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 diregard. I found my mistake.

It appears that there may have been some errors in your calculations. Let's go through each step and see where the mistakes may have occurred:

1) For the D(mm), it seems that you have recorded the measurements correctly. The average of your measurements is 15.9 mm.

2) For V=1/2(pi)D^3, the formula you used is correct. Plugging in each D value correctly, the calculations for trial 1 and trial 2 seem accurate. However, for trial 3, trial 4, and trial 5, there seem to be some inconsistencies. Double-check your calculations for those trials.

3) For |dvi|=|Vi - V(the mean of volume)|, it seems that you have correctly subtracted the mean volume from each trial volume. However, the calculations for trial 1 and trial 5 seem incorrect. Recheck your calculations for those trials.

4) For m(g), if you have correctly weighed the ball using a scale, your measurements seem accurate. The average mass is 15.9 g.

5) For Density (g/mm^3), dividing each mass by the volume of each trial seems correct. However, the calculation for trial 2 seems incorrect. Check your math for that trial.

6) For |dpi|=|density1 - the mean of density|, it seems that you have calculated the differences correctly. However, the calculation for trial 2 seems incorrect. Verify your calculation for that trial.

7) When comparing the measured mean of density with the accepted density for Fe (7.8 X 10^3 kg/m^3), you need to convert the average density from g/mm^3 to kg/m^3. To do this, you should multiply the average density by 10^6 since there are 10^6 mm^3 in 1 m^3. Then, you can calculate the percent error using the formula: (|measured density - accepted density| / accepted density) * 100.

Make sure you perform the conversions correctly, recheck your calculations, and then calculate the percent error. If the error is still high, there might be some systematic errors in your experiment or measurements. Double-check your experimental procedures to ensure accuracy.