Question

In: Advanced Math

Q5. The laser at the doctor’s office is graduated in 1/20th of an inch intervals. It...

Q5. The laser at the doctor’s office is graduated in 1/20th of an inch intervals. It measures your height. A tape measure instead is graduated in 1/8th of an inch intervals. Which one is more accurate? Which one is more precise? Illustrate your rationale with a few examples of hypothetically measured heights using the two instruments. [20]

Solutions

Expert Solution

Accuracy means how close the results are to the actual value of a certain measurement. Precision means how close the results are compared to each other.

The least count (that is, the smallest measurement that can be taken by a measuring instrument) of the laser is 1/20th of an inch (=0.05 inch) while the least count of the tape measure is 1/8th (=0.125 inch) of an inch. Thus, the least count of the laser is less than the least count of the tape measure. Hence, meaurements made with the laser will be closer to the both the actual value and to each other than measurements made with the tape measure. Hence, the laser is more accurate and more precise.

Let us consider the following examples:

(1) Suppose, my height= 5 feet 3.656 inch.

Then, height measured by the laser= 5 feet 3.65 inch.

And, height measured by the tape measure= 5 feet 3.625 inch.

Thus the laser's measurement is 0.006 inches less while the tape measure's measurement is 0.031 inches less. Hence, the laser is more accurate.

The laser will also be more precise.

(2) Suppose, my height= 6 feet 5.118 inch.

Then, height measured by the laser= 6 feet 5.1 inch.

And, height measured by the tape measure= 6 feet 5 inch.

Thus the laser's measurement is 0.018 inches less while the tape measure's measurement is 0.118 inches less. Hence, the laser is more accurate.

The laser will also be more precise.


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