i = Table[10*n, {n, 0, 20}];

p = {3.9, 5.3, 7.2, 9.6, 12.9, 17.1, 23.2, 31.4, 38.6, 50.2, 62.9, 
          76, 92, 105.7, 122.8, 131.7, 150.7, 179.3, 203.3, 226.5, 
          248.7};

MatrixForm[
      daten1 = Table[{1780 + 10*n, p[[n]]}, {n, 1, 21}]]

ListPlot[daten1, 
      PlotStyle -> PointSize[0.02], 
      PlotRange -> {0, 250}]

daten2 = 
      Table[(p[[n + 1]] - p[[n - 1]])/2/p[[n]], {n, 2, 
          8}]

daten3 = 
      Table[{p[[n]], (p[[n + 1]] - p[[n - 1]])/2/
            p[[n]]}, {n, 2, 20}]

bild1 = ListPlot[daten3, PlotStyle -> PointSize[0.01]]

HINWEIS;

Clear[x, neu, i]

x = {4, 5, 7, 9, 11, 22, 67, 100, 187}

neu = Table[{i, x[[i + 1]]/x[[i]]}, {i, 1, 8}]

ListPlot[neu, PlotStyle -> PointSize[0.02]]

Clear[k, n, xmean, ymean, sigmaxy, sigmax, sigmay, m, q, 
        corr];

n = 15;

x = Table[daten3[[k]][[1]], {k, 1, 19}];

y = Table[daten3[[k]][[2]], {k, 1, 19}];

xmean = (1/n)*Sum[x[[k]], {k, 1, n}];

ymean = (1/n)*Sum[y[[k]], {k, 1, n}];

sigmaxy = (1/n)*
          Sum[(x[[k]] - xmean) (y[[k]] - ymean), {k, 1, 
              n}];

sigmax = 
        Sqrt[(1/n)*
            Sum[(x[[k]] - xmean)^2, {k, 1, n}]];

sigmay = 
        Sqrt[(1/n)*
            Sum[(y[[k]] - ymean)^2, {k, 1, n}]];

m = N[sigmaxy/sigmax^2]

q = N[ymean - m*xmean]

corr = N[sigmaxy/(sigmax*sigmay)]

bild2 = 
        Plot[m*t + q, {t, Min[x], Max[x]}, 
          PlotRange -> {Min[y], Max[y]}, 
          DisplayFunction -> Identity];

Show[bild1, bild2]