Correct Answer  Option 1 : between 9.69 m/s
^{2} and 9.93 m/s
^{2}
CONCEPT:

Error: The result of every measurement of experiments by any measuring instrument contains some uncertainty. This uncertainty is called error.

Absolute error: The magnitude of the difference between the measurement of the experimental readings and the true value of the quantity is called the absolute error.
 This is denoted by Δa .
 Absolute error is always positive.
 If there is no true value, we can take the mean of all measured values as a true value.
CALCULATION:
 The mean value of gravitational acceleration
\(g= {9.86\; + \;9.72\; + \;9.68\; + \;9.98 \over 4}=9.81\)

Absolute error is the magnitude of the difference between the measured value while doing the experiment measurement and the true value.
 When there is no true value, we take mean value of measurements as a true value.
So true value of g = 9.81
 Now, The errors in the measurements are
Absolute error = measured value  true value
Now, The errors in the measurements are
9.86  9.81 = 0.05 = 0.05
9.72  9.81 = 0.09 = 0.09
9.64  9.81 = 0.17 = 0.17
9.98  9.81 = 0.17 = 0.17
 The arithmetic mean of all the absolute errors (for the arithmetic mean, we take only the magnitudes i.e. positive value) is
\(\Delta g_{mean} = {0.05\;+\;0.09\;+\;0.17\;+\;0.17 \over 4}\)
\(\Delta g_{mean} = 0.12\)
 So mean absolute error is 0.12 m/s2
 That means the gravitational acceleration at that place is (9.81 ± 0.12) m/s^{2} i.e.
It lies between (9.81 + 0.12) m/s2 and (9.81  0.12) m/s2 or between 9.69 m/s2 and 9.93 m/s2.
 Hence the correct answer is option 1.