Question

Repeated observations in an experiment gave the values 1.29, 1.33, 1.34, 1.35, 1.32,1.36, 1.30 and 1.33. Find the relative error.

• A. $\pm$ 0.025
• B. $\pm$ 0
• C. $\pm$ 0.0175
• D. $\pm$ 0.015

Answer 1

The correct option is D

$\pm$ 0.015

Mean = $\frac{1.29+1.33+1.34+1.35+1.32+1.36+\mathrm{1.30.1.33}}{8}$

= 1.3275

= 1.33 (Rounding off to 3 digits)

$\begin{array}{cccc}Sl.No.& Observetion& changeinx& changein{x}^2\\ 1& 1.29& 0.04& 0.0016\\ 2& 1.33& 0.00& 0.000\\ 3& 1.34& -0.01& 0.0001\\ 4& 1.35& -0.02& 0.0004\\ 5& 1.32& 0.01& 0.0001\\ 6& 1.36& -0.03& 0.0009\\ 7& 1.30& 0.03& 0.0009\\ 8& 1.33& 0.00& 0.0000\end{array}$
$\sigma =\sqrt{\frac{\sum \Delta x^2}{n}}=\sqrt{\frac{0.004}{8}}$

= 0.022

= 0.02

Absolute error = 0.02

Relative error = $\frac{0.02}{1.33}=\pm 0.015$