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# The normal distribution Essay

1. Discrete data are those data that can take on only particular and definite values. They are composed of individual values, typically represented by integers over an interval. In contrast, continuous data are data that can take on any intermediate value over an applicable range. Continuous data vary without discontinuity across an interval. The interval can be assumed to be infinitely divisible. Although it may be argued that money is continuous, it is discrete. In the United States, money has the smallest increment of one penny.

Hence, it has a particular and definite value. Normal distribution is usually used to analyze continuous data, but it can also be used on discrete data. Discrete data can be analyzed using normal distribution if there are a number of equally spaced data points. The greater the number of equally spaced data points used, the closer the discrete model will be to the actual continuous distribution itself, with the limit of the number of equally spaced data points approaching infinity where the discrete model approaches the continuous exactly.

2. The normal distribution has several properties. The normal curve is symmetrical about the mean ?. The mean is at the middle and divides the area into halves. The total area under the curve is equal to 1. The normal distribution is completely determined by its mean and standard deviation ? (or variance ? 2). There are an infinite number of distinct normal distributions because there is a different normal distribution for each combination of mean and standard deviation.

We want to assume that our sample data represent a population distribution so that we can make generalizations about the population. In order to make a valid statistical inference about a population, it must be assumed that the sample data are representative of the population. For each population, there are many possible samples. A sample data give information about a corresponding population parameter. For instance, the sample mean for a set of data would give about the overall population mean.

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