Calculate the weighted arithmetic mean, standard deviation, standard error of th
ID: 802625 • Letter: C
Question
Calculate the weighted arithmetic mean, standard deviation, standard error of the 8 measurements of 206Pb/238U and their uncertainties, and the mean age of the sample using the give equations: weighted avg or bar x = w_1 x_1 + w_2 x_2 + ...+ w_n x_n/w_1 + w_2 +...+ w_n std.dev.or s = Squareroot sigma_i (x_i - bar x)^2 std.error or SE = s/Squareroot n, where n is the number of measurements time (t) = 1/1.55125 times 10^-10 * ln (^206 Pb/^238 U + 1) weighted arithmetic mean: standard deviation: standard error: Calculate the age of the sample (using the arithmetic mean and the following equation).Explanation / Answer
206 Pb/238U +- 2sigma uncertainity deviations=m-i sd=devation^2
1.86E-3 2.79E-5 0.03 E-3 0.0009E-3
1.71E-3 2.56E-5 0.18E-3 0.0324E-3
1.88E-3 2.82E-5 0.01E-3 0.0001 E-3
2.02E-3 3.03E-5 -0.13E-3 0.0169E-3
1.89E-3 2.84E-5 0 0
1.87E-3 2.81E-5 0.02E-3 0.0004E-3
1.99E-3 2.98E-5 -0.1E-3 0.01E-3
1.91E-3 2.86E-5 -0.02E-3 0.0004E-3
Sum=15.13 E-3 Sum=0.0611E-3
Mean m=sum of observation/total no of observations
=15.13E-3/8
=1.89E-3
b.Standard deviation=0.0611E-3/n-1
n=8
=0.0611E-3/7
=square root 8.72*10-3=2.95/31.6=0.0093
c.Standard error=SD/root n
=0.0093/square root(8)
=0.0093/2.82
=3.29*10-3
d.time=1/1.55*10-10*In(206pb/238pb+1)
=1/1.55*10-10In(1.89*10-3+1)
=1/1.55*10-10 In(2.89*10-3)
=0.645*10-10*(-5.846)
=3.77*10-10
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