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  • The following information relates to a sample of size 60: ∑x2=18000, ∑x = 960. The variance is A. 6.63 B. 16 C. 22 D. 44

The following information relates to a sample of size 60:  \sum x\textsuperscript{2}=18000, \sum x = 960.\\
 
The variance is
A. 6.63
B. 16
C. 22
D. 44

Answers (1)

\\ \text{We know that S.D can be written as }\sigma = \sqrt {\frac{ \Sigma x_{i}^{2}}{n}- \left( \frac{ \Sigma x_{i}}{n} \right) ^{2}}~ \\ \\ \text{But given } \Sigma x^{2}=18000, \Sigma x=960,~N=60, \\ \\ \text{substituting these corresponding values, we get }\sigma =\sqrt {\frac{18000}{60}- \left( \frac{960}{60} \right) ^{2}}= \sqrt {300- \left( 16 \right) ^{2}}=\sqrt {300-256}= \sqrt {44}~ \\ \\ \text{Now for variance we square both the sides } \sigma ^{2}=44 \\

 

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