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Answer :
Final answer:
The average mass from the measurements is 100.2 grams, with a range of 0.2 grams. The precision of measurements is better, but the accuracy is poor with a 9.07% percent error in comparison to the known mass of 110.2 grams.
Explanation:
When you are given a block of metal that has a ‘known’ mass of 110.2 grams and you measure its mass three times, obtaining the following readings: 100.2 g, 100.1 g, and 100.3 g, here's how you can analyze the data:
a. Average mass
To calculate the average mass, you sum the three measurements and divide by the number of measurements:
(100.2 g + 100.1 g + 100.3 g) / 3 = 100.2 grams.
b. Range
The range of your data is the difference between the highest and lowest measurements, which is 100.3 g – 100.1 g = 0.2 grams.
c. Accuracy vs. Precision
In this instance, the precision of the measurements is better because the three readings are close to each other, indicating consistent results. However, the accuracy is poor since the measured values are significantly different from the known mass of 110.2 grams.
d. Percent Error
To find the percent error, you use the formula: (|measured value – true value| / true value) × 100%. In this case, using one of the measured values, say 100.2 g, the percent error is (|100.2 g - 110.2 g| / 110.2 g) × 100% = 9.07%.
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