MHT CET · Maths · Statistics
The sum of 10 values is 12 and the sum of their squares is 16.9 , then their standard deviation \((S, D)\) is
- A \(0.05\)
- B 5
- C \(0.5\)
- D \(0.005\)
Answer & Solution
Correct Answer
(C) \(0.5\)
Step-by-step Solution
Detailed explanation
Given \(\sum x=12, \sum x^2=16.9\) and \(n=10\)
\(
\begin{aligned}
& \because \text { S.D. }=\sqrt{\frac{\sum x^2}{n}-\left(\frac{\sum x}{n}\right)^2}=\sqrt{\frac{16.9}{10}-\left(\frac{12}{10}\right)^2} \\
& =\sqrt{\frac{169-144}{100}}=\frac{5}{10}=0.5
\end{aligned}
\)
\(
\begin{aligned}
& \because \text { S.D. }=\sqrt{\frac{\sum x^2}{n}-\left(\frac{\sum x}{n}\right)^2}=\sqrt{\frac{16.9}{10}-\left(\frac{12}{10}\right)^2} \\
& =\sqrt{\frac{169-144}{100}}=\frac{5}{10}=0.5
\end{aligned}
\)
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