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Parametric statistical procedures are based on a number of "statistical assumptions" that need to be met...

Parametric statistical procedures are based on a number of "statistical assumptions" that need to be met in order for the conclusions drawn to be valid. One of these statistical assumptions is that the distribution of the population data from which the sample is drawn meets the definition of a “normal distribution”. A first step in data analysis is to first check to see if there is evidence that the statistical assumptions have been met. This involves the researcher reviewing the sample data for evidence that the data was selected from a larger data set (i.e. population) that is normally distributed. It is always important to check this assumption of normality. One part of this involves a review of the sample's measures of central tendency. What would you expect to find when you calculate the mean, median and mode statistics of a random sample drawn from a population of normally distributed data? In other words, explain how each of these statistics will relate to each other, or, be similar or different, given they represent sample data that was selected from a normal distribution?

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If the mean, median, and mode of sample values are equal then we can say that the distribution of sample data is normal. If these values are not exactly the same but do not differ from each other to a great extent then we might find that the sample data is approximately normally distributed. For example, mean = 58, median = 58.4, and mode = 58.

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