AP EAMCET · Maths · Statistics
The mean and variance of the observations \(\mathrm{x}_1, \mathrm{x}_2, \mathrm{x}_3, \ldots, \mathrm{x}_{15}\) are respectively 2 and 4. If the mean and variance of the observations \(y_1, y_2, \ldots, y_{10}\) are respectively 2 and 5, then the variance of the observations \(\mathrm{x}_1, \mathrm{x}_2, \ldots \mathrm{x}_{15}, \mathrm{y}_1, \mathrm{y}_2, \ldots, \mathrm{y}_{10}\) is
- A \(6.5\)
- B \(5.3\)
- C \(3.4\)
- D \(4.4\)
Answer & Solution
Correct Answer
(D) \(4.4\)
Step-by-step Solution
Detailed explanation
\( \sum x_i^2 = n_x(\sigma_x^2 + \mu_x^2) = 15(4+2^2) = 15(8) = 120 \) \( \sum y_i^2 = n_y(\sigma_y^2 + \mu_y^2) = 10(5+2^2) = 10(9) = 90 \) \( \mu_{combined} = \frac{n_x \mu_x + n_y \mu_y}{n_x + n_y} = \frac{15 \times 2 + 10 \times 2}{15+10} = \frac{50}{25} = 2 \)…
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