3) The following questions refer to the four data sets below, which represent da

Question

3) The following questions refer to the four data sets below, which represent data point values recorded relative to the true measurement of 5.0.

a. Which set represents high precision error predominantly?

b. Which set represents high bias error predominantly?

c. Which results could be more significantly improved by calibration?

d. Which results could be significantly improved by taking more samples?

Set 1 Set 2 Set 3 Set 4
5.5    4.9    5.6     5.0
5.6    4.6    5.3     5.0
5.6    5.2    5.9     5.1
5.4    4.8    5.5     5.0
5.5    5.5    6.2     4.9
5.6    5.1    5.8     5.0
5.5    4.7    5.4     4.9
5.5    5.4    6.1     5.1
5.7    5.0    5.7     5.0
5.6    4.8    5.5     4.9

*show all work and explain

Explanation / Answer

a) Set 4 has values that are really close together and they are centered on the true value. If the precision were higher, the measured values would be even better. All that remains is precision error. b) Set 3 shows bias error, with all of the values high. So, bias error is there, with other errors also, since the range of errors is large. So, bias error predominantly, with other errors also there. c) Set 1 has values which are all really close together, but they are offset from the true value. This is a systematic error, also known as a bias error, if the experiment could be calibrated, the results would be excellent. The precision is quite good. d) Set 2 seems like it is centered on the true value only the precision isn't very good. If more samples were taken, the average would get closer and closer to the true value.

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