AP EAMCET · Maths · Statistics
If the mean of two samples of sizes 20 and 30 are 25 and 10 respectively, their variances are 9 and 16 respectively, their combined variance is
- A \(67.9\)
- B \(68.2\)
- C \(68.1\)
- D \(67.2\)
Answer & Solution
Correct Answer
(D) \(67.2\)
Step-by-step Solution
Detailed explanation
\(\bar{x}_{combined} = \frac{n_1\bar{x}_1 + n_2\bar{x}_2}{n_1 + n_2} = \frac{(20)(25) + (30)(10)}{20 + 30} = \frac{500 + 300}{50} = \frac{800}{50} = 16\) \(d_1 = \bar{x}_1 - \bar{x}_{combined} = 25 - 16 = 9\) \(d_2 = \bar{x}_2 - \bar{x}_{combined} = 10 - 16 = -6\)…
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