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## Homework Statement

Sally, Bob and Charlie each measure the period of the same pendulum to determine the

acceleration of gravity, g. The lab instructions say that you should determine the period by

timing the time of 100 swings (complete cycles) of the pendulum. Sally is the first to do the

experiment and she times 100 swings of the pendulum. Bob does the experiment next and

decides to make two such measurements of 100 swings each and averages the values to get a

better result while Charlie decides to make 10 sets of measurements and average them. The

final data set consists of three times (TS, TB, and TC) for 100 swings. Assume that the dominant

uncertainty in timing the 100 swings is random and that all three students have the same

reaction time.

If Sally obtains a standard deviation [tex]\sigma[/tex]S, what are the standard deviations calculated by

Bob and Charlie ([tex]\sigma[/tex]B and [tex]\sigma[/tex]C) expressed in units or multiples of [tex]\sigma[/tex]S?

## Homework Equations

[tex]\sigma[/tex] = sqrt[(sum(x-x

_{avg})

^{2})/(N-1)]

where N is number of trials, x is each measured value and x

_{avg}is the mean of the measured values.

## The Attempt at a Solution

I'm not quite sure where to start with this because I don't know how sally could have gotten a standard deviation with only one measurement.

I feel like this should be pretty simple, but I must be overlooking something easy or misreading the question. I would like to figure this out on my own, but I cant seem to even get out of the batters box, so if maybe if someone could just get me started, I think i could finish on my own.

Thanks.