A digital scale reports a 10kg weight as weighing 8.975kg. which of the following is true?

1 answer:

6 0

That question is accompanied by these answer choices:

<span>A. The scale is accurate but not precise.
B. The scale is precise but not accurate.
C. The scale is neither precise nor accurate.
D. The scale is both accurate and precise.

Then you need to distinguish between accuracy and precision.

Accuracy refers to the closeness of the measure to the real value, while precision, in this case, refers to the level of significant figures that the sacle report.

The fact that the scale reports the number with 4 significant figures means that it is very precise, but the fact that the result is not so close to the real value as the number of significan figures pretend to be, means that the scale is not accurate.

So, the answer is that the scale is precise but not accurate (the option B).
</span>

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Let's figure this out as though we have no idea what the answer would be.

Step One
Find the new five numbers.
3*3, 8*3, 12*3, 17*3, 25*3
9 , 24 , 36, 51, 75

Step 2
Find the average
(9 + 24 + 36 + 51 + 75)/5 = 195/5 = 39

Step 3
Subtract the individual numbers from the average
(39 - 9) = 30
(39 -24) = 15
(39 - 36) = 3
(39 - 51) = - 12
(39 - 75) = -36

Step 4
Square the results from Step 3
30^2 = 900
15^2 = 225
3^2 = 9
(-12)^2 = 144
(-36)^2 = 1296

Step 5
Take the average of the results from step 4
(900 + 225 + 9 + 144 + 1296)/5
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Step 6
Take the square root of the result from step 5
deviation = sqrt(514.8)
deviation = 22.689

Step seven
Compare the two standard deviations.
s2/s1 = 22.689 / 7.563 = 3

Conclusion
If you are given 1 set of numbers to find a population standard deviation and you multiply each member by a, then the result will be a * the standard population deviation of the first set of numbers.

Note
Your calculator will do this as well, but you have to know how to enter the data into your calculator. That requires that you follow the directions carefully.

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