how do i add more major / labeled ticks and get non linear mean of a nested list / ListPlot

Question

I understand I can use Ticks in order to change the ticks, but I don't seem to be able to choose the number of ticks but only automatic/none or each individual tick.

My graph currently shows each tick on the y-axis as a exponent, but I would like it to show each half or quarter exponent as a labeled tick.

And how do I get a non-linear mean similar to FindFit when I only have a nested list? Since I'd like to get a line showing the average of all the plots to better visualize the data.

Edit: and how would I get the mean of y for every x?

I don't seem to find any answers and been searching for some time now.

Edit2: its readings of wifi, x is distance in meters and y is mW

data = {{5, 4.2180506341246474`*^-6}, {10, 8.52072632483756`*^-8}, {15, 
1.9122244963644555`*^-7}, {20, 4.583863072516606`*^-8}, {25, 
8.138004722270266`*^-9}, {30, 1.5236067293781787`*^-9}, {35, 
1.9689607977818997`*^-8}, {40, 1.0356015584142407`*^-9}, {45, 
5.1171329242687634`*^-9}, {50, 1.3150023891748594`*^-9}, {55, 
2.75925031324734`*^-10}, {60, 6.44739787013969`*^-10}, {65, 
1.269501699841764`*^-9}, {70, 3.368354766378623`*^-11}, {75, 
2.882696661780091`*^-11}, {80, 2.4182183464215087`*^-10}, {85, 
3.982588451684898`*^-10}, {90, 6.737749787589035`*^-11}, {95, 
8.116170964273532`*^-11}, {100, 6.030125496210169`*^-10}, {5, 
2.1476267234440643`*^-6}, {10, 2.3244825805810026`*^-6}, {15, 
1.376564833236655`*^-7}, {20, 2.972699644181631`*^-8}, {25, 
4.737092876342727`*^-8}, {30, 8.191016754218927`*^-9}, {35, 
8.898775290782262`*^-9}, {40, 6.666360149797248`*^-9}, {45, 
7.417481547646882`*^-10}, {50, 1.739062622942222`*^-9}, {55, 
4.842018315239307`*^-10}, {60, 6.521126861389932`*^-10}, {65, 
1.3985827036122423`*^-9}, {70, 1.492147178019141`*^-10}, {75, 
4.2134547161500933`*^-10}, {80, 6.831201201202558`*^-11}, {85, 
1.0802444285398891`*^-10}, {90, 1.820839088556722`*^-11}, {95, 
1.7132267011413344`*^-10}, {100, 3.754919516870398`*^-10}, {5, 
0.00001044694319643655`}, {10, 5.69674157685483`*^-8}, {15, 
8.315750786932738`*^-8}, {20, 1.0019648005036426`*^-7}, {25, 
5.5374731613526704`*^-8}, {30, 1.9485705516272266`*^-9}, {35, 
1.0113888568168166`*^-8}, {40, 1.7883852014284595`*^-10}, {45, 
1.3475441439488888`*^-9}, {50, 9.038105865797945`*^-9}, {55, 
1.5816145773480966`*^-9}, {60, 9.346731416982425`*^-10}, {65, 
1.9747183113229924`*^-10}, {70, 7.813851506825158`*^-10}, {75, 
1.8343422005958098`*^-10}, {80, 2.432821218173799`*^-11}, {85, 
4.1395116687213914`*^-10}, {90, 2.1055234143168004`*^-10}, {95, 
7.072714932230835`*^-10}, {100, 1.0580839584733221`*^-10}}

Answer 1

You can get the average of your data like this:

avg = Mean@Select[data, Function[p, p[[1]] == #]] & /@ DeleteDuplicates[data[[All, 1]]];

The right part finds all distinct x-values. The left function calculates the mean value for one x-value and the /@ calls this for each of the x values. You can then fit a function to the averaged data:

fit1 = NonlinearModelFit[avg, a/r^b, {a, b}, r];

Probably there is some reason why you want to fit the averaged data, but note that in this case fitting to the original data gives the same result (fit2 = NonlinearModelFit[data, a/r^b, {a, b}, r];).

Plot data and fit with something like:

Show[ListLogPlot[{data, avg}], LogPlot[fit1[x], {x, 0, 100}]]

You can find a very simple way to customize your ticks in this answer.

Just out of curiosity: Wifi power is said to follow an inverse-square law, but in your case it seems to be stronger attenuated!?

Answer 2

You can use Merge or GroupBy or GatherBy to group by the first column and get the mean of each group:

means1 = KeyValueMap[List] @ Merge[Mean][Rule @@@ data]
means2 = KeyValueMap[List] @ GroupBy[data, First -> Last, Mean];
means3 = {#[[1, 1]], Mean[#[[All, 2]]]} & /@ GatherBy[data, First];
means1 == means2 == means3

True

ListLogPlot[{data, means1}, Joined -> {False, True}, ImageSize -> Medium]

Answer 3

Anybody can set Ticks using Table like here:

ListLogPlot[data, 
 Ticks -> {Automatic, 
   Table[{10^-i, ScientificForm[10.^-i, 2]}, {i, 5, 11, 0.5}]}]