6-5 Assessing Normality 295 Histograms and Normal Quantile Plots In Part 2 of this section we describe the process of constructing a normal quantile plot, but for now we focus on interpreting a normal quantile plot. The following displays show histograms of data and the corresponding normal quantile plots. Normal: The first case shows a histogram of IQ scores that is close to being bellshaped, so the histogram suggests that the IQ scores are from a normal distribution. The corresponding normal quantile plot shows points that are reasonably close to a straight-line pattern, and the points do not show any other systematic pattern that is not a straight line. It is safe to assume that these IQ scores are from a population that has a normal distribution. Uniform: The second case shows a histogram of data having a uniform (rectangular) distribution. The corresponding normal quantile plot suggests that the points are not normally distributed. Although the pattern of points is reasonably close to a straight-line pattern, there is another systematic pattern that is not a straight-line pattern. We conclude that these sample values are from a population having a distribution that is not normal. Skewed: The third case shows a histogram of the amounts of rainfall (in inches) in Boston for every Monday in one year. The shape of the histogram is skewed to the right, not bell-shaped. The corresponding normal quantile plot shows points that are not at all close to a straight-line pattern. These rainfall amounts are from a population having a distribution that is not normal.
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