Let's break down the task step by step.

1. Separate the data for the different particles: GatherBy
2. Sort data by frame number (not really necessary as it's sorted, but let's do it anyway): SortBy
3. Extract the positions and calculate the MSD.

I have your data stored in the variable data.

GatherBy[data, First] separates into sublists having the same first element (same particle). Let's take the first sublist, sublist = First@GatherBy[data, First].

sublist = SortBy[sublist, #[[2]]&] sorts the sublist by the second element (frame number).

Now take the difference of sequential coordinates, take the squared norm of that difference, and calculate the mean: Mean[#.#& /@ sublist].

Putting it all together:

gatheredData = GatherBy[data, First];

msd = Function[sublist, 
  Mean[#.# & /@ 
    Differences@SortBy[sublist, #[[2]] &][[All, {3, 4}]]
  ]
] /@ gatheredData

You may wish to pair up this list of results with the particle indices:

Transpose[{gatheredData[[All, 1, 1]], msd}]

(* ==> {{1., 0.513101}, {2., 2.69401}, {3., 0.887661}} *)

Again, this is not necessary if your list was originally sorted by particle index, but it's important if it wasn't.

Recommended reading to understand this code:

• Map and list manipulation

• Pure functions

• List indexing (Part)

Let's break down the task step by step.

1. Separate the data for the different particles: GatherBy
2. Sort data by frame number (not really necessary as it's sorted, but let's do it anyway): SortBy
3. Extract the positions and calculate the MSD.

I have your data stored in the variable data.

GatherBy[data, First] separates into sublists having the same first element (same particle). Let's take the first sublist, sublist = First@GatherBy[data, First].

sublist = SortBy[sublist, #[[2]]&] sorts the sublist by the second element (frame number).

Now take the difference of sequential coordinates, take the squared norm of that difference, and calculate the mean: Mean[#.#& /@ sublist[[All, {3,4}]] ].

Putting it all together:

gatheredData = GatherBy[data, First];

msd = Function[sublist, 
  Mean[#.# & /@ 
    Differences@SortBy[sublist, #[[2]] &][[All, {3, 4}]]
  ]
] /@ gatheredData

You may wish to pair up this list of results with the particle indices:

Transpose[{gatheredData[[All, 1, 1]], msd}]

(* ==> {{1., 0.513101}, {2., 2.69401}, {3., 0.887661}} *)

Again, this is not necessary if your list was originally sorted by particle index, but it's important if it wasn't.

Recommended reading to understand this code:

• Map and list manipulation

• Pure functions

• List indexing (Part)

Let's break down the task step by step.

1. Separate the data for the different particles: GatherBy
2. Sort data by frame number (not really necessary as it's sorted, but let's do it anyway): SortBy
3. Extract the positions and calculate the MSD.

I have your data stored in the variable data.

GatherBy[data, First] separates into sublists having the same first element (same particle). Let's take the first sublist, sublist = First@GatherBy[data, First].

sublist = SortBy[sublist, #[[2]]&] sorts a sublist by the second element (frame number).

Now take the difference of sequential coordinates, take the squared norm of that difference, and calculate the mean: Mean[#.#& /@ sublist].

Putting it all together:

Function[sublist, 
  Mean[#.# & /@ 
    Differences@SortBy[sublist, #[[2]] &][[All, {3, 4}]]]
] /@ GatherBy[data, First]

Let's break down the task step by step.

1. Separate the data for the different particles: GatherBy
2. Sort data by frame number (not really necessary as it's sorted, but let's do it anyway): SortBy
3. Extract the positions and calculate the MSD.

I have your data stored in the variable data.

GatherBy[data, First] separates into sublists having the same first element (same particle). Let's take the first sublist, sublist = First@GatherBy[data, First].

sublist = SortBy[sublist, #[[2]]&] sorts the sublist by the second element (frame number).

Now take the difference of sequential coordinates, take the squared norm of that difference, and calculate the mean: Mean[#.#& /@ sublist].

Putting it all together:

gatheredData = GatherBy[data, First];

msd = Function[sublist, 
  Mean[#.# & /@ 
    Differences@SortBy[sublist, #[[2]] &][[All, {3, 4}]]
  ]
] /@ gatheredData

You may wish to pair up this list of results with the particle indices:

Transpose[{gatheredData[[All, 1, 1]], msd}]

(* ==> {{1., 0.513101}, {2., 2.69401}, {3., 0.887661}} *)

Again, this is not necessary if your list was originally sorted by particle index, but it's important if it wasn't.

Recommended reading to understand this code:

• Map and list manipulation

• Pure functions

• List indexing (Part)