Question

Three students (A, B, and C) are asked to determine the volume of a sample of ethanol. Each student measures the volume three times with a graduated cylinder. The results in milliliters are: A (87.1, 88.2, 87.6); B (86.9, 87.1,87.2);C (87.6, 87.8, 87.9). The true volume is 87.0 mL. Comment on the precision and the accuracy of each student's results.

Answer 1

Answer :

Student A results have neither accuracy nor precision.

Student B results have accuracy and precision.

Student C results have no accuracy but have precision.

Explanation :

Accuracy : It is defined as the closeness of a measured value to a standard or known value.

For Example: If the mass of a substance is 50 kg and one person weighed 48 kg and another person weighed 55 kg. Then, the weight measured by first person is more accurate.

Precision : It is defined as the closeness of two or more measurements to each other.

For Example: If you weigh a given substance five times and you get 1.8 kg each time. Then the measurement is said to be precise.

Level of precision is determined by the maximum number of decimal places.

As we are given that the true value of the volume of sample is 87.0 mL and the values measured by a 3 students are:

Student A : (87.1, 88.2, 87.6)

Student B : (86.9, 87.1,87.2)

Student C : (87.6, 87.8, 87.9)

From the trial values of volume of a sample we conclude that:

Student A results have neither accuracy nor precision because the given value are not close to each other and true value.

Student B results have accuracy and precision because the given value are close to each other and true value.

Student C results have no accuracy but have precision because the given value are close to each other but not equal to true value.

Answer 2

Answer:

Explanation:

Mean of observation of A = 87.63

Mean of observation of B = 87.06

Mean of observation of C=87.76

So reading of B is closest to true volume hence his result is most accurate. Reading of C is least accurate.

As far as precision of measurement is concerned, it depends upon measuring instrument. From the reading it appears that the measuring instrument is the same because the no of  significant figure  of the reading is same ( three) . Hence their reading are equally precise.