Question

The dataset for two factories are given:
Factory 1: $10.1,9.9,10.1,9.9,9.9,10.1,9.9,10.1,9.9,10.1$
Factory 2: $16,5,7,14,6,15,3,13,9,12$
Which factory is more reliable?

• A. Factory 1
• B. Factory 2
• C. Both
• D. Cannot be concluded.

Answer 1

Answer: (A)

Factory 1

$Factory110.109.910.109.909.910.109.910.109.910.1\_\_\_\_\_\_100$ $x-\overline{x}0.1-0.10.1-0.1-0.10.1-0.10.1-0.10.1$ ${(x-\overline{x)}}^{2}0.010.010.010.010.010.010.010.010.010.01\_\_\_\_\_\_\_\_0.1$ $Factory216050714061503130912\_\_\_\_\_\_\_\_100$ $(x-\overline{x})06-5-304-405-703-102$ ${(x-\overline{x})}^{2}36250916162549090104\_\_\_\_\_190$

$\overline{x}=\frac{100}{10}=10$ $\overline{x}=\frac{100}{10}=10$

Therefore,$\sigma =\sqrt{\frac{190}{9}}=459$

Therefore,$\sigma =\sqrt{\frac{0.1}{9}}=0.0105$

Step deviation is less in $factor1$. Hence, it is more reliable.