Measures of Central Tendency and Dispersion | Skew and Kurtosis

Summarizing Data through numbers


Measures of Central Tendency

Dispersion

Skew and Kurtosis



Measures of Central Tendency

Data set: 3,4,3,1,2,3,9,5,6,7,4,8
Mean
               3+4+3+1+2+3+9+5+6+7++8 /12  = 4.583
Median 
     1,2,3,3,3,4,4,5,6,7,8,9  Hence Answer = 4
Mode
   The value 3 appears 3 times, and 4 appears 2 times and all other values appear once. Hence 3 is the mode.

Where do we want to use Mean, Median and Mode

Choosing between mean and median
    - Bad outliers
            Errors
            Do not provide a realistic picture of the story
    - Good outlierss
            The story is in the outliers

Mode
    - Useful with nominal variables
    - Multi modal distributions


[ Strategy: Lose 1 rupee everyday on 99% of the days. But on 1% of the days , It gave re. 10,00,00,000. ]

Example :- 
   40% - voted for garbage can at 25th meter mark
   45% - voted for garbage can at 75th meter mark
   15% - uniform between 0 and 100 

Measures of Dispersion 

Data set: 3,4,3,1,2,3,9,5,6,7,4,8
Range (Max-Min)  (9-1 = 8)
Inter Quartile Range: 3rd quartile - 1st quartile (75th Percentile- 25th Percentile) (6.5-3 = 3.5)
Sample Standard deviation

Questions that go with Standard deviation
  - Why do we use the square function on the deviations ? What are its implications ?
  - Why do we work on standard deviation and not the variance ?
  - Why do we average by dividing by N-1 and not N ?

Mean absolute Deviation and its variants
  - Use |𝒳i-𝒳| instead of (𝒳i-𝒳)2