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The Normal or Gaussian distribution is a probability distribution which depends on two parameters: the mean and the variance (or standard deviation). In may real life situations measurements are found to be approximately normal. Furthermore, even if the underlying distribution of a variable is not normal, the mean of a number of repeated observations of the variable will approximate the normal distribution.
The term "approximate" is important because, although the heights of adult males (for example) appear to be normally distributed, the true normal distribution must allow negative heights whereas that is not physically possible!
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What Percent of data is below the mean in a normal distribution?
In the normal distribution, the mean and median coincide, and 50% of the data are below the mean.
What is a normal data set?
A normal data set is a set of observations from a Gaussian distribution, which is also called the Normal distribution.
What is the mean of the sampling distribution of the sample mean?
Frequently it's impossible or impractical to test the entire universe of data to determine probabilities. So we test a small sub-set of the universal database and we call that the sample. Then using that sub-set of data we calculate its distribution, which is called the sample distribution. Normally we find the sample distribution has a bell shape, which we actually call the "normal distribution." When the data reflect the normal distribution of a sample, we call it the Student's t distribution to distinguish it from the normal distribution of a universe of data. The Student's t distribution is useful because with it and the small number of data we test, we can infer the probability distribution of the entire universal data set with some degree of confidence.
What percentage of the data in a normal distribution is represented by 1 SD of a sample?
Assuming that we have a Normal Distribution of Data, approx. 65% of the data will fall within One Sigma.
What percentage of data values of a normal distribution will fall within one standard deviation below the mean?
34.1% of the data values fall between (mean-1sd) and the mean.
