1.After several tries of measuring, Lydia gets the results of 2.75, 2.76, 2.30 cm. She realized that the results of measurement is closest to the actual measurement which is 3.25. What is the implication of her measurements? Is it Accurate and precise? 2.I measured the length of cabinet 3 times. The results of my measurements are 3.44 m, 3.55 m, 3.47 m. Afterwards, I compared it to the results with each other. What did I was trying to find out? Is it precision?

1.After several tries of measuring, Lydia gets the results of 2.75, 2.76, 2.30 cm. She realized that the results of measurement is closest to the actual measurement which is 3.25. What is the implication of her measurements? Is it Accurate and precise? 2.I measured the length of cabinet 3 times. The results of my measurements are 3.44 m, 3.55 m, 3.47 m. Afterwards, I compared it to the results with each other. What did I was trying to find out? Is it precision?

Question
Measurement
asked 2021-02-13
1.After several tries of measuring, Lydia gets the results of 2.75, 2.76, 2.30 cm. She realized that the results of measurement is closest to the actual measurement which is 3.25. What is the implication of her measurements? Is it Accurate and precise?
2.I measured the length of cabinet 3 times. The results of my measurements are 3.44 m, 3.55 m, 3.47 m. Afterwards, I compared it to the results with each other. What did I was trying to find out? Is it precision?

Answers (1)

2021-02-14
Step 1
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Difference between the calculated value and actual value of a quantity is called error. Difference in true value and individually measured value of a quantity is called absolute error. The mean of the data is termed as mean absolute error. .
Accuracy of a measurement is a measure of how much close the value measured to the actual value of quantity. Precision provides the measuring instrument resolution capability. Smaller least count greater will be the precision.
Let \(a_{1} = 2.75 cm,\ a_{2} = 2.76 cm,\ a_{3} = 2.30 cm\)
Mean value of measurements
\(\overline{a}=\frac{2.75+2.76+2.30}{3}\)
\(\overline{a}=2.60cm\)
Actual measurement is 3.25 cm.
This difference can be due to instrumental error or personal error, it can be due to imperfection in performing the experiment or due to some external causes like temperature, pressure, humidity etc.
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