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The normal distribution has two parameters, the mean and the standard deviation Once we know these parameters, we know everything we need to know about a particular normal distribution. This is a very nice feature for a distribution to have. Also, the mean, median and mode are all the same in the normal distribution. Also, the normal distribution is important in the central limit theorem. These and many other facts make the normal distribution a nice distribution to have in statistics.
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Why normal distribution is better than other distributions?
It may not be better, but there is a lot of information on the normal distribution. It is one of the most widely used in statistics.
Why you prefer normal distribution as compare to others in statistics?
Perhaps a mistaken impression, after completing an initial course in statistics, is that one distribution is better than another. Many other distributions exists. Usually, introductory statistics classes concern confidence limits, hypothesis testing and sample size determination which all involve a sampling distribution of a particular statistic such as the mean. The normal distribution is often the appropriate distribution in these areas. The normal distribution is appropriate when the random variable in question is the result of many small independent random variables that have been are summed . The attached link shows this very well. Theoretically, a random variable approaches the normal distribution as the sample size tends towards infinity. (Central limit theory) As a practical matter, it is very important that the contributing variables be small and independent.
When it comes to comparing data from different distributions what is the benefit of normal standard distribution?
There may or may not be a benefit: it depends on the underlying distributions. Using the standard normal distribution, whatever the circumstances is naive and irresponsible. Also, it depends on what parameter you are testing for. For comparing whether or not two distributions are the same, tests such as the Kolmogorov-Smirnov test or the Chi-Square goodness of fit test are often better. For testing the equality of variance, an F-test may be better.
How do you check for normal distribution?
There are two main methods: theoretical and empirical. Theoretical: Is the random variable the sum (or mean) of a large number of imdependent, identically distributed variables? If so, by the Central Limit Theorem the variable in question is approximately normally distributed. Empirical: there are various goodness-of-fit tests. Two of the better known are the chi-square and the Kolmogorov-Smirnov tests. There are others. These compare the observed values with what might be expected if the distribution were Normal. The greater the discrepancy, the less likely it is that the distribution is Normal, the smaller the discrepancy the more likely that the distribution is Normal.
Explain how you could create a distribution of means by taking a large number of samples of four individuals each?
As the sample size increases, and the number of samples taken increases, the distribution of the means will tend to a normal distribution. This is the Central Limit Theorem (CLT). Try out the applet and you will have a better understanding of the CLT.
