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handout_1_3_normal_quantile

handout_1_3_normal_quantile - Normal Quantile Plots How can...

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Normal Quantile Plots How can you tell whether or not a distribution is normal? •histogram or stemplot can tell us whether or not distribution is obviously nonnormal •if distribution appears roughly symmetric and unimodal, need a more sensitive way to tell Normal Quantile Plot (Figure 1.34) 1. Arrange the observed data values from smallest to largest. Record what percentile of the data each value occupies. For example, the smallest observation in a set of 10 is at the 10% point, the second smallest is at the 20% point, and so on. 60 65 70 75 76 80 86 90 95 99 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 2. Do normal distribution calculations to find the z-scores at these same percentiles. For example, z= -1.282 is the 10% point of the standard normal distribution. z-score -1.282 -0.842 -0.524 -0.253 0 0.253 0.524 0.842 1.282 percentile 10% 20% 30% 40% 50% 60% 70% 80% 90% 3. The variable of interest we call x. Plot each data point x (on y axis) against the corresponding z (on x axis). • If the data distribution is close to normal , the plotted points will lie close to some straight line.
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