1. Tardigrade
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  3. Physics
  4. A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be :

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Q. A student measures the time period of $100$ oscillations of a simple pendulum four times. The data set is $90\, s, 91\, s, 95\, s$ and $92\, s$. If the minimum division in the measuring clock is $1 \,s$, then the reported mean time should be :

JEE MainJEE Main 2016Physical World, Units and Measurements

Solution:

$\overline{x} = \frac{\sum x_i}{N} = \frac{90 + 91+ 95 + 92}{4} = 92$
Mean deviation = $\frac{\sum |\bar{x} - x_i|}{N} = \frac{2 + 1+ 3 +0}{4} = 1.5$
$L.C. = 1\,s$.
$\therefore $ Required value $= 92 \pm 2\, s$