Two brands of digital scales that are purpose designed for measuring small weigh

Question

Two brands of digital scales that are purpose designed for measuring small weights are being evaluated for purchase by the university to replace old analog scales. The two brands both display weights to the nearest 1/100 of a gram and should not be used for weights of more than 150g. Only one brand will be purchased, and the purchase order will be for 150 sets of scales. The lab sta have obtained 25 sets of scales from both manufacturers and have decided that there is no real reason why either brand should be preferred over the other in terms of their usefulness. Brand A is slightly cheaper than Brand B however so the decision is not a matter of randomly choosing among the brands. On the advice of the senior lab technician, a benchmark weight of 50g and another of 100g are weighed on all sets of scales to test the consistency of each brand. She believed that these two weights were fairly representative of the weights that will need to be measured in the future.

101.44

(a) Accuracy is a measure of biasedness and is calculated as the average of the sampled readings of an instrument minus the target reading that should have been seen. Contrast this with precision, which measures how consistent an instrument is in its readings. Precision is measured by the standard deviation of the readings. What is the accuracy and precision of each brand?

(b) Form a recommendation on which brand should be purchased.

A50 A100 B50 B100 49.5 100.2 50.28 100.53 50.03 99.75 51.34 99.36 49.32 100.1 50.37 101.62 49.95 100.71 49.59 99.71 50.28 100.16 50.49 101.01 50.46 99.36 50.35 100.31 50.16 100.4 50.97 100.64 49.23 99.47 50.62 99.44 49.51 99.46 50.58 99.79 49.73 100.22 49.12 100.86 49.81 99.61 49.58 100.01 50.53 100.71 49.65 99.48 50.41 100.32 50.76 100.28 49.71 99.39 49.83 100.12 49.12 99.37 49.4 99.58 50.01 100.73 51.3 101.41 50.11 99.98 51.28 100.81 50.12 99.81 51.45

101.44

50.39 100.14 50 100.25 49.96 100.72 50.8 99.28 50.12 99.72 50.17 100.25 50.07 99.33 49.94 100.16 49.98 100.22 50.5 99.68 49.67 101.50 25 101.41 49.45 99.59 49.6 99.31

Explanation / Answer

Find the difference between actual and expected reading. (for eg. "A2 - 50" is the formula in B2)
Accuracy is the average of these values. (=AVERAGE(B2:B26) is the formula in B27

For precision, find the sample standard deviation(=STDEV.S(A2:A26) is the formula in cell B28)

Higher accuracy is seen for BRAND A as the average for both A50 and A100 is closer to 0.
Higher Precision is seen for BRAND A as the standard deviation values are smaller compared to BRAND B.

To top all this, BRAND A is cheaper than BRAND B. Buy BRAND A

A50 A50 - 50 A100 A100-100 B50 B50-50 B100 B100 - 100 49.5 -0.5 100.2 0.2 50.28 0.28 100.53 0.53 50.03 0.03 99.75 -0.25 51.34 1.34 99.36 -0.64 49.32 -0.68 100.1 0.1 50.37 0.37 101.62 1.62 49.95 -0.05 100.71 0.71 49.59 -0.41 99.71 -0.29 50.28 0.28 100.16 0.16 50.49 0.49 101.01 1.01 50.46 0.46 99.36 -0.64 50.35 0.35 100.31 0.31 50.16 0.16 100.4 0.4 50.97 0.97 100.64 0.64 49.23 -0.77 99.47 -0.53 50.62 0.62 99.44 -0.56 49.51 -0.49 99.46 -0.54 50.58 0.58 99.79 -0.21 49.73 -0.27 100.22 0.22 49.12 -0.88 100.86 0.86 49.81 -0.19 99.61 -0.39 49.58 -0.42 100.01 0.01 50.53 0.53 100.71 0.71 49.65 -0.35 99.48 -0.52 50.41 0.41 100.32 0.32 50.76 0.76 100.28 0.28 49.71 -0.29 99.39 -0.61 49.83 -0.17 100.12 0.12 49.12 -0.88 99.37 -0.63 49.4 -0.6 99.58 -0.42 50.01 0.01 100.73 0.73 51.3 1.3 101.41 1.41 50.11 0.11 99.98 -0.02 51.28 1.28 100.81 0.81 50.12 0.12 99.81 -0.19 51.45 1.45 101.44 1.44 50.39 0.39 100.14 0.14 50 0 100.25 0.25 49.96 -0.04 100.72 0.72 50.8 0.8 99.28 -0.72 50.12 0.12 99.72 -0.28 50.17 0.17 100.25 0.25 50.07 0.07 99.33 -0.67 49.94 -0.06 100.16 0.16 49.98 -0.02 100.22 0.22 50.5 0.5 99.68 -0.32 49.67 -0.33 101.5 1.5 25 -25 101.41 1.41 49.45 -0.55 99.59 -0.41 49.6 -0.4 99.31 -0.69 Accuracy -0.0948 0.0388 -0.6812 0.2696 Precision 0.390919 0.556172 5.107819 0.727384

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