1.What is the central limit theorem and why is it important in
statistics? 2.Explain the differences between the mean, mode and
median. Which is the most useful measure of an average and why?
3.Which is a more useful measure of central tendency for stock
returns – the arithmetic mean or the geometric mean? Explain your
answer.
This week we’ve introduced the central limit theorem. According to
the central limit theorem, for all samples of the same size n with
n>30, the sampling distribution of x can be approximated by a
normal distribution.
In your initial post
use your own words to explain what this theorem means. Then provide
a quick example to explain how this theorem might apply in real
life. At last, please share with us your thoughts about why this
theorem is important.
Central limit theorem is important because?
For a large , it says the population is approximately
normal.
For a large , it says the sampling distribution of the sample
mean is approximately normal, regardless of the shape of the
population.
For any population, it says the sampling distribution of the
sample mean is approximately normal, regardless of the sample
size.
For any sized sample, it says the sampling distribution of the
sample mean is approximately normal.
Summarize the implications of the central limit
theorem. What is the most important application of it and explain
why? please be detailed in your response and give examples.
The central limit theorem is an important concept in research.
It allows several key assumptions to be made, and facilitates
several key practices.
Implications
For this discussion, you will reflect
on the application of the central limit theorem to research.
Develop the main response in which you address the following
Summarize the implications of the central limit theorem.
Identify what you believe to be the most important application
of it.
Explain your position, providing examples where possible.
Give as much...
Use the Central Limit Theorem to calculate the following
probability. Assume that the distribution of the population data is
normally distributed. A person with “normal” blood pressure has a
diastolic measurement of 75 mmHg, and a standard deviation of 4.5
mmHg.
i) What is the probability that a person with “normal” blood
pressure will get a diastolic result of over 80 mmHg, indicating
the possibility of pre-hypertension?
ii) If a patient takes their blood pressure every day for 10
days,...