How Excel calculate the "Quartile" function for 25th and 75th percentile?

Question

by detail, please

Answer 1

The following is the algorithm used to calculate QUARTILE():

1. Find the kth smallest member in the array of values, where:

        k=(quart/4)*(n-1))+1

If k is not an integer, truncate it but store the fractional portion (f) for use in step 3.

And where:

quart = value between 0 and 4 depending on which  

        quartile you want to find.

n = number of values in the array

2. Find the smallest data point in the array of values that is

         greater than the kth smallest -- the (k+1)th smallest

         member.

3. Interpolate between the kth smallest and the (k+1)th

         smallest values:

         Output = a[k]+(f*(a[k+1]-a[k]))

         a[k] = the kth smallest

         a[k+1] = the k+1th smallest