The rare earth element gadolinium is often used as a contrasting agent for MRIs.

Question

The rare earth element gadolinium is often used as a contrasting agent for MRIs. The concentration of gadolinium was measured in the discharge from a wastewater treatment plant near a large medical facility. The following eight measurements were obtained. 1.361 ppm, 1.363 ppm, 1.359 ppm, 1.352 ppm, 1.924 ppm, 1.354 ppm, 1.368 ppm, 1.358 ppm Calculate the standard deviation, s, to determine whether one of the above points can be rejected as an outlier. You may generally reject a data point as an outlier if it lies more than 2 standard deviations from the mean, or average, of the data. Number O O The potential outlier should be kept. The potential outlier should be rejected. Based on the outcome above, calculate the mean (x) and standard deviation (s) for the results. Number Number

Explanation / Answer

Initially we calculate the average:

X = Data Sum / Data Number = 11,439 / 8 = 1,430 ppm

Next the Standard Deviation:

S = [Sum (Xi-X) ^ 2 / N] = 0.200 ppm

Taking into account that the maximum limit to accept values is:

Lmax = X + 2 * S = 1.430 + 2 * 0.200 = 1830 ppm

the value 1924 ppm is rejected.

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