**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

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