Your data covers a very narrow frequency range, the gain variations are small and the standard deviation is just slightly smaller than the largest differences in gain. I did not see any adjacent pair of frequencies where the gain difference was larger than the standard deviation of the gain at either frequency. Most implementations of filters using physical components would likely have larger variations than your data shows. Given the size of the standard deviations I doubt that any gain figures to the right of the decimal point have much meaning. How many measurements did you take at each frequency?
To answer your original question about equalization: I will assume that you have an FFT with bins at each of the frequencies listed in your file and that you will make no corrections to any other frequencies. Loop through the FFT output array. Let g[i] represent the measured gain at the ith bin. Let g0 be the desired nominal gain (assumed to be equal for all frequencies). Let ge[i] be the gain equalization adjustment. Then ge[i] = g0/g[i].
If you multiply each component by ge[i] then all your gains will be g0.
If you apply this to some sort of signal. you need to consider several things. 1. The output of the FFT is complex even if the inputs are real. By looking only at the gain you are losing any phase information. 2. Spectral leakage. If the sampling frequency is not synchronous with the signal or the length of the sample set is not an integral multiple of the sample period, the frequency components of the signal spill over into adjacent bins. This may create errors in your equalization. 3. Can you even tell the difference on a real signal? Given the relatively small gain variations and the large standard deviation, will the corrections be lost in the noise?
Lynn
