A laboratory instructor gives a sample of powdered metal to each of four student

Question

A laboratory instructor gives a sample of powdered metal to each of four students, I, II, III, and IV, and they weigh the samples. The results of their multiple trials follow. The true value is 8.63 g.

: 8.64 g, 8.75 g, 8.85 g

: 8.54 g, 8.62 g, 8.73 g

: 8.78 g, 8.50 g, 8.53 g

: 8.66 g, 8.79 g, 8.56 g

yes no     

(c) Which set of data has the best combination of accuracy and precision?
---Select--- I. II. III. IV.

(d) Which set of data has the worst combination of accuracy and precision?
---Select--- I. II. III. IV.

Explanation / Answer

Average mass from

I) (8.64 + 8.75 + 8.85) / 3 = 8.75 g

II) (8.54 + 8.62 + 8.73) / 3 = 8.63 g

III) (8.78 + 8.50 + 8.53) / 3 = 8.60 g

IV) (8.66 + 8.79 + 8.56) / 3 = 8.67 g

The most accurate data is the one with average value closest to the true value of 8.63 g.

We see that II has an average weight of 8.63 g ( closest to the true value) it is the most accurate among the four

b) To measure precision we measure the average deviation of each data from the average values of those data

Deviation for I) (8.75 - 8.64) + (8.75 - 8.75) + (8.85 - 8.75) = 0.21

Similarily For II) 0.09 + 0.01 + 0.1 = 0.20

III) 0.18 + 0.10 + 0.07 = 0.35

IV) 0.01 + 0.12 + 0.11 = 0.24

We see that the deviation for II is the minimum, hence II is the most precise as well

c) I do not see options for c and d, but you could figure them out easily. I have listed out the precision for all the data in part b. Remember the lower the deviation the higher the precision. Precision has nothing to do with the true value.

To check for accuracy we use the true value. The higher the deviation of average from true value the lower the accuracy.

Hope this helps!

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