The density of mercury if 13.59g/mL at 20 C. three students obtained the following experiemntal results?

Question

Student A 13.8, 13.4, 13.0 g/mL
Syudent B 13.4 13.3, 13.3 g/mL
Sudent C 13.9, 13.8, 14.1 g/mL
Which results are accurate ?
Which results are most precise.

Answer 1

Student A is most accurate = closest to accepted value.

Student A mean value = 13.4
Student B mean value = 13.3
Student C mean value = 13.9

Student A differs from true value by 0.19
Student B differs from true value y 0.26
Student C differs from true value by 0.34

The mean value is calculated by adding the three measurements, and dividing by 3. Subtract the mean value from the true value. Only the difference is important, you can ignore any minus sign.


Student B has the most precise results = difference between the mean and measurements is the smallest. The "standard deviation" is a commonly used statistic. A smaller std. dev. is a more precise measurement.

Use your calculator to calculate the standard deviation. The calculation is a lot of work. Use the "sample" standard deviation function, not the population standard deviation.

Student A standard deviation = 0.40
Student B standard deviation = 0.06
Student C standard deviation = 0.15

Answer 2

Precision has to do with repeatability. If a measurement is repeatable it is precise. Usually this means that a measuring tool has lots of lines on it. In other words, someone else can repeat a measurement because the tool has so many lines on it that the likelihood is any two people will read the same measurement since there is little room for guessing.

So, of the three sets of measurements you have been given, student B is the most precise because their measurements were repeated, or nearly so, three different times.

Accuracy has to do with how well a measurement agrees with an established standard. Since the established standard for the density of mercury is 13.59g/mL the measurements that most closely agree with this number is those of student C.

Now, I realize that student C is no where near the accepted standard, if you round 13.59 to 14 than you can see that student C is closest to this number.