JEE Mains · Maths · STD 11 - 13. statistics
A data consists of \(20\) observations \(x_1, x_2, \ldots, x_{20}\). If \(\sum_{i=1}^{20}(x_i + 5)^2 = 2500\) and \(\sum_{i=1}^{20}(x_i - 5)^2 = 100\), then the ratio of mean to standard deviation of this data is:
- A \(2:1\)
- B \(3:1\)
- C \(3:2\)
- D \(4:1\)
Answer & Solution
Correct Answer
(B) \(3:1\)
Step-by-step Solution
Detailed explanation
Given \(\sum_{i=1}^{20}(x_i + 5)^2 = 2500\) and \(\sum_{i=1}^{20}(x_i - 5)^2 = 100\). Expanding the first equation: \(\sum_{i=1}^{20} (x_i^2 + 10x_i + 25) = 2500\) \(\sum_{i=1}^{20} x_i^2 + 10 \sum_{i=1}^{20} x_i + 500 = 2500\)…
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