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Normal Distribution of Data A normal distribution is a common probability distribution .It has a shape often referred to as a "bell curve." Many everyday data sets typically follow a normal distribution: for example, the heights of adult humans, the scores on a test given to a large class, errors in measurements.

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The center of a normal distribution is located at its peak, and 50% of the data lies above the mean, while 50% lies below. It follows that the mean, median, and mode are all equal in a normal ...

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Real phenomena only follow discrete empirical distributions and even they are vulnerable to perturbative noise (alas we are creators of finitist measurement). The CLT puts the Gaussian on a pedestal as an asymptotic distribution for weighted avera...

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But there are many cases where the data tends to be around a central value with no bias left or right, and it gets close to a "Normal Distribution" like this: A Normal Distribution. The "Bell Curve" is a Normal Distribution. And the yellow histogram shows some data that follows it closely, but not perfectly (which is usual).

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Other examples of normally distributed variables include IQ measurements, population and test scores. Variables tend to fall between two extremes but are more likely to fall towards the middle of the sample group. In the example of test scores, most students receive an average score on a test, with some students performing better and some worse.

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What could be good examples of normally distributed variables that I can use to illustrate Normal Distribution? IQ scores and heights of adults are often cited as examples of normally distributed ...

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When you have normally distributed data, the standard deviation becomes particularly valuable. You can use it to determine the proportion of the values that fall within a specified number of standard deviations from the mean. For example, in a normal distribution, 68% of the observations fall within +/- 1 standard deviation from the mean.

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The normal distribution is symmetric, so we can flip this around to Pr(x < -2). Notice the change in the inequality. This is the opposite of what we want. The total probability under a normal curve is 1, though, so we can take 1 – Pr(x < -2) to find Pr(x is NOT less than -2), or Pr(x > -2).

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Insufficient Data can cause a normal distribution to look completely scattered.For example, classroom test results are usually normally distributed. An extreme example: if you choose three random students and plot the results on a graph, you won’t get a normal distribution.

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A normal distribution, sometimes called the bell curve, is a distribution that occurs naturally in many situations.For example, the bell curve is seen in tests like the SAT and GRE. The bulk of students will score the average (C), while smaller numbers of students will score a B or D.