JEE Mains · Maths · STD 11 - 13. statistics
If both the means and the standard deviation of \(50\) observations \(x_1, x_2, ………, x_{50}\) are equal to \(16\) , then the mean of \((x_1 - 4)^2, (x_2 - 4)^2, …., (x_{50} - 4)^2\) is
- A \(400\)
- B \(380\)
- C \(525\)
- D \(480\)
Answer & Solution
Correct Answer
(A) \(400\)
Step-by-step Solution
Detailed explanation
Mean \(\left( \mu \right) = \frac{{\sum {{x_i}} }}{{50}} = 16\) Standard deviation \(\left( \sigma \right) = \sqrt {\frac{{\sum {x_i^2} }}{{50}} - {{\left( \mu \right)}^2}} = 16\) \( \Rightarrow \left( {256} \right) \times 2 = \frac{{\sum {x_i^2} }}{{50}}\) \(\Rightarrow\) New…
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