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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

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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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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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
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I graduated with honors in both my BS and MS degrees.
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Master of Science at OSU with high honors in mathematics.
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