Understanding central tendency properties in statistics

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Understanding central tendency properties in statistics

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