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Chapter 13 Class 11 Statistics | 5 questions | about 4 minutes

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Question 1 of 5
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Question 1 of 5
For the dataset \(x = 3, 7, 11, 15, 19\), find the value of \(c\) that minimizes \(f(c) = \sum_{i=1}^{5} (x_i - c)^2\), and calculate this minimum sum of squared deviations.
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Question 2 of 5
The standard deviation of \(x_1, x_2, \dots, x_n\) is \(\sigma_x = 6\). Calculate the standard deviation of \(y_i = -2x_i + 5\).
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Question 3 of 5
The variance of \(20\) observations is \(5\). If each observation is multiplied by \(2\), calculate the variance of the resulting observations.
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Question 4 of 5
The mean and standard deviation of \(100\) observations were calculated as \(40\) and \(5.1\) respectively. It was later found that one observation was incorrectly recorded as \(50\) instead of \(40\). Calculate the correct standard deviation.
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Question 5 of 5
Investment Fund P has average return \(\bar{x}_P = 12\%\) with \(\sigma_P = 2\%\). Fund Q has average return \(\bar{x}_Q = 15\%\) with \(\sigma_Q = 5\%\). Calculate the Coefficients of Variation \(C.V._P\) and \(C.V._Q\).
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