5_Standard_Scores

5_Standard_Scores - Standard Scores and Normal...

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Unformatted text preview: Standard Scores and Normal Distributions You should be able to . . . • Describe the normal density curve • Describe the standard normal curve – And know its mean and standard deviation • Define and compute z scores • Define probability – Compute simple probabilities • Define random samples – Representativeness Standard Normal Curve • We will first review the normal curve – Normal density curve • We will then discuss a special case of the normal curve – Standard normal curve • We will then discuss the scores that make up the standard normal curve – Standard scores or z scores Normal curve • Symmetrical • Bell-shaped • Unimodal • Mean = Median = Mode Normal curve Example: Normal curve Smooth, unlike a histogram (or frequency polygon) Example: • In statistics, when we plot a smooth curve instead of a histogram (or frequency polygon), we are plotting a probability density curve Histogram Frequency Histogram Frequency Shows the frequency of the variable plotted on the x axis Probability Density Curve Variable Probability Probability Density Curve Probability Shows the probability or likelihood of the variable plotted on the x axis Variable Probability Density Curve Probability Variable Very Probable Probability Density Curve Probability Variable Not Probable Not Probable Some Different Probability Density Curves Probability Probability Probability Probability Some Different Probability Density Curves Probability Probability Probability Probability Don’t need to be normal When the probability density function is in the shape of a normal curve, it is called a normal density curve Normal curve — this shape: PLUS It shows probability = Normal Density Curve To Review Normal Density Curve Probability Normal Density Curve Probability Very Probable Normal Density Curve Probability Not Probable Not Probable Normal Density Curve • Describes many naturally occurring phenomena Probability Probability Most probable weight Probability Lower probability weights Normal Density Curve • There are many possible normal density curves, each having a different mean and standard deviation Normal Density Curve: Means • Normal curves will have different means if they are centered around different values – e.g., mean IQ vs. mean weight Normal Density Curve: Standard Deviations • Normal curves will have different standard deviations if values in the distribution cluster around the mean differently • As standard deviation increases, the distribution flattens – Low standard deviation “skinnier” distribution – High standard deviation “flatter” distribution Concept Check Which distribution has a higher mean? Which distribution has a higher standard deviation? A B A B C “Normal Density Curve” \/ “Normal Curve” (We’re lazy.) (We say a curve “has a normal shape” or is “normal in shape” when talking about shape.) Normal Curves • There are many possible normal curves – Each with a different mean and standard deviation • Let’s talk now about one special normal curve Standard Normal Curve...
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5_Standard_Scores - Standard Scores and Normal...

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