Question

Three students (A, B, and C) are asked to determine the volume of a sample of water. 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:

Precision means how closely the answers are from each other; mathematically it can be expressed as the standard deviation.  

Student A has a mean of 87.6 and a standard deviation of 0.55; student B got a mean of 87.0 with a Sd of 0.15 and student C got a mean of 87.8 with an Sd of 0.15.

Accuracy means how close the measurement is to the real value. It’s evaluated from the mean of a given data set, so the best measurement was performed by student B.

The best data set was obtained by B, because it has the closest mean to the real value and has an low Sd; second best was C, even thou its mean was not as close as A it had a low Sd; A had its mean closer to the real value, but its Sd was too high, meaning it has too much error in its measurement.

Ste.-by-step explanation:

The standard deviation, symbolized by the geek letter "δ" (lower case sigma) -  $Sd=\sqrt[2]{\frac{S(x-M^{2}) }{n} }$  (I'm sorry, could not input the formula using the usual symbology, so I'm attaching a pic of this formula)

n my input, "Sd" stands for the standard deviation; "S" stands for summation; "x" is a data point, i.e. for student A x would be 87.1, 88.2 and 87.6; "M" stands for the mean and "n" stands for the number of data points in a given data set, i.e. for each of the students n=3

The mean is summation of all data points divided by the number of data points $M=\frac{Sx}{n}$ (again, I could not input a capital sigma, so I used "S" instead)

Calculating for the student A

M=(87.1+88.2+87.6)/3=87.6

$Sd=\frac{((87.1-87.6)^{2} +(88.2-87.6)^{2} +(87.6-87.6)^{2} )}{3} = 0.55$

Calculating for the student B

M=(86.9+87.1+87.2)/3=87.0

$Sd=\frac{((86.9-87.0)^{2} +(87.1-87.0)^{2} +(87.2-87.0)^{2} )}{3} = 0.15$

Calculating for the student C

M=(87.6+87.8+87.9)/3=87.8

$Sd=\frac{((87.6-87.8)^{2} +(87.9-87.8)^{2} +(87.8-87.8)^{2} )}{3} = 0.15$