Uncertanties and errors question

[Xelb]

*Before I start, I just want to say that this is only my second day in IB Physics. I had never taken Physics at in in high school prior to IB Physics, so I really had to read up and pretty much self-teach myself a bit of it over the summer. Of course, even now I still have absolutely no idea what I'm reading (but neither does anyone else in my class). The answers and explanations to these problems are only based on my meager understanding of Physics.*

Homework Statement

You measure the oscillations of a pendulum four times, and find that it makes 15 complete swings in times of:

8.13 s, 8.22 s, 8.19 s, and 8.15 s.

You calculate a standard deviation (read from your calculator) of 0.0403112887416037 s.

The correct way to report the answer (with the proper number of significant figures!) is to say that the period is: ? seconds

With an uncertainty of: ? seconds

*There is little tolerance for error in this specific question*

Homework Equations

-I entered the variables in my calculator just to see what the average was. I got an average of 8.17 seconds using the sig-fig calculator and the standard deviation was the same.
(There really aren't any relevant "equations" in this problem)

The Attempt at a Solution

-Based on what I learned, you can only express uncertainties in one sig-fig, and that it must match the level of precision. So, based on that I wrote down: 8.17 ± .04 seconds. But, apparently this is wrong. Why? Any help is gratefully appreciated.

 

[Xelb]

I'm not sure if there is more to this problem that I don't know about, but this is all of the information I have so far, as I'm still trying to figure this problem out. *Also, I noticed that a pretty lackluster thread titled *help* seemed to be getting more attention when, clearly, the OP didn't read the FAQ. -.-*

 

[hage567]

Is the question asking you to find the actual period? Because the data you show is the time it takes the pendulum to go 15 swings, not one (which is what the period would be).

Am I misreading what you've written?

 

[Xelb]

I copied the problem directly from the website from which it was assigned, so I suppose it is asking me to find the actual period.

 

[rwisz]

First of all, congratulations on taking on the challenge of IB Physics and self-teaching yourself over the summer! It can be a difficult subject, but with hard work and dedication, you can definitely succeed.

Now, let's address the issue at hand. You are correct in saying that uncertainties should only be expressed in one significant figure. However, this rule applies to the number of digits after the decimal point, not the whole number. So in this case, the uncertainty should be expressed as 0.04 seconds, not 0.0403112887416037 seconds.

Additionally, when reporting the period with the proper number of significant figures, you should round up or down the last digit based on the next digit. In this case, since the next digit after the hundredths place is a 1, we round down the hundredths place to get 8.16 seconds as the period.

Therefore, the correct way to report the answer is 8.16 seconds, with an uncertainty of 0.04 seconds. This means that the actual period of the pendulum can be anywhere between 8.12 seconds and 8.20 seconds.

Remember, when dealing with uncertainties and errors, it is important to be as precise as possible and follow the proper rules for significant figures and rounding. This may seem tedious, but it is crucial in accurately representing your data and results. Keep up the good work and don't be discouraged by the challenges in IB Physics!