Right, the *tool to narrow the search* is what I was most concerned with, and why I suggested that using the provided data plots to find the real index median of applicants accepted.

why is the median any more useful than the 25th and 75th percentiles?

I misspoke. At least it seems GCoop understood me. Let me explain.

There are 4 students admitted to school Z, with the following scores:

A: 170 and 3.6

B: 169 and 3.8

C: 168 and 3.65

D: 166 and 3.81

The 25% would be 166, and 75% would be 170 for LSAT.

The 25% would be 3.6, and the 75% would be 3.81 for GPA.

If the index is calculated with =10*(GPA)+LSAT:

A: 206

B: 207

C: 204.5

D: 204.1

This puts the 25% and 75% index numbers at 204.1 and 207, respectively.

Conversely, using the 25% and 75% numbers with either counterparts, the index numbers are 202 and 208.1.

If I have the time I may do this for a school or two to see how it compares.