In a experiment refractive index of glass is measured and following values are obtained - 1.32,1.4,1.31,1.29,1.33,1.3. Find its mean value, absolute value,relative error and percentage error.
Answers
Answer:
Explanation:
Given values ⇒
1.29 1.33 1.34 1.35 1.32 1.36 1.30 and 1.33
Now, there are total of the 8 term.
Mean value = Sum of all the
observations/No. of observations.
:: Mean value = (1.29 + 1.33 + 1.34 +1.35 +
1.32 +1.36 +1.30 + 1.33)/8
= 10.62/8
= 1.3275
= 1.33
Now, for absolute error in each term,
X₁11.33- 1.291 = 0.04
X₂ = 11.33 -1.33/ = 0.00
X3 = 11.33 1.34/= 0.01
X4 11.33 1.35/= 0.02
Xs = /1.33 - 132| = 0.01
X6 = 11.33 1.36/= 0.03
X7 = 11.33 1.30l = 0.03
Xg = 11.33 1.33/ = 0.00
.: Mean Absolute error = (0.04 + 0.00 + 0.01 +0.02 +0.01 +0.03 +0.03 +0.00)/8
:: Mean Absolute error = (0.04 + 0.00 +
0.01 +0.02 +0.01 + 0.03 +0.03 + 0.00)/8
= 0.14/8
= 0.0175
= 0.018
Vol 49
.: Relative Error = Mean absolute error/ Mean Value
= 0.018/1.33
= 0.135
= 0.12
:: % Error = 0.12 × 100
% Error = 12%
Hope it helps. :-)