the normal distribution: comparing apples and oranges
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Frequency and Relative Frequency Distributions for HeightsTRANSCRIPT
The Normal Distribution:Comparing Apples and Oranges
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Three Normal Distributions
Frequency and Relative Frequency Distributions for Heights
Relative Frequency Histogram for a Normally Distributed Variable
The Standard Normal Curve
Properties of the Standard Normal Curve
• 1. The Standard Normal Distribution has a mean of 0 and a standard deviation of 1.
• 2. The total area under the curve is equal to 1.• 3. The Standard Normal Curve extends indefinitely
in both directions, approaching, but never touching the horizontal axis.
• 4. The Standard Normal Curve is symmetric about 0; that is, the part of the curve to the left of 0 is a mirror image of the part of the curve to the right of it.
• 5. Most of the area under the curve lies between -3 and 3 (99.74%).
Normal CurveStandard Normal Curve
Standardizing Normal Distributions
The Empirical Rule Revisited
Assessing Normality• Pearson’s Index of Skewness (I) – The closer to a value of
zero, the less skewed, or more normal, the data set. Recall that if I lies between -1 and +1 the distribution is considered to be approximately normally distributed.
• Normal Probability Plot – a plot of the observed values of the variable being considered versus the normal scores.