Hide Notes 

Slide 1: Understanding Central Tendency Properties in Statistics Click to edit Master subtitle style 2/11/11 www.HelpWithAssignment.com
Slide 2: Numerical Data Properties & M easures Numerical Data Centra l Mea Tende Media ncy n n Mod e Properties Variati Relati ve Standi ng les Z– Percenti on Rang Range Varian e Interquartile ce Standard scores Deviation 2/11/11 www.HelpWithAssignment.com
Slide 3: Mean 1. 2. 3. 4. 5. Measure of central tendency Most common measure Acts as ‘balance point’ Affected by extreme values (‘outliers’) Formula (sample mean) X i X + X +…+ X 2 n X = i =1 = 1 n n 2/11/11 ∑ n
Slide 4: Raw Data: X = =1 n = 0 10.3 4.9 8.9 11.7 6.3 7.7 X +X +X +X +X +X 2 3 4 5 6 =1 6 61 ∑X 1 . + . + 89+1 . + 63+ . = .3 0 2/11/11
Slide 5: Numerical Data Properties & M easures Numerical Properti Data es Variati on Centr Tenden al cy Mea n Medi Mod an e Relati ve Standi ng Percenti les Z– scores e Interquartile Range Varian ce Standard Rang Deviation 2/11/11
Slide 6: Median 1. 2. 3. 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 4. n Not affected by extreme values + 1 = Positioni 2 ng Point 2/11/11
Slide 7: Median Example Odd-Sized Sample  Raw Data: 24.1 22.6 21.5   Ordered: Position: 21.5 1 22.6 2 22.6 3 23.7 23.7 4 22.6 24.1 5 Positioni ng Media n Point = 2 .6 2 = n+1 2 = 5+1 2 = 3.0 2/11/11
Slide 8: Median Example Even-Sized Sample Raw Data: Ordered: 11.7 Position: Positioni ng Media n = 2 10.3 4.9 8.9 11.7 6.3 7.7 4.9 6.3 7.7 8.9 10.3 1 2 = Point 7.7 + 8.9 2 = 8.3 0 2/11/11 3 n+1 = 4 6+1 2 5 = 3.5 6
Slide 9: Numerical Data Properties & M easures Numerical Properti Data Centr Tenden al cy Mea n Media n Mod es Variati on Relati ve Standi ng Percenti les Z– scores Rang e Interquartile Range Varian ce Standard e Deviation 2/11/11
Slide 10: Mode 1. 2. 3. 4. 5. 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 2/11/11
Slide 11: Mode Example  No Mode Raw Data: One Mode Raw Data: 10.3 6.3 4.9 4.9 28 8.9 8.9 28 11.7 6.3 41 6.3 4.9 43 7.7 4.9 43   More Than 1 Mode Raw Data: 21 2/11/11
Slide 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 prices in terms of central tendency. 2/11/11
Slide 13: Central Tendency Solution Mean X + X +…+ X 2 8 X = i= 1 = 1 n 8 = 1 +1 + 2 +1 +1 +1 +1 +1 7 5 6 1 8 83 6 2 1 ∑Xi n = 1 .5 2/11/11
Slide 14: Central Tendency Solution Median • Raw Data: • Ordered: • Position: 17 16 21 18 13 16 12 11 11 12 13 16 16 17 18 21 12345678 = Positioning Point Media n = 1 +1 6 2 6 n+1 2 6 = 8+1 2 = 4.5 =1 2/11/11
Slide 15: Central Tendency Solution Mode Raw Data: 11 Mode = 16 17 16 21 18 13 16 12 2/11/11
Slide 16: Summary of Central Tendency Measu Mea re Media n n Mod e Formu Σ la X i / n (n+1 2 ) Positio non n e Descript Balance ion Middle Point When Value Most Ordered Frequent 2/11/11
Slide 17: HelpW ithAssign ment.com  At HelpWithAssignment.com we provide best quality Assignment help, Homework help, Online Tutoring and Thesis and Dissertation help as well. For any of the above services you can contact us at http://www.helpwithassignment.com/ and http://www.helpwithassignment.com/statistics-a 2/11/11
Slide 18: HelpW ithAssign ment.com  You can follow us on our blogs at http://helpwithassignment.blogspot.com/ and http://helpwithassignment.wordpress.com/ Thank You 2/11/11