So what is a Normal Distribution When you think you know wha

So, what is a Normal Distribution? When you think you know what it is, post a real-example of one (other than height)? Is it really normally distributed?

1) Can everything be normally distributed, that is, fall along a \'bell curve\'?

2) More Importantly, WHY do we make the \'assumption of normality\' for Inferential statistics?

Solution

Sol)

\'NORMAL DISTRIBUTION:

A continuous random variable is a variable whose possible values form some interval of numbers. Typically, a continuous variable involves a measurement of something, such as the height of a person, the weight of a newborn baby, or the length of time a car battery lasts.

EXAMPLES: 1. Let x = the amount of milk a cow produces in one day. This is a continuous random variable because it can have any value over a continuous span. During a single day, a cow might yield an amount of milk that can be any value between 0 gallons and 5 gallons. It would be possible to get 4.123456 gallons, because the cow is not restricted to the discrete amounts of 0, 1, 2, 3, 4, or 5 gallons. 2. The measure of voltage for a smoke-detector battery can be any value between 0 volts and 9 volts. It is therefore a continuous random variable.

1) No, Not everything be normally distributed. In statistics we have non normal distribution also exist. Those distribution are not bell shaped. But we can convert any distribution to Normal distribution by taking Z transformations.

22) IN statistics primary assumpation is that any data should follow Normal distribution.

When you take the parametric approach to inferential statistics, the values that are assumed to be normally distributed are the means across samples. To be clear: the Assumption of Normality (note the upper case) that underlies parametric stats does not assert that the observations within a given sample are normally distributed, nor does it assert that the values within the population (from which the sample was taken) are normal.

For example:

Example: Imagine (again) that you are interested in the average level of anxiety suffered by graduate students when they are asked to revise what they believed to be true about inferential statistics. Therefore, you take a group of grads (i.e., a random sample) and tell them that something that they believed about stats is actually false, and then, while they are digesting this, you measure their levels of anxiety. Finally, when you have measured everyone in the group, you calculate the mean level of anxiety across all of the subjects. This final value is the sample mean. The Assumption of Normality says that if you repeat the above sequence many many many times and plot the sample means, the distribution would be normal. Note that I never said anything about the distribution of anxiety levels within given samples, nor did I say anything about the distribution of anxiety levels in the population that was sampled. I only said that the distribution of sample means would be normal. And again, there are two ways to express this: “the distribution of sample means is normal” and/or “the sampling distribution of the mean is normal.” Both are correct as they imply the same thing.