data = {{x1,y1},{x2,y2},...}

dataBinned = {{(x1+x2)/2, (y1+y2}/2, N/((x2 - x1)(y2-y1))},{(x1+x2)/2, (y2+y3}/2, N/((x2 - x1)(y3-y2))}, …, {(x2+x3)/2, (y1+y2}/2, N/((x3 - x2)(y2-y1))},{(x2+x3)/2, (y2+y3}/2, N/((x3 - x2)(y3-y2))}, …}

(*Organizing data into bins*)
data1Bins = Partition[Sort[#], Round[Length[#]/#2]] &[data1, n];
(*Construction the binned data*)
data1Binned =
  Table[{(data1Bins[[i]][[1]] + data1Bins[[i]][[Length[data1Bins[[i]]]]])/2 //. {x_} :> x, Length[data1Bins[[i]]], Length[data1Bins[[i]]]/(data1Bins[[i]][[
Length[data1Bins[[i]]]]] - data1Bins[[i]][[1]]) //. {x_} :> x}, {i, 1, n, 1}];