CJUS K300 1nd Edition Lecture 8 Outline of Last Lecture I Probability Outline of Current Lecture II Z score Current Lecture Properties of a normal curve as close to symmetrical as possible given that it would be close to impossible for it to be perfectly symmetrical Two curves can be normal with the same standard deviations but different means or the same mean and different standard deviations See power point for examples In cases of normal distribution Once you find the mean of the curve for normal curves it is in the middle of the curve 50 of the data is on the left side and 50 of the data is on the right The area between the mean and one standard deviation is 34 meaning 34 of the data points lie in between the mean middle and one standard deviation away in either direction The area between the mean and two standard deviations is 47 5 The area between the mean and 3 standard deviations is 49 5 Example Janes IQ score is 3 standard deviations above the mean What do we know about her IQ She is in the 99 5th percentile 50 49 5 from 3 standard deviations American IQ test x 100 s 10 Marys score was 110pts She was above the average by exactly 1 standard deviation 10 so we know that she is in the 84th percentile 50 34 Comparing 2 different tests These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute American IQ test x 100 s 10 Mary 110 European IQ test x 350 s 36 Pierre 382 Who has the higher IQ Mary does Pierre is not a full standard deviation above the mean whereas Mary is Z X Mean S Pierre z 382 350 36 89 Mary z 110 100 10 1 If it is not a full SD above the mean you have to take it to the z table Look up the z score on the table and find the corresponding number and add it to the 50 Z 88 80 15 53 53 corresponds to 2019 so you add 20 to 50 and which makes it the 70 th percentile
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