How to form a discrete function using table data

Question

I have table with three column given as $a$, $\alpha_\min$ and $\chi^2$ value respectively. Now a need a function such that we define a function $\alpha_\min$[a_ ], which will order the data table that you have defined in ascending order of $\chi^2$ and then extract the alpha_min value corresponding to the minimum $\chi^2$ value in the sorted table. I have tried the Ordering but it dos work. Please let me know if there is some other way to do it.

TableForm[{{0.95, 0.01, 0.9516524102395575`}, {0.9, 0.0838456, 
   0.00017651695169002194`}, {0.85, 0.295003, 
   0.00281306937265338`}, {0.8, 0.437487, 0.22125292245500258`}, {0.7,
    0.701135, 3.467778186791209`}, {0.6, 0.915587, 
   12.713765652663328`}, {0.5, 1.11048, 25.81960204984133`}, {0.4, 
   1.27876, 42.07377320682969`}, {0.3, 1.41499, 
   61.02588755852117`}, {0.2, 1.51511, 82.35647352296047`}, {0.1, 
   1.5763, 105.82242501504311`}}, 
 TableHeadings -> {{""}, {"a", 
    "(\[Alpha]\), \(min\)]\)", 
    "(\[Chi]\), \(2\)]\)"}}]

Answer 1

Try

t={{0.95, 0.01, 0.9516524102395575`},{0.9, 0.0838456,  0.00017651695169002194`},
  {0.85, 0.295003,  0.00281306937265338`},{0.8, 0.437487, 0.22125292245500258`},
  {0.7, 0.701135, 3.467778186791209`},{0.6, 0.915587,  12.713765652663328`},
  {0.5, 1.11048, 25.81960204984133`},{0.4,  1.27876, 42.07377320682969`},
  {0.3, 1.41499,  61.02588755852117`},{0.2, 1.51511, 82.35647352296047`},
  {0.1,  1.5763, 105.82242501504311`}};
First[SortBy[t,Last]][[3]]

which returns

0.000176517

Just be careful that you don't use

t=TableForm[{{0.95, 0.01, 0.9516524102395575`},{0.9, 0.0838456,  0.00017651695169002194`},...

because TableForm produces something nice to look at, but usually cannot be used for further calculations.

Answer 2

Here is a version using Ordering :

t={{0.95, 0.01, 0.9516524102395575`},{0.9, 0.0838456,  0.00017651695169002194`},
  {0.85, 0.295003,  0.00281306937265338`},{0.8, 0.437487, 0.22125292245500258`},
  {0.7, 0.701135, 3.467778186791209`},{0.6, 0.915587,  12.713765652663328`},
  {0.5, 1.11048, 25.81960204984133`},{0.4,  1.27876, 42.07377320682969`},
  {0.3, 1.41499,  61.02588755852117`},{0.2, 1.51511, 82.35647352296047`},
  {0.1,  1.5763, 105.82242501504311`}};

index=Ordering[t[[All,3]]];(*{2, 3, 4, 1, 5, 6, 7, 8, 9, 10, 11}*)
t[[First[index]]]  (*{0.9, 0.0838456, 0.000176517}*)
t[[First[index]]][[3]]  (* 0.000176517  *)