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Lecture 2 - Measures of Position The most commonly used...

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Measures of Position The most commonly used measure of location: mean The most commonly used measure of variation: std. deviation The z-score measures how many standard deviations away from the mean a particular observation is. The z-score is also called a standardized value. z-Scores are positive if the observation is greater than the mean. z-Scores are negative if the observation is less than the mean. s x x z - =
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Observations in different data sets having the same z-score have the same relative location from the means of the data sets. This standardization allows you to compare the data.
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Example: In a certain city the mean price of a quart of milk is 63 cents and the standard deviation is 8 cents. The average price of a package of bacon is $1.80 and the standard deviation is 15 cents. If we pay $0.89 for a quart of milk and $2.19 for a package of bacon at a 24-hour convenience store, which is relatively more expensive? To answer this, we compute Z -scores for each:
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Example: A student had a z-score of - 1.5 for his ACT score on the ACT test with mean 18 and standard deviation 6.
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