Hi Lea,
So I begin by reusing the last result
Table[With[{i = i}, Defer[data[[i]]]], {i, 1, 10}]
{data[[1]], data[[2]], data[[3]], data[[4]], data[[5]], data[[6]],
data[[7]], data[[8]], data[[9]], data[[10]]}
I don't use FoldLIst often so I started with a generic case to test
FoldList[f, 0, Table[With[{i = i}, Defer[data[[i]]]], {i, 1, 10}]]
{0, f[0, data[[1]]], f[f[0, data[[1]]], data[[2]]],
f[f[f[0, data[[1]]], data[[2]]], data[[3]]] ,...}
It seems to work so far. Now we define f to add whatever is passed to it and we obtain the result
FoldList[Plus[##] &, 0,
Table[With[{i = i}, Defer[data[[i]]]], {i, 1, 10}]]
Then for data=Range[10]
the above would evaluate to
{0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55}