Question 330905: Why is the population shape a concern when estimating a mean? What effect does sample size, n, have on the estimate of the mean? Is it possible to normalize the data when the population shape has a known skew? How would you demonstrate the central limit theorem to your classmates?
Answer by jrfrunner(365)   (Show Source):
You can put this solution on YOUR website! Why is the population shape a concern when estimating a mean?
the shape is a concern because if the shape is symmetrical, the mean will be near the center of the distribution. The mean is very sensitive to extreme values and if the distribution is not symmetrical, the mean will be away from the center and toward the extreme values. Also, since most statistics rely on normality, its important that to use those statistics, that the underlying population is normally distributed.
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What effect does sample size, n, have on the estimate of the mean?
The larger the sample size the smaller the standard error (standard deviation/sqrt(n)) and thus a more reliable estimate. Also when analyzing the mean with large samples, you can rely on all the tests and statistics which assume normality, based on the central limit theorem
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Is it possible to normalize the data when the population shape has a known skew?
Yes there are various methods for normalizing skewed distribution, such as the Square root transformation and logarithmic transformation to name two.
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How would you demonstrate the central limit theorem to your classmates?
1. Begin with a set of data which is obviously not normal, something like the uniform distribution or any nnon-normal distribution. In fact draw a histogram to show that it is not normal.
2.Select samples from the set of data of size 5, compute the average, repeat say several hundred times, and draw a histogram of this set of averages
3. Repeat step 2 with larger samples size and draw histogram
4. You will see the histogram of averages resembling a normal distribution as your sample sizes increase
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