Question

A student measures time for 20 oscillations of a simple pendulum as \(30\text{ s}, 32\text{ s}, 35\text{ s}\) and \(35\text{ s}\) . If the minimum division in the measuring clock is \(1\text{ s}\) , then correct mean time (in second) is

• A. \((33 \pm 2)\)
• B. \((32 \pm 3)\)
• C. \((33 \pm 3)\)
• D. \((32 \pm 2)\)

Hint:

Mean Absolute Error is simply the average of "how far each measurement was from the average."

Answer 1

The Correct Option is A

Step 1: Concept
Mean time $T_m = \frac{\sum T_i}{n}$ and Mean Absolute Error $\Delta T_m = \frac{\sum |T_i - T_m|}{n}$.

Step 2: Meaning
The error should be rounded to the least count of the instrument if the calculated error is less, but here we calculate the mean absolute error.

Step 3: Analysis
$T_m = \frac{30+32+35+35}{4} = \frac{132}{4} = 33\text{ s}$.
Absolute errors: $|30-33|=3, |32-33|=1, |35-33|=2, |35-33|=2$.
Mean Absolute Error $= \frac{3+1+2+2}{4} = \frac{8}{4} = 2\text{ s}$.

Step 4: Conclusion
The mean time is $(33 \pm 2)\text{ s}$. Final Answer: (A)