from some of my fellow classmates. I started to understand what was being asked and which functions I needed to use and which bits and pieces of information that was missing. I understand the majority of the functions and which each does now, the only thing I'm not to sure on is making a histogram. Tomorrow is the test, Good luck to everyone :D

Statistics Reflection

Well here we are, at the end of another unit.

And as one might expect, the trip here wasn't easy. For example, I'm still not clear on how to create a histogram. I know I have to put the data in List One, I know I use Zoom Stat in the 2nd Trace menu, and I know I have to select the bar-ed graph from the stat plot menu, and put L1 in the top section and L2 in the bottom section. Unfortunately for me, I haven't a clue what goes in L2. Furthermore, it doesn't appear to be in any of the slides. or any of the scribe posts. I checked more than once. Damnit.

Also, I missed the class on Confidence Intervals and Margins of Error. Thankfully, the process by which they are found is simple enough. Confidence Interval is merely 1.96 σ above and below the mean. Easily expressed as (µ-1.96σ, µ+1.96σ). Likewise, Margin of Error is calculate by (1.96σ)÷(# of trials). For instance, if you had 100 trials with a standard deviation of 10 and a mean of 50, you'd have a confidence interval of (50-1.96(10), 50+1.96(10)), or (30.4, 69.6). The margin of error would be 19.6÷100, or 0.196. Also known as 19.6%

the problem I had with these concepts is the meaning of "Confidence" in this context. My assumption was that if the data was within the confidence interval, I could be confident in the probability of that occurrence. Not so. In fact, all it says is that, were I to repeat the experiment, 19 times out of 20 I'd be likely to find 95% of the data lying between the aforementioned interval. To reuse my previous example, 19 times out of twenty, 95% of the data of an experiment which (when previously tested) resulted in the data µ=50, #trials=100, and σ=10 would lie between 30.4 and 69.6.

Reflection on Statistics

There had been a lot of complications about this unit. Today, I finally understood what each command does. We did a lot of calculations and analyzed datas. It was pretty confusing at first. Especially for those who does not pay attention. I find binomial distribution easier than normal distribution. The invNorm command still confuses me sometimes. I'm not sure when to shade right or left. Besides that, I think I understand most of it.

Tomorrow will be our Unit Test. Good luck to everyone.

Statistics Reflection

I thought that this unit on statistics to be a little challenging but not that hard. I understood what I was doing during the class and I got how to solve the problems. I think that this unit is a little better for me than the probability unit. 

In this unit I had a little trouble on how to do the histogram and that was basically it. I knew how to do everything else. There is a lot of things that you have to remember on the calculator but i guess you just have to understand the problem to know which calculator function to use. I have been doing all my homework, which was helping me understand and how to do the problems more. 

Hopefully I do well on the test tomorrow! (: 

Good luck everyone! 

Statistics Reflection

The Statistics Unit, was a hard but yet understandable unit. I was scared when I missed one class, which was yesterday, that I might of missed a lot of important things. But the day after that when I actually got to class in time, I understood what was given to us as a class. And I caught on quickly. The test might be a bit challenging for me as I do understand the unit, but I also get confused at times. I guess studying and looking into the problems deeper, and reviewing the slides that Mr. K puts up every night may help me. The unit was very hard for me to understand during the process of learning, but as we kept on solving problems, it came to me just like that. Hopefully I will do good on the test on Thursday!! Good luck to everyone!

Reflection

I found the statistics unit to be easier than the probability unit.
I didn't have any problems with the calculator commands. Ideas such as
Z-scores and finding the area between certain ones and what that represents I
found to be easy as well. The last part of the unit concerning the binomcdf and
binompdf functions I found to be a bit confusing at first. Also the confidence
interval I found confusing in the beginning as well. I am not as comfortable in
using those functions but hopefully I will do well on the test. 

Today's Slides: April 22

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Applied 40S April 22, 2009

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Niwatori-san's Reflection (Statistics unit)

Ah well Statistics it wasn't entirely hard but not entirely easy... Just following the Concept of changing from a probability to an area was confusing if a person was to look and normal distribution. Anywho I'm fine with the details of the unit by now being some more practice should spruce up any minor areas where I don`t feel confident about where sources of error may occur at a high percentage if I don't be careful >_<

People for words of encouragement...

