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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!
Is a normally distributed variable needed to have a normally distributed sampling distribution.?
Yes, it is.
What is a variable that is normally distributed?
x
Can you think of a variable that is normally distributed?
The value of a roll of two dice is normally distributed.
Is it true that the mean of a normally distributed variable can be any real number?
no
How to present a variable that is not normally distributed?
There are many variables that are not normally distributed. You can describe them using a probability distribution function or its cumulative version; you can present them graphically.
What does it mean when you say a variable is normally distributed?
It means that the probability distribution function of the variable is the Gaussian or normal distribution.
Does it matter if your dependent variable is normally distributed?
No, it does not. In fact, for many statistical analyses, it is a definite advantage.
What do results tell you with regard to whether the data is normally distributed?
Your question may be a little overly complex. Usually you start with some degree of confidence that the variable(s) you are studying are normally distributed; you don't do an experiment and wait for the results to tell you. Your confidence that a variable is normally distributed helps you to determine whether or not your results are significantly different from what you would expect by chance. If I have missed the meaning of your question, my apologies.
Give example of variable that is normally distributed?
Some examples of anormal distribution are: heights of men and women, weights of men and women, IQ's, body temperature, and many manufacturing processes to name a few.
Why is the central limit theorem an important idea for dealing with a population not normally distributed?
According to the Central Limit Theorem, even if a variable has an underlying distribution which is not Normal, the means of random samples from the population will be normally distributed with the population mean as its mean.
When doing a t-test what does normal distributed in population mean?
It means that the random variable of interest is Normally distributed and so the t-distribution is an appropriate distribution for the test rather than just an approximation.
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.
