Learn the calculation method of quantile value in n minutes

It is often seen in technical or business indicators 「 Quantile value 」, How is the quantile calculated ？

The simple calculation is  

1. Calculate the total number of intervals  S（ Number of all elements -1  Is the total number of intervals ）,

2. The element values are arranged from small to large

3. Calculate the quantile position , Such as  M  Quantile position  =  Rounding down (S*(M/100) + 1 )

4. Calculate the quantile value ,M  Quantile value  = M  The element value corresponding to the position of the quantile value

If calculated in a precise way ,3  and  4  Step by step

3. M  Quantile position  = (S*(M/100) + 1 )

X  by  M  The integer part of the quantile position .

P  by  M  The decimal part of the position of the quantile .

4.M  Quantile value  = X Position element value  + （X+1 Position element value  - X Position element value ）* P

Take a chestnut

Suppose a live broadcast has 4  Audience , The viewing duration is 20  second ,10  second ,40  second , 30  second

The viewing time of this live broadcast  50  What is the quantile value ？

The calculation process ： 

1. S = 3,

2. Sort  10  second ,20  second ,30  second , 40  second

3.50 Quantile position  = 3*(50/100) +1 = 2.5

X = 2

P = 0.5

4.50 Quantile value  = 20  second  + （30-20）* 0.5 = 25  second