Mean on subsets of a subset

Question

Still learning R, but I've personally accepted that this is impossible, and I hope one of you can prove me wrong.

I'm looking to find the mean for values <= 25th percentile, and the mean for values >= 75th percentile; but not for the whole data set. I would like to find these means for subsets of data, from which the percentiles were found.

This will generate data that resembles my own:

library(data.table)
DT <- data.table(V1 <- c('AR','AR','AR','AR','AR','AR','AD','AD','AD','AD','AD','AD','BD',
                         'BD','BD','BD','BX','CX','DX','DX','DD','DD','DD','DD','DR','DR',
                         'DR','DR','DR','DR'),
                 V2 <- c(.12,.02,.03,.22,.44,.09,.11,.17,.15,.26,.29,.27,.16,.16,.02,.12,.02,
                         .03,.22,.44,.09,.11,.17,.15,.26,.29,.27,.16,.16,.02))

Looks like:

    V1   V2
 1: AR 0.12
 2: AR 0.02
 3: AR 0.03
 4: AR 0.22
 5: AR 0.44
 6: AR 0.09
 7: AD 0.11
 8: AD 0.17
 9: AD 0.15
10: AD 0.26
11: AD 0.29
12: AD 0.27
13: BD 0.16
14: BD 0.16
15: BD 0.02
16: BD 0.12
17: BX 0.02
18: CX 0.03
19: DX 0.22
20: DX 0.44
21: DD 0.09
22: DD 0.11
23: DD 0.17
24: DD 0.15
25: DR 0.26
26: DR 0.29
27: DR 0.27
28: DR 0.16
29: DR 0.16
30: DR 0.02

First step: Calulate median, 25th percentile, 75th percentile, and count appearances of each A_, B_, C_, D_. Got it:

dt.qtile <- DT[, list(Bottom = quantile(V2, .25), 
                      Middle = quantile(V2, .5),  
                         Top = quantile(V2, .75),
                 Appearances = .N), by = V1]

Produces:

   V1 Bottom Middle    Top Appearances
1: AR  0.045  0.105 0.1950           6
2: AD  0.155  0.215 0.2675           6
3: BD  0.095  0.140 0.1600           4
4: BX  0.020  0.020 0.0200           1
5: CX  0.030  0.030 0.0300           1
6: DX  0.275  0.330 0.3850           2
7: DD  0.105  0.130 0.1550           4
8: DR  0.160  0.210 0.2675           6

This is where I think it's impossible. I would like to find the values in the original V2 (DT$V2) that are less than or equal to the value of the 25th percentile, then greater than or equal to 75th percentile for each letter combination in V1.

    V1   V2
 1: AR 0.12 -  Ignore   -
 2: AR 0.02 <= 0.045    \
 3: AR 0.03 <= 0.045    / mean = 0.05 (Bottom)
 4: AR 0.22 >= 0.1950   \
 5: AR 0.44 >= 0.1950   / mean = 0.33 (Top)
 6: AR 0.09 -  Ignore   -
    ------
 7: AD 0.11 <= 0.155    > mean = 0.11 (Bottom)
 8: AD 0.17 -  Ignore   -
 9: AD 0.15 -  Ignore   -
10: AD 0.26 >= 0.2675   \
11: AD 0.29 >= 0.2675    | mean = 0.2733 (Top)
12: AD 0.27 >= 0.2675   /
      ...
25: DR 0.26 -  Ignore   -
26: DR 0.29 >= 0.2675   \
27: DR 0.27 >= 0.2675   / mean = 0.28 (Top)
28: DR 0.16 <= 0.16    \
29: DR 0.16 <= 0.16     | mean = 0.17 (Bottom)
30: DR 0.02 <= 0.16    /

Average the values in V2 that are <= 25th percentile, then average the values that are >= 75th percentile.

The new output should be something like this:

   V1 Bottom Middle    Top Appearances
1: AR  0.025  0.105 0.3300           6
2: AD  0.110  0.215 0.2733           6
                   ...
8: DR  0.170  0.210 0.2800           6

This gets me close:

DT[V2 < quantile(V2, .25), mean(V2), by = V1]

But it's computing the quantile for the whole data set, not each letter combination.

So I try:

 DT[V2 < DT[, quantile(V2, .25), by = V1], mean(V2), by = V1]

I get this:

Error in `[.data.table`(DT, V2 < DT[, quantile(V2, 0.25), by = V1], mean(V2),  : 
  i is invalid type (matrix). 
Perhaps in future a 2 column matrix could return a list of elements of DT
 (in the spirit of A[B] in FAQ 2.14). 
Please let datatable-help know if you'd like this, or add your comments to FR #657.

I know this has to be simple, but I just can't see it. What am I missing? Let me know where I can clarify.

I appreciate your help in advance!

EDIT

DT[, list( Bottom = mean(V2[V2 <= quantile(V2, 0.25)]), 
           Middle = median(V2), 
              Top = mean(V2[V2 >= quantile(V2, 0.75)]), 
      Appearances = .N), by = V1]

I would never have found this on my own.

Answer 1

DT[, mean(V2[V2 < quantile(V2, 0.25)]), by = V1]
   V1    V1
1: AR 0.025
2: AD 0.130
3: BD 0.020
4: BX   NaN
5: CX   NaN
6: DX 0.220
7: DD 0.090
8: DR 0.020

DT[, mean(V2[V2 > quantile(V2, 0.75)]), by = V1]
   V1   V1
1: AR 0.33
2: AD 0.28
3: BD  NaN
4: BX  NaN
5: CX  NaN
6: DX 0.44
7: DD 0.17
8: DR 0.28