Advanced Math/statistics

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Question
1.   “Statistical unit is necessary not only for the collection of data, but also for the interpretation and presentation”. Explain the statement.
2.   Find the standard deviation and coefficient of skewness for the following distribution
Variable    0-5   5-10   10-15   15-20   20-25   25-30   30-35   35-40
Frequency   2   5   7   13   21   16   8   3

3.   A salesman has a 60% chance of making a sale to any one customer. The behaviour of successive customers is independent. If two customers A and B enter, what is the probability that the salesman will make a sale to A or B.

4.   To verify whether a course in Research Methodology improved performance, a similar test was given to 12 participants before and after the course. The original marks and after the course marks are given below:
Original Marks   44   40   61   52   32   44   70   41   67   72   53   72
Marks after the course   53   38   69   57   46   39   73   48   73   74   60   78
Was the course useful? Consider these 12 participants as a sample from a population.
5.   Write short notes on
a)   Bernoulli Trials
b)   Standard Normal distribution
c)   Central Limit theorem

Answer
1. When statistical units are involved in the collection of data, it implies that there is a tally chart that is filled in on what is collected.  From this, a histogram can be developed and the approximate mean and standard deviation seen by inspection of the chart.

2. The standard deviation is found by the (A-B/n)/(n-1) where A is the sum of the squares
(40768.75), B is the square of the sum (1642.5), and n is the sample size (8).
It turns out to be roughly 8.05.  According to http://mathworld.wolfram.com/Skewness.html ,
the skewness depends on the type of distribution that is used.  There are variations in approximating it known as the Person Skewness and the Bowley Skewness.

3. The P(A) is 0.60 and the P(B) is 0.60. This gives P(A only) at 0.6*0.4 = 0.24.
This is the same as P(B only).  The P(A&B) = 0.6*0.6 = 0.36.  That makes the probability of either happening being 0.24 + 0.24 + 0.36 = 0.84.  It makes the probability of only one happening at 0.24 + 0.24 = 0.48.

4. The standard deviations calculate out to be 14.1 and 14.3, so there is only a difference of 0.2 between these, which doesn't amount to a statistical difference in standard deviations.
The means calculate out to be 54 and 59, so the difference between them is 5.  Since the standard deviation is almost 3 times this value, there is no statistical significance to this.

5. Look up Bernoulli Trials, Standard Normal distribution, and Central Limit Theorem.
This sample data is from a Binomial distribution,  which can be approximated by the Normal distribution.  According to the central limit theorem, increasing population would give an average that is closer to the true average.

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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.

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