# Percentile and Moments

Percentile

It gives the level of an element in data. Lets discuss with an example :- 1,2,3,4,5,6,7,8,9 ,10 we have this data in increasing order. To find Kth percentile :-

Step 1 : Arrange the elements in ascending order

Step 2 : multiple K percent with number of elements

Step 3 : Let result be x. If the result is a whole number then find the average of xth and (x+1)th element that would be the percentile.

Step 4 : If result is not a whole number then round it to the nearest whole number and then the xth element will be the result.

From resultant percentile we can check if a certain value falls in the above region or below region of that percentile.

Lets find result for our example for 50th percentile and 85th percentile.

In our example data we have N = 10 ( number of elements)

So for K = 50

(50*10)/100 = 5 , whole number.

Percentile = (5+6)/2 = 5.5

For K = 85

(85*10)/100 = 8.5 , rounding off = 9

Percentile = 9th element from starting i.e 9

Moment

It basically measures the shape of our data distribution. Everything will be clear by an example. First just keep in mind that first moment is Mean , second is Variance , third is Skew and fourth is Kurtosis.

First Moment : Mean

It is average of all the elements. To know mean check this out https://datascience.travel.blog/2018/12/18/mean-median-and-mode/

Second Moment : Variance

To know variance check this out https://datascience.travel.blog/2018/12/19/variance-and-standard-deviation/

Third Moment : Skew

It talks about lopsidedness of data distribution. It could be negative (left side skewed) or positive (right side skewed).

Fourth Moment : Kurtosis

It indicates the spread of tail of data distribution. It basically talks about the sharpness of the peak of data distribution.

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