# Experiment on friction coefficient

Here you can see the results of the experiment about a friction coefficient:

The mean of the friction coefficient becomes 0.262 but when I do a linear regression in the form of y=mx the slope is 0.31. Shouldn't it be the same? I used $F_N$ as x values and $F_D$ (friction force) as y values.

regression: https://www.desmos.com/calculator/njj4utvsdk

• There seems to be a systematic trend in your data. Possibly a systematic error in the measurements of mass. The force $F_D$ appears to be measured only to 1 decimal place or 1 significant figure, so there is room for a lot of error there also. Can you post more details of how you did your experiments and how you made your measurements? – sammy gerbil Jan 6 '18 at 17:34

The mean of the friction coefficient becomes 0.262 but when I do a linear regression in the form of y=mx the slope is 0,31. Shouldn't it be the same?

No.

Linear regression and arithmetic mean are not the same thing.

Linear regression is trying to fit a linear plot to the points you gave it with the best $R^2$ value.

Arithmetic mean is just the sum of all the values divided by the total number of values. Statistically they measure different things, so you can't expect the same value from them.

• So what would be the best number for the coefficient of friction? – Ali Bakly MBGY Jan 6 '18 at 1:18

Expounding on sammy's comment, when you divide $F_D$ by $F_N$, since $F_D$ only is measured to one significant figure you can only report $\mu_S$ to one significant figure.

Value of $\mu_S$ from calculating the mean of all experiments: 0.262 = 0.3
Value of $\mu_S$ from linear regression: 0.311 = 0.3

So for your case you do get the same answer either way.

If you would take a ton more data points with more significant figures on $F_D$ you should still get the same answer both ways. It would probably be a crapshoot to guess which way will give you a more accurate answer with four data points. Plotting the data points and looking at the regression will at least give you a heads up if the experiment shows non-linearity (which would be an indication of some limitation of the experimental setup to reflect the model).