Lesson03_new

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 =

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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