# Median interpolation on logarithmic data

1. Sep 14, 2009

### thomas49th

1. The problem statement, all variables and given/known data
Hello, I have a set of data that is grouped into bins. The bin sizes increase logarithmically by 10% (1.1 x the previous bin).

2. Relevant equations
Bin
Mean
1.03 4924
1.10 9938
1.21 14009
1.32 12269
1.44 15813
1.58 18723
1.74 21471
... ...

My total frequency is 612574
I used excel's frequency function. For the first group any data that is greater than 1.03 and less than 1.10 is put into that group. So you can write it

1.03<= x < 1.10

so the lower class boundary is 1.03

3. The attempt at a solution

using the median interpolation formulae

lower class boundary + ((n/2*[culmalative frequency of the previous classes])/frequency of class) * class width

So for the 10% percentile:

it lies in class 1.58.

1.58 + (((612574/2)-56953)/18723) . (1.74 - 1.58)

= 3.7107

Which cannot be. Is this because im using logarithmic data? Is there a more suitable way?
Thanks