Understanding Central Tendency Properties in Statistics www.HelpWithAssignment.com

Numerical Data Properties Mean Median Mode Variation Range Variance Standard Deviation Interquartile Range Percentiles Relative Standing Z–scores Central Tendency Numerical Data Properties & Measures www.HelpWithAssignment.com

Measure of central tendency Most common measure Acts as ‘balance point’ Affected by extreme values (‘outliers’) Formula (sample mean) Mean www.HelpWithAssignment.com

Raw Data: 10.3 4.9 8.9 11.7 6.3 7.7 X X n X X X X X X                 1 1 2 3 4 5 6 6 10 8 9 11 6 3 6 30 . . . . . www.HelpWithAssignment.com

Numerical Data Properties & Measures Mean Median Mode Range Variance Standard Deviation Interquartile Range Numerical Data Properties Central Tendency Variation Percentiles Relative Standing Z–scores www.HelpWithAssignment.com

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 Positioning Point   n 1 2 www.HelpWithAssignment.com

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 Positioning Point Median       n 1 2 5 1 2 3 0 22 6 . . www.HelpWithAssignment.com

Median Example Even-Sized Sample Positioning Point Median         n 1 2 6 1 2 3 5 7 7 8 9 2 8 30 . . . . Raw Data: 10.3 4.9 8.9 11.7 6.3 7.7 Ordered: 4.9 6.3 7.7 8.9 10.3 11.7 Position: 1 2 3 4 5 6 www.HelpWithAssignment.com

Numerical Data Properties & Measures Mean Median Mode Range Variance Standard Deviation Interquartile Range Numerical Data Properties Central Tendency Variation Percentiles Relative Standing Z–scores www.HelpWithAssignment.com

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

No Mode Raw Data: 10.3 4.9 8.9 11.7 6.3 7.7 One Mode Raw Data: 6.3 4.9 8.9 6.3 4.9 4.9 More Than 1 Mode Raw Data: 21 28 28 41 43 43 Mode Example www.HelpWithAssignment.com

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 prices in terms of central tendency. www.HelpWithAssignment.com

Central Tendency Solution Mean X X n X X X i i n                 1 1 2 8 8 17 16 21 18 13 16 12 11 8 15 5 … . www.HelpWithAssignment.com

Central Tendency Solution Median Raw Data: 17 16 21 18 13 16 12 11 Ordered: 11 12 13 16 16 17 18 21 Position: 1 2 3 4 5 6 7 8 Positioning Point Median         n 1 2 8 1 2 4 5 16 16 2 16 . www.HelpWithAssignment.com

Mode Raw Data: 17 16 21 18 13 16 12 11 Mode = 16 Central Tendency Solution www.HelpWithAssignment.com

Summary of Central Tendency Measures Measure Formula Description Mean  X i / n Balance Point Median ( n +1) Position 2 Middle Value When Ordered Mode none Most Frequent www.HelpWithAssignment.com

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