Median interpolation on logarithmic data

[thomas49th]

Homework Statement

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).

Homework Equations

Bin
Mean
Radius Frequency
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

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 I am using logarithmic data? Is there a more suitable way?
Thanks

 

[mighty2000]

Hi there,

Thank you for sharing your data and the approach you have taken so far. It appears that you are using the median interpolation method to find the 10th percentile of your data set. This method can be used for data that is evenly distributed, but it may not be the most suitable for logarithmically increasing data.

In this case, you may want to consider using the geometric mean method to find the 10th percentile. This method takes into account the fact that your data is increasing logarithmically and can provide a more accurate estimate.

To use the geometric mean method, you can follow these steps:

1. Calculate the geometric mean of the lower and upper boundaries of the class where the 10th percentile falls. In this case, it would be:

√(1.58 * 1.74) = 1.659

2. Next, calculate the ratio of the frequency of the class where the 10th percentile falls to the total frequency. In this case, it would be:

18723/612574 = 0.0305

3. Finally, multiply the geometric mean by the frequency ratio to get the estimated 10th percentile. In this case, it would be:

1.659 * 0.0305 = 0.0506

Therefore, the 10th percentile of your data set is estimated to be 0.0506. I hope this helps and I encourage you to explore other methods that may be more suitable for logarithmically increasing data in the future. Best of luck with your research!