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Normal Curve
Lecture
Goals
Reading
Rectangular Shaped Polygon (graph) Area & Rectangular
Polygon (graph)
Area & Rectangles (graph) The Area of a Rectangle (graph) Finding the Area
of a Rectangle
Normal Curve (graph)
Bell-shaped
curve (graph)
Importance
2) As sample size ______________ distributions become more "________________" 3) Some statistical procedures
__________ a normal distribution
(graphs)
Relative Frequency Indicates the _______________ of scores in a category Relative freq. = # scores in category
Indicates the ________________ of scores up to and including a category Cumulative
Frequencies (graph)
For the general population IQ scores are normally
distributed with a mean of 100 and a standard deviation of 16. (graph)
What percentage of the general population have IQ
scores lower than 52? (graph)
What percentage of the general population have IQ
scores lower than 84? (graph)
What percentage of the general population have IQ
scores between 84 and 116? (graph)
What percentage of the general population have IQ
scores greater than 132? (graph)
What % of the general population have IQ scores less
then 52 or greater than 148? (graph)
To get the answer we: 1) matched scores to standard deviations from the mean (e.g., m +1s = 116) We converted raw scores to _________________________ Standard
scores are also called ____________________
Standard Scores
Allows comparisons between scores that are not otherwise directly comparable How? General
formula depends on:
- distribution _________________ z = desired score's distance from the mean standard deviation z =
for samples
What percentile rank of someone with an IQ score
of 132?
Shows that score 132 is ________ standard deviations
form the mean
Ex. For a normally distributed pop. of rats - s = 20 g s 20 20 s 16 16 Characteristics
of Standard Scores
Z-scores transform raw scores into units based on S.D. S.D. = distance form the mean The distance from the mean to itself is 0 Thus, raw scores that are identical to the mean have a z-score of _________ Raw scores that are identical to the mean have a z-score of 0 z = Xi-m = 100 - 100 = 0 = 0 s 16 16 The z-score of the raw value exactly 2 S.D. from the mean = _____ The z-score of the raw value exactly 3S.D. from the mean = _____ Proofs s s z = Xi-m = (m + 2s ) - m = 2s = 2 s s s z = Xi-m
= (m -1s
) - m =
-1s = -1
Can find percentiles without calculating relative and cumulative frequencies 1) Match scores to standard deviations 2) Find score of interest 3) Find percentile rank by summing areas under appropriate portions of curve Finding Percentile
Ranks
z = Xi-m = 120 - 100 = 20 = s 16 16 Shows that score 120 is _____ standard deviations form the mean Okay..so how do we convert 1.25
standard deviations form the mean into a percentile?
What is percentile rank of someone with an IQ score of 120???? (graph) |
