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A variable that shows serious departure from the classic bell-shaped, or "Gaussian", curve is described as being not normally distributed. This departure could take the form of skew and/or kurtosis and/or multi modality.
An example might be weekly wages. If you drew a histogram of a population's earnings you would most likely see a distribution skewed significantly toward the right. That is, toward the higher incomes.
Another example is height. If you drew a histogram of a population's height you would see a bimodal distribution. One peak for males and another peak for females. The distribution of height for males and females might be normal when looked at individually, but not normal when you combine them.
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How chi square distribution is extension of normal distribution?
Given "n" random variables, normally distributed, and the squared values of these RV are summed, the resultant random variable is chi-squared distributed, with degrees of freedom, k = n-1. As k goes to infinity, the resulant RV becomes normally distributed. See link.
Why are z-scores used to check for outliers?
If a variable is Normally distributed then the z-score describes how far from the mean/median a particular observation is. For example, a z score of 1.96 implies that fewer than 0.025% of the observations will be at least that extreme.
What does it mean for a population to be normally distributed?
A Gaussian distribution is the "official" term for the Normal distribution. This is a probability density function, of the exponential family, defined by the two parameters, its mean and variance. A population is said to be normally distributed if the values that a variable of interest can take have a normal or Gaussian distribution within that population.
Scores on an examination are assumed to be normally?
...normally distributed.
Is weight normally distributed?
NO!
