The majority of the data is normally distributed if there are enough subjects. F

Question

The majority of the data is normally distributed if there are enough subjects. For instance, if you collected test scores of only a few honor students, the data will most likely not be normally distributed because you would have a sample that did not represent the entire population. But the identical test scores (for honor students) collected from all schools in a state will result in a normal distribution.

Identify an example of a population that you would expect to be normally distributed. Explain why, according to you, it would be normally distributed. Then, describe a subset of the population you identified and explain why it would not be normally distributed and what the distribution would look like.

Explanation / Answer

If we collect huge data for the test scores of honor students, most of the data will fall near to the mean of the data and spread on both the side in a symmetric in nature. But collected test scores of only a few honor students may happen asymmetrically. Becuase, if the sample size is small, the chances of selecting the students either of the high or low test score group may highly possible. Hence, the assumption of the normal distribution on this sample is violated and the distribution will like skew-normal distribution in this case.

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