This is an aggregation problem, not a reshaping problem as the question originally suggested — we wish to aggregate each column into a mean and standard deviation by ID. There are many packages that handle such problems. In the base of R it can be done using aggregate like this (assuming DF is the input data frame):
ag <- aggregate(. ~ ID, DF, function(x) c(mean = mean(x), sd = sd(x)))
Note 1: A commenter pointed out that ag is a data frame for which some columns are matrices. Although initially that may seem strange, in fact it simplifies access. ag has the same number of columns as the input DF. Its first column ag[[1]] is ID and the ith column of the remainder ag[[i+1]] (or equivalanetly ag[-1][[i]]) is the matrix of statistics for the ith input observation column. If one wishes to access the jth statistic of the ith observation it is therefore ag[[i+1]][, j] which can also be written as ag[-1][[i]][, j] .
On the other hand, suppose there are k statistic columns for each observation in the input (where k=2 in the question). Then if we flatten the output then to access the jth statistic of the ith observation column we must use the more complex ag[[k*(i-1)+j+1]] or equivalently ag[-1][[k*(i-1)+j]] .
For example, compare the simplicity of the first expression vs. the second:
ag[-1][[2]]
## mean sd
## [1,] 36.333 10.2144
## [2,] 32.250 4.1932
## [3,] 43.500 4.9497
ag_flat <- do.call("data.frame", ag) # flatten
ag_flat[-1][, 2 * (2-1) + 1:2]
## Obs_2.mean Obs_2.sd
## 1 36.333 10.2144
## 2 32.250 4.1932
## 3 43.500 4.9497
Note 2: The input in reproducible form is:
Lines <- "ID Obs_1 Obs_2 Obs_3
1 43 48 37
1 27 29 22
1 36 32 40
2 33 38 36
2 29 32 27
2 32 31 35
2 25 28 24
3 45 47 42
3 38 40 36"
DF <- read.table(text = Lines, header = TRUE)