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MEASURES OF CENTRAL TENDENCY Measures of central tendency try to describe what we refer to as the center of the data

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Here are four sets to look at A = {2,3,6,7,7,8,9} B = {2,4,7,7,8,8} C = {2,7,9} D = {2,2,2,6,8,9,9,10} Where does the center appear to be for each?

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Lets look at them graphically. x x x x x x x 1 2 3 4 5 6 7 8 9 10 A = {2,3,6,7,7,8,9} x x x x x x 1 2 3 4 5 6 7 8 9 10 B = {2,4,7,7,8,8} x x x 1 2 3 4 5 6 7 8 9 10 C = {2,7,9}

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x x x x x x x 1 2 3 4 5 6 7 8 9 10 A = {2,3,6,7,7,8,9} x x x x x x 1 2 3 4 5 6 7 8 9 10 B = {2,4,7,7,8,8} x x x 1 2 3 4 5 6 7 8 9 10 C = {2,7,9} x x x x x x x x 1 2 3 4 5 6 7 8 9 10 D = {2,2,2,6,8,9,9,10}

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Here are four sets to look at A = {2,3,6,7,7,8,9} B = {2,4,7,7,8,8} C = {2,7,9} D = {2,2,2,6,8,9,9,10} There are three basic measures of central tendency we will discuss. Mean, Median and Mode

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Mode- the most frequent data value Mode A = {2,3,6,7,7,8,9} B = {2,4,7,7,8,8} C = {2,7,9} D = {2,2,2,6,8,9,9,10}

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Mode- the most frequent data value Mode A = {2,3,6,7,7,8,9} 7 B = {2,4,7,7,8,8} 7 & 8 C = {2,7,9} ? D = {2,2,2,6,8,9,9,10} 2 Weakness to Mode: May not exist May not be unique Unaffected by extreme values Does not always reflect the center of the data

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Mode- the most frequent data value Mode A = {2,3,6,7,7,8,9} 7 B = {2,4,7,7,8,8} 7 & 8 C = {2,7,9} ? D = {2,2,2,6,8,9,9,10} 2 Weakness to Mode: May not exist May not be unique Unaffected by extreme values Does not always reflect the center of the data Strength- The mode provides information about common values or concentration of data. It can be used with nominal data Application- Inventory in a shoe store or pizza store

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Median- the middle value in a set of data arrange in increasing/ decreasing order. If there is an even number of entries, the median it the average of the two middle values. Mode Median A = {2,3,6,7,7,8,9} 7 B = {2,4,7,7,8,8} 7 & 8 C = {2,7,9} ? D = {2,2,2,6,8,9,9,10} 2

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Median- the middle value in a set of data arrange in increasing/ decreasing order. If there is an even number of entries, the median it the average of the two middle values. Mode Median A = {2,3,6,7,7,8,9} 7 7 B = {2,4,7,7,8,8} 7 & 8 7 C = {2,7,9} ? 7 D = {2,2,2,6,8,9,9,10} 2 7 Weakness to Median: It is not always a data value It does not represent the concentration of data It is not influenced by the data values Strength- Unique It is unaffected by extreme values Application- prices of homes, salaries of employees

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Mean- The mean is the average of all the data values. Mode Median Mean A = {2,3,6,7,7,8,9} 7 7 B = {2,4,7,7,8,8} 7 & 8 7 C = {2,7,9} ? 7 D = {2,2,2,6,8,9,9,10} 2 7

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Mean- The mean is the average of all the data values. The parameter for mean is µ the statistic is Mode Median Mean A = {2,3,6,7,7,8,9} 7 7 6 B = {2,4,7,7,8,8} 7 & 8 7 6 C = {2,7,9} ? 7 6 D = {2,2,2,6,8,9,9,10} 2 7 6 Weakness to Mean: Affected by extreme values Is not always a data value Is sometimes confusing Ex: 2.3 kids in a family Strength- Most commonly used Involves all the data values It is unique Application- Student test scores

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Symbols for Measures of Center PopulationStatistics Meansmu- µ

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