Chapter 3 notes

# Chapter 3 notes - Measures of Center Measures of central...

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Measures of Center Measures of central tendency—descriptive measures that indicate where the center or most typical value is located Mean—average of the data Median Arrange the data in increasing order Number of observations is odd, then the median is exactly in the middle Number of observations is even, then the median is the mean of the two middle observations

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Measures of Center Mode No mode exists if the greatest frequency is 1 If the greatest frequency is 3 or greater, then any value that occurs with that greatest frequency is the mode
Measures of Center Population mean—mean of the population Sample mean—mean of the sample

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Statistics Sample Mean Sample mean—the mean of the sample Summation notation—sigma the sum of all the x’s x n n
Statistics Sample Mean Notation for the sample mean— Therefore, the formula for finding the sample mean can be written as: x x x n n =

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Statistics Sample Mean Other important sums— Used to help find the variance (section 3.3) 2 x n
Statistics Measure of Variance Measures of variation—amount of variation, or spread, in a data set Also known as measures of spread Range—max – min Sample standard deviation-- ( 29 2 1 x x s n - = -

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Statistics Measure of Variance Standard deviation—how far, on the average, the observations are from the mean Preferred when the mean is used as the measure of center Interquartile range—3 rd quartile – 1 st quartile Preferred when the median is used as the measure of center
Statistics Measure of Variance To compute the standard deviation Step 1: Calculate the sample mean Step 2: Construct a table to obtain the sum of the squared deviations Step 3: Calculate the square root of step 2 Variation and the Standard Deviation The more variation there is in a data set, the larger the standard deviation The less variation there is in a data set, the smaller the standard deviation

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Statistics Measure of Variance Computing formula for a Sample Standard Deviation ( 29 2 2 / 1 x x n s n - = -
Statistics Measure of Variance Three-Standard-Deviations Rule Almost all the observations in any data set lie within three standard deviations to either side of the mean Chebychev’s rule—for all data sets and implies that 89% of the observations lie within three standard deviations to either side of the mean Empirical rule—if the data set is approximately bell-shaped, then about 99.7% of the observations lie within three standard deviations to either side of the mean

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## This note was uploaded on 09/12/2008 for the course MATH 1431 taught by Professor Unkown during the Spring '08 term at Georgia Perimeter.

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Chapter 3 notes - Measures of Center Measures of central...

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