Correct Answer  Option 2 : 0.01223
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.

Relative error: the ratio of the mean absolute error (or final absolute error) to the mean value of the experimental value measured.
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/s2

The relative error is the ratio of the mean absolute error (or final absolute error) Δgmean to the mean value gmean of the experimental value measured.
\(Relative~ error = {Δg_{mean} \over g_{mean}}\)
The relative error is = \({0.12 \over 9.81}=0.0122324\)
 The relative error is ≈ 0.01223
 Hence the correct answer is option 2.