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Unformatted text preview: Chapter 13 Normal Distributions In this chapter Density curves Identifying shape of a distribution Standardized scores Density curves Statistical software can replace the separate bars of a histogram with a smooth curve that represents the overall shape of a distribution Density curve a smooth curve which is the most common way of representing a population Density curves are useful in determining what proportion, percentage, or probability of the population falls within an interval (proportion, percentage, and probability is the same value) We set up these curves so that the area under the curve represents the proportion, percentage, or probability of observations Therefore, the total area for any density curve is 1 If the density curve follows a normal distribution (Gaussian distribution) then it will be a bell-shaped curve. Identifying shape of a distribution The shape of a density curve can be determined as was done with histograms Another way to determine shape is by comparing the mean and median. This idea is illustrated well in the textbook. If you are ever in doubt about the shape of a distribution comparing the mean and median is the most accurate way to identify skewness. There is still some judgment here because you have to decide if the mean and median are close enough to be considered approximately equal or if there is enough of a difference to say they are not equal....
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