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the normal distribution are a very important class of statistical distributions.all normal distributions are symmetric and have bell- shaped density curves with a single peak.both the normal and symmetrical distributions are u-shape and equal from both sides.
the normal distribution is considered the most prominent probability distribution in statistics.There are several reasons for this first, the normal distribution is very tractable analytically. that is a large number of results involving this distribution can be derived in explicit from.Second, the normal distribution arises as the outcome of the central limit theorem, which states that under mild conditions the large number of variables is distributed approximately normally.finally, the "bell" shape of the normal distribution marks it is a convenient choice for modeling a large variety of random variables encountered in practices.
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Normal distribution is symmetric with single peak.Does this mean that all distibutions are normal?
No, not all distributions are symmetrical, and not all distributions have a single peak.
What is the definition of 'bell curve'?
A bell curve is a graph that depicts a large rounded peak tapering away at each end of normal distribution. A bell curve is a mathematical concept with the curve concentrated in the center.
What is a single peaked distribution in statistics?
The classic example is a Bell curve. IQ testing (using the WAIS, or Wechsler Adult Intelligence Scale) yields a peak at the 100-105 IQ mark, with a downward curve on either side of the peak - representing the higher and lower IQ scores, respectively.
What is an example of a variable that is not normally distributed?
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.
What is the relationship between the relative size of the starndard deviation and the kurtosis of a distribution?
It is inversely proportional; a larger standard deviation produces a small kurtosis (smaller peak, more spread out data) and a smaller standard deviation produces a larger kurtosis (larger peak, data more centrally located).
