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Statistics  for Management  Lesson 3 Summarizing and Describing Numerical Data
Lesson Topics ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Summary Measures  Central Tendency Mean Median Mode Midrange Quartile Midhinge Summary Measures Variation Variance Standard Deviation Coefficient of Variation Range
Measures of Central Tendency Central Tendency Mean Median Mode Midrange Midhinge
The Mean  (Arithmetic Average) ,[object Object],[object Object],[object Object],0  1  2  3  4  5  6  7  8  9  10 0  1  2  3  4  5  6  7  8  9  10  12  14  Mean = 5 Mean = 6 Sample Mean
The Median 0  1  2  3  4  5  6  7  8  9  10 0  1  2  3  4  5  6  7  8  9  10  12  14  Median = 5 Median = 5 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Mode 0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  Mode = 9 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],0  1  2  3  4  5  6 No Mode
Midrange ,[object Object],[object Object],[object Object],[object Object],Midrange 0  1  2  3  4  5  6  7  8  9  10 0  1  2  3  4  5  6  7  8  9  10 Midrange = 5 Midrange  = 5
Quartiles ,[object Object],[object Object],[object Object],25% 25% 25% 25% Q 1 Q 2 Q 3 Q i(n+1) i  4 Data in Ordered Array:  11  12  13  16  16  17  18  21  22  Position of Q 1  = 2.50  Q 1 =12.5 = 1•(9 + 1) 4
Midhinge ,[object Object],[object Object],[object Object],Midhinge =  Data in Ordered Array:  11  12  13  16  16  17  18  21  22 Midhinge =
Summary Measures  Central Tendency Mean Median Mode Midrange Quartile Midhinge Summary Measures Variation Variance Standard Deviation Coefficient of Variation Range
Measures of Variation Variation Variance Standard Deviation Coefficient of Variation Population Variance Sample  Variance Population Standard Deviation Sample  Standard  Deviation Range Interquartile Range
[object Object],[object Object],[object Object],[object Object],[object Object],The Range 7  8  9  10  11  12 Range = 12 - 7 = 5 7  8  9  10  11  12 Range = 12 - 7 = 5
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Interquartile Range Data in Ordered Array:  11  12  13  16  16  17  17  18  21 = 17.5 - 12.5 = 5
[object Object],[object Object],[object Object],[object Object],Variance For the  Population : use  N  in the denominator. For the  Sample  : use  n - 1   in the denominator.
[object Object],[object Object],[object Object],[object Object],Standard Deviation For the   Population:   use   N   in the denominator. For the   Sample  : use   n - 1   in the denominator .
Sample Standard Deviation For the  Sample  : use   n - 1   in the denominator. Data:   10  12  14  15  17  18  18  24 s =  n = 8  Mean =16 =   4.2426 s
Comparing Standard Deviations s  =  =  4.2426 =  3.9686 Value for the Standard Deviation is   larger   for data considered as a   Sample . Data :   10  12  14  15  17  18  18  24 N= 8  Mean =16
Comparing Standard Deviations Mean = 15.5 s  =  3.338   11  12  13  14  15  16  17  18  19  20  21 11  12  13  14  15  16  17  18  19  20  21 Data   B Data  A Mean = 15.5 s =   .9258 11  12  13  14  15  16  17  18  19  20  21 Mean = 15.5 s =   4.57 Data  C
Coefficient of Variation ,[object Object],[object Object],[object Object],[object Object],[object Object]
Comparing Coefficient of Variation ,[object Object],[object Object],[object Object],[object Object],Coefficient of Variation: Stock A:   CV   = 10% Stock B:   CV   =  5%
Shape ,[object Object],[object Object],[object Object],Right-Skewed Left-Skewed Symmetric Mean =  Median =  Mode Mean Median Mode Median Mean Mode
Box-and-Whisker Plot ,[object Object],Median 4 6 8 10 12 Q 3 Q 1 X largest X smallest
Distribution Shape &  Box-and-Whisker Plots Right-Skewed Left-Skewed Symmetric Q 1 Median Q 3 Q 1 Median Q 3 Q 1 Median Q 3
Lesson Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Mean =  Median =  Mode Mean Median Mode Mode Median Mean

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Lesson03_new

  • 1. Statistics for Management Lesson 3 Summarizing and Describing Numerical Data
  • 2.
  • 3. Summary Measures Central Tendency Mean Median Mode Midrange Quartile Midhinge Summary Measures Variation Variance Standard Deviation Coefficient of Variation Range
  • 4. Measures of Central Tendency Central Tendency Mean Median Mode Midrange Midhinge
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11. Summary Measures Central Tendency Mean Median Mode Midrange Quartile Midhinge Summary Measures Variation Variance Standard Deviation Coefficient of Variation Range
  • 12. Measures of Variation Variation Variance Standard Deviation Coefficient of Variation Population Variance Sample Variance Population Standard Deviation Sample Standard Deviation Range Interquartile Range
  • 13.
  • 14.
  • 15.
  • 16.
  • 17. Sample Standard Deviation For the Sample : use n - 1 in the denominator. Data: 10 12 14 15 17 18 18 24 s = n = 8 Mean =16 = 4.2426 s
  • 18. Comparing Standard Deviations s = = 4.2426 = 3.9686 Value for the Standard Deviation is larger for data considered as a Sample . Data : 10 12 14 15 17 18 18 24 N= 8 Mean =16
  • 19. Comparing Standard Deviations Mean = 15.5 s = 3.338 11 12 13 14 15 16 17 18 19 20 21 11 12 13 14 15 16 17 18 19 20 21 Data B Data A Mean = 15.5 s = .9258 11 12 13 14 15 16 17 18 19 20 21 Mean = 15.5 s = 4.57 Data C
  • 20.
  • 21.
  • 22.
  • 23.
  • 24. Distribution Shape & Box-and-Whisker Plots Right-Skewed Left-Skewed Symmetric Q 1 Median Q 3 Q 1 Median Q 3 Q 1 Median Q 3
  • 25.