JEE Mains · Maths · STD 11 - 13. statistics
For \(10\) observations \(x_1, x_2, \ldots, x_{10}\), if \(\sum_{i=1}^{10}(x_i+2)^2=180\) and \(\sum_{i=1}^{10}(x_i-1)^2=90\), then their standard deviation is:
- A \(2\)
- B \(\sqrt{3}\)
- C \(2\sqrt{2}\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
Given \(\sum_{i=1}^{10}(x_i+2)^2=180\) \(\Rightarrow \sum_{i=1}^{10} x_i^2 + 4\sum_{i=1}^{10} x_i + 40 = 180\) \(\Rightarrow \sum_{i=1}^{10} x_i^2 + 4\sum_{i=1}^{10} x_i = 140\) Also given \(\sum_{i=1}^{10}(x_i-1)^2=90\)…
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