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Understanding Central Tendency Properties in Statistics www.HelpWithAssignment.com
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Numerical Data Properties RelativeStanding Central Tendency Variation Mean Range Percentiles Interquartile Range Median Z–scores Variance Mode Standard Deviation Numerical DataProperties & Measures www.HelpWithAssignment.com
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Measure of central tendency Most common measure Acts as ‘balance point’ Affected by extreme values (‘outliers’) Formula (sample mean) Mean n X i X X X … n 1 2 1 i X n n www.HelpWithAssignment.com
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Raw Data: 10.3 4.9 8.9 11.7 6.3 7.7 X X X X X X X 1 2 3 4 5 6 1 X n 6 10 8 9 11 6 3 . . . . 6 30 . www.HelpWithAssignment.com
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Numerical DataProperties & Measures Numerical Data Properties RelativeStanding Central Variation Tendency Percentiles Mean Range Median Interquartile Range Z–scores Mode Variance Standard Deviation www.HelpWithAssignment.com
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Measure of central tendency Middle value in ordered sequence If n is odd, middle value of sequence If n is even, average of 2 middle values Position of median in sequence Not affected by extreme values Median n 1 Positioning Point 2 www.HelpWithAssignment.com
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Raw Data: 24.1 22.6 21.5 23.7 22.6 Ordered: 21.5 22.6 22.6 23.7 24.1 Position: 1 2 3 4 5 Median Example Odd-Sized Sample n 1 5 1 Positioning Point 3 0 . 2 2 Median 22 6 . www.HelpWithAssignment.com
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Median Example Even-Sized Sample Raw Data: 10.3 4.9 8.9 11.7 6.3 7.7 Ordered: 4.9 6.3 7.78.9 10.3 11.7 Position: 1 2 34 5 6 n 1 6 1 Positioning Point 3 5 . 2 2 7 7 8 9 . . Median 8 30 . 2 www.HelpWithAssignment.com
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Numerical DataProperties & Measures Numerical Data Properties RelativeStanding Central Variation Tendency Range Mean Percentiles Interquartile Range Median Z–scores Mode Variance Standard Deviation www.HelpWithAssignment.com
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Measure of central tendency Value that occurs most often Not affected by extreme values May be no mode or several modes May be used for quantitative or qualitative data Mode www.HelpWithAssignment.com
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No ModeRaw Data: 10.3 4.9 8.9 11.7 6.3 7.7 One ModeRaw Data: 6.3 4.9 8.9 6.3 4.9 4.9 More Than 1 ModeRaw Data: 21 28 28 41 4343 Mode Example www.HelpWithAssignment.com
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Thinking Challenge You’re a financial analyst for Prudential-Bache Securities. You have collected the following closing stock prices of new stock issues: 17, 16, 21, 18, 13, 16, 12, 11. Describe the stock pricesin terms of central tendency. www.HelpWithAssignment.com
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Central Tendency Solution Mean n X i X X X … 1 2 8 i 1 X n 8 17 16 21 18 13 16 12 11 8 15 5 . www.HelpWithAssignment.com
n 1 8 1 4 5 . Positioning Point 2 2 16 16 Median 16 2 www.HelpWithAssignment.com
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Mode Raw Data: 17 16 21 18 13 16 12 11 Mode = 16 Central Tendency Solution www.HelpWithAssignment.com
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Summary of Central Tendency Measures Measure Formula Description Mean Balance Point X / n i Median ( n +1) Middle Value Position 2 When Ordered Mode none Most Frequent www.HelpWithAssignment.com
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