Question

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 :

• A. $92 \pm 2\, s$
• B. $92 \pm 5.0 \,s$
• C. $92 \pm 1.8 \,s$
• D. $92 \pm 3 \,s$

Answer 1

Answer: (A)

$92 \pm 2\, s$

Answer 2

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