A) 22
B) 20
C) 16
D) 18
Correct Answer: B
Solution :
Combined variance\[=\frac{1}{{{n}_{1}}+{{n}_{2}}}\left( {{n}_{1}}\sigma _{1}^{2}+{{n}_{2}}\sigma _{2}^{2}+\frac{{{n}_{1}}{{n}_{2}}}{{{n}_{1}}+{{n}_{2}}}{{({{{\bar{x}}}_{1}}-{{{\bar{x}}}_{2}})}^{2}} \right)\] |
Put, \[{{n}_{1}}=5,\]\[{{n}_{2}}=1,\] |
\[\sigma _{1}^{2}=18,\] \[\sigma _{2}^{2}=0\] |
\[{{\bar{x}}_{1}}=150,\] \[{{\bar{x}}_{2}}=156\] |
\[\therefore \]combined variance \[=\frac{1}{6}\left( 90+0+\frac{5}{6}(36) \right)=20\] |
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