'' Pay yourself some worth rather something fancy ''

Statistics Reflection

The statistics unit is a rather very long unit. I found most of the things easy to under stand,but after we finished learning about the normal curve and how it is distributed, we learned about binomial distribution. Binomial distribution is what i found the hardest to understand and grasp. I do not think it was the concept that was hard, but how the problems are worded. The problems are worded with lots of "math words" that often confuse me. It has always been difficult for me to get the important info out of a math word problem, but other than that it pretty much all makes sense to me.
Ooh and another thing a little hard to me is remembering what calculation to use to find each missing piece of info. For example:_finding the mean, s.d., the z-scores and now the confidence interval are tough to remember....... This divided by this times that, that minus this over those,yadayada.

Today's Slides: April 21

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Applied 40S April 21, 2009

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Today's Slides: April 20

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Applied 40S April 20, 2009

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Today's Notes

In today's note, we further our knowledge of Theoretical Binomial Distribution and learning how a mean is developed through Binomial Distribution. TBD is the method of estimating what the percentage of the outcomes would be before doing the experiment itself. On a graph, a TBD histogram would have a symmetrical look whilst the actual experiment has an assymmetrical look.

Example(s):






The method for finding the TBD that uses specific details is the same method as we have done in our Probability unit. Yet there is an easier way using our graphing caluclators. Through the use of the Binomial Probability Distrobution Function we could quickly identify the success chances for each and every outcome. To use it, go into your distribution menu and select binompdf. From there, input number of trials first, then the probability of success. If you wish, you could input an optional command and input the specific outcome, if you're only interested in one outcome. Though binompdf would not be the used if the problem asks for something more (or less).

Example(s):







In the case that it is not wise to use binompdf we would use binomcdf, or Binomial Cumulative Probability Distribution Function. To use it, binomcdf is right beneath binompdf. From there, it would be the same as we have done for binompdf. Except, that we add in the third value "- 1". We subtract 1 from the third option as it would add in an undesired value into the calculation. Binomcdf works similiarly like the invNorm function, so it would be wise to subtract from 1 sometimes.

Example(s):




In addition to all of this, we have learned how the Binomial Distribution affects the mean. Each time the number of trials are increased (or decreased), the mean will always hop to different number, albeit it that looks the same. Though with each additional trials, a histogram would start to look like a Normal Curve. By increasing or decreasing the probability of success, the mean would also hop to a different number, moving the histogram horizontally on the scale.

Examples(s):

An example of this would be in this website:
http://www.math.uah.edu/stat/applets/binomialcoinexperiment.xhtml

Done for today, next scribe is Amanda or Eugene.

Today's Slides: April 17

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Applied 40S April 17, 2009

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PoP QuIz

Today we had a surprise quiz. After the surprise we got handed out a worksheet for homework. Everyone make sure you do it because tommorrow Mr.K will be calling people up to show how they did their answers on the board. I will do the first part of the first question with you incase some one is confused how to go about doing them still.



The Stanford-Binet IQ scores of Canadians are normally distributed with a mean of 100 and a standard deviation of 16. According to this test, what is the probability that a randomly selected Canadian will have the following IQs?



a) an IQ less than 100



First you have to find the z-score. Now remember to get the z-score you have to subtract the mean from the number your trying to find the z-score for. Then you divide by the standard deviation. So in this case it would look like...

99-100/16=-0.0625 . Why did i not use a 100 to subtract a 100? This is because the questions asks for a score less than a 100. After finding out the z-score you want to go to shadenorm here you would put in the area you want to find. In our problem here it would look like this...shadenorm(-5,-.0625). Then on your calculator you'd get an area which would be .475082 You then multiply by 100 to make it into a percent which turns out to be 47.5%



the next scribe is Jason

In today's class we started off by solving a problem together with our group about what we have been learning. After that we reviewed the TYPES OF DISTRIBUTION and learned about BINOMIAL DISTRIBUTION.

TYPES OF DISTRIBUTION
a.) UNIFORM DISTRIBUTION
: a distribution that has constant probability
: data may be discrete or continous.
*discrete data- can be represented by using only integers (eg number of people, number of cars, number or animals, etc...)
*continous data- can be represented using real numbers (eg height, weight, time etc...)
: Every outcome in the experiment is equally likely.
b.) NORMAL DISTRIBUTION
: data is contionous when certain experiments are carried out many, many times the probability graph of the data tend to be "bell-shaped" known as the NORMAL CURVE.
c.) BINOMIAL DISTRIBUTION
: one of the discrete probability distribution.
: It is used when there are exactly two mutually exclusive outcomes of a trial.
: These outcomes are appropriately labeled Success and Failure.

