#### Numericals on Error Calculation of the NCERT class XI

#### Q-1 :: The diameter of a wire measured in an experiment was 0.022 cm, 0.023 cm, 0.026 cm, 0.025 cm, 0.024 cm and 0.025 cm find

(i) the mean value of diameter

(ii) absolute error in a each measurement

(iii) Percentage error

#### Q-2:: Refractive index of a flint glass (μ) was measured in an experiment and was found to be 1.655, 1.667, 1.666 , 1.659, 1.669 and 1.654. Find

(i) the mean value of μ

(ii) mean absolute error

(iii) Relative error

(iv) Percentage error

#### Q-3:: While determining the time period of oscillation of a simple pendulum, the readings from various measurements are 1.73 s, 1.62 s, 1.52 s, 1.45 s and 1.83 s. Calculate the values of mean value of time period, absolute error, mean absolute error and relative error.

#### Q-4:: While determining the density of a sea water , the readings from various measurements are 1.03 g/cc, 1.12 g/cc, 0.92 g/cc, 1.05 g/cc and 1.13 g/cc. Calculate the values of mean density , absolute error, mean absolute error and relative error.

#### Q-5:: The resistance of a wire as measured in an experiment was found to be 10.3 Ω , 10.7Ω , 9.8 Ω , 10.4 Ω and 9.6Ω . Calculate

(i) mean value of resistance

(ii) absolute error in each measurement

(iii) mean absolute error

(iv) fractional error

(v) percentage error.

#### Q-6:: The diameter of a wire as measured by a screw gauge was found to be 1.328 mm, 1.330 mm, 1.325 mm, 1.334 mm and 1.336 mm. Calculate

(i) mean value of diameter

(ii) absolute error in each measurement

(iii) mean absolute error

(iv) fractional error

(v) percentage error.

#### Q-7:: Using a screw gauge, the diameter of a metal rod was measured. The observation are given as follows : 0.39 mm, 0.38 mm, 0.37 mm, 0.41 mm, 0.38 mm, 0.38 mm, 0.37 mm, 0.40 mm, 0.39 mm. Calculate

(i) the most accurate value of the diameter,

(ii) the relative error, and

(iii) the percentage error in the measurement of the diameter.

#### Q-8::A student performs an experiment and found following values of the refractive index of

1.29, 1.33, 1.34, 1.35, 1.32, 1.36, 1.30, 1.33

Find the mean value of refractive index, the mean absolute error. The relative error and percentage error.

.