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Understanding Central Tendency Properties in Statistics

In Statistics, Measures of Central Tendency are numerical values that locate, in some sense, the centre of a set of data. The term average is often associated with all measures of central tendency.

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Understanding Central Tendency Properties in Statistics

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  1. Understanding Central Tendency Properties in Statistics www.HelpWithAssignment.com

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

  3. n  X i X  X  …  X  1 2 n 1 i X   n n Mean • Measure of central tendency • Most common measure • Acts as ‘balance point’ • Affected by extreme values (‘outliers’) • Formula (sample mean) • www.HelpWithAssignment.com

  4. 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

  5. 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

  6. Median • 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 n  1 Positioning Point  2 • www.HelpWithAssignment.com

  7. Median Example Odd-Sized Sample • 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 n  1 5  1 Positioning Point    3 . 0 2 2 Median  22 . 6 • www.HelpWithAssignment.com

  8. 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

  9. 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

  10. Mode • 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 • www.HelpWithAssignment.com

  11. Mode Example • 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 • www.HelpWithAssignment.com

  12. 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

  13. 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

  14. 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 n  1 8  1    4 . 5 Positioning Point 2 2 16  16 Median   16 2 • www.HelpWithAssignment.com

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

  16. 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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