Here are the examples that we did in class...
How many girls are there in a family of four children



The experiment was done by flipping 4 coins (20 times). Each trial represented one family of four. The probabily for each outcome (0,1,2,3 girls...) was divided by 20 which is the total number of times the experiment was done for.

That's all we did for class today. Hope this helped some of y'all. :)

Amanda is the next scribe.

Today's Slides: April 14

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Applied 40S April 14, 2009

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Statistics

Hi everyone, are today's lesson is about the disscussion of the assignments.








for example:





Find the probability of getting a z-score less than 0.90 in a standard normal distribution.



-as we can see, the normal distribution is equal to 1 and the middle or the mean is 0.50. Like in fraction, 0.75 is about three fourth (3/4) in normal standard curve and it is approximately between the mean and in 1 standard deviation.




-in solving the the probability of getting a z-score less than 0.90 is:
normalcdf(-5,0.90) is equal to o.8159 or 0.82.

-by using a calculator, you simply first:
*the home screen must be cleared and press 2nd.
*then, hit the VARS
*next is press 2 to move in normalcdf(
*after that it will back to home screen with normalcdf( , and just add like normalcdf(-5,0.90).

NOTE: you must always put an closing brackets after you put the numbers.






another example is:

What is the z-score if the probability of getting less than this z-scroe is 0.65?
-in solving this question, we will use invNorm, because the question ask is not about the area compare to the first one.

*first, press 2nd
*then,hit the VARS key again just like the procedure in using normalcdf(
*next is, press 3
*after that, put the numbers like invNorm(0.65) is equal to 0.3853 or 0.39.



the last question would be is:


What is our assignment today?



guys sorry for being kind of late in blogging our lecture today, I hope you will correct me if i have mistakes.

Today's Slides: April 13

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Applied 40S April 13, 2009

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April 8th 2009

OK... so today we reviewed a few old concepts and started on some new ones.

FIRST things first...

That, my friends, is the "normal" bell curve. The curve pretty much everything everywhere falls into. But what does it show us exactly?

Lets take a peek at how its devided up...

OK... so between the red lines lies 68% of all data.
between the Green lines lies 95% of all data.
between the Yellow Lines lies 99.7% of all data.

Now what these sections show us is not JUST the % of data within each sections.
Between any two z-scores chosen along the axis of the curve we can find the are, the percentage AND a probability all in one.

On another point, remeber how befor we had to worry about window settings and clearing pictures ans so on jsut to find the ara between two z-scores? Well frett no more. Mr.K showed us the quick-fast way to do it. Get your calculators ready...

STEPS :
-ON
-2nd
-VARS
-2
You will then on your home screen see somthing that looks like "normalcdf( ". At this point, you type in your z-scores (lowest,highest) OR your range, mean then the standard deviation.. in that order , seperated by commas... like so (low end of the range,high end of the range, mean, standard deviation).
-Don't forget to CLOSE the bracket! )

Quick example of the FIRST way using the Z-scores.
Ex 1. Q. Given the Z scores -.2 and 1.4, what percentage of the data lies in that particular range?
A. normalcdf(-.2,1.4)
*hit enter*
The number you get is 0.4985
That number gives you three things.
-The area between those two numbers is .4985
-The percent of data within those two numbers (49.85%)
-The probability that of all the data collected, that something would be "picked" out of that specific section.
What the question asked for was percentage... so your answer would be 49.85%

Next example of the OTHER way by using the range, mean and standard deviation.
Ex 2. Q. A selection of numbers has been aquired. Given a high of 190 and a low of 160, a mean of 150 and a standard deviation of 10, what is the probability that a selected number from a particular group of numbers is within that range?
A. normalcdf(160,190,150,10)
*hit enter*
You get 0.1586

Final thing we used was the Reverse norm function. It is a function we have that allows us to find the z score using the area.
STEPS:
-ON
-2nd
-VARS
-3
At this point you enter in the area/persentage/prabability.

Well that about summs it up. Gnight.
Next scribe is Eugene.