An experiment was done where a tiny steel ball was measured with a micrometer. I know I already posted a question about this before and was given a respond but after trying to fix my answers I am still lost. If someone could please review my results and tell me where I went wrong. Thank you very much.


1) For the D(mm) my results were: Trial 1= 15.90, tr 2= 16.01, tr 3 = 16.0, tr 4 = 16.0 and trial 5 = 15.9 , average=15.9

2) For V=1/2(pi)D^3: trial 1= 2019 , tr 2 = 2061, tr 3 = 2058, tr 4 = 2058, trial 5 = 2019, average 2043. I just plugged in each D value into the equation.

3) |dvi|= |Vi - V(the mean of volume)|: Trial 1 = 24 , tr 2= 18, tr 3 = 15, tr 4 =15, trial 5 = 24, average= 19.2
For this I took the average volume and subtracted it from each volume for each trial.

4) m(g) : Trial 1 = 16.1 , tr 2 = 15.8, tr 3 = 16.0 , tr 4 = 15.6, trial 5 = 15.9, average= 15.9. For this I had to weigh the ball using a scale.

5) Density (g/mm^3) : Trial 1= 8.0, trial 2 = 7.7, tr 3 = 7.8 , tr 4 = 7.6 , trial 5 = 7.9, average = 7.8
For this I divided each mass by volume of every trial.

6) This is where I am confused. |dpi|= |density1 - the mean of density|. For this I took the average density which was 7.8 and subtracted it from each density for the 5 trials.
Trial 1 = 0.1, trial 2 = 0.2, tr 3 = 0.1, tr 4 = 0.1, trial 5 = 0.1, average= 0.12

7) Now it says to compare the measured mean of density (D with the line above) with accepted Density for Fe(7.8 X 10^3 kg/m^3) and calculate the percent error.

I converted 0.12 g/mm^3 into kg/mm^3 and then subtracted that from 7.8X10^3 and then divided by 7.8 X 10^3 and my error was extremely high.

Is my data just incorrect or did I do the calculations wrong?

Please disregard. I found my mistake.

Let's go through your results step by step:

1) For the diameter measurements, it looks like you have recorded five trials. The average diameter you calculated is 15.9 mm.

2) For the volume calculations, you correctly used the formula V = 1/2(pi)D^3 and plugged in the diameter values from each trial. The average volume you calculated is 2043 mm^3.

3) To calculate the absolute deviation in volume (|dvi|), you subtracted the average volume from each individual volume in each trial. The average absolute deviation you calculated is 19.2 mm^3.

4) For the mass measurements, you obtained five trials, and the average mass you calculated is 15.9 g.

5) To calculate the density, you divided each mass value by the corresponding volume value. The average density you calculated is 7.8 g/mm^3.

6) For the absolute deviation in density (|dpi|), you correctly subtracted the average density from each individual density in each trial. The average absolute deviation you calculated is 0.12 g/mm^3.

7) Now, let's calculate the percent error. You converted the average absolute deviation in density from g/mm^3 to kg/m^3. However, there seems to be an error in your conversion. To convert g/mm^3 to kg/m^3, you need to multiply by 1000 (since there are 1000 mm in a meter and 1000 g in a kg). Thus, the average absolute deviation in density would be 0.12 * 1000 = 120 kg/m^3.

To calculate the percent error, you then subtracted the accepted density for Fe (7.8 * 10^3 kg/m^3) from the converted average absolute deviation (120 kg/m^3), divided by the accepted density, and multiplied by 100. However, it seems like you might have made an error in your calculation here. Let's redo the calculation:

Percent Error = [(Average Absolute Deviation - Accepted Density) / Accepted Density] * 100

Percent Error = [(120 - 7.8 * 10^3) / (7.8 * 10^3)] * 100

Please re-calculate this part of the calculation and let me know if you get a different result.