ExamBro
ExamBro
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

  1. A \(67.9\)
  2. B \(68.2\)
  3. C \(68.1\)
  4. D \(67.2\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(67.2\)

Step-by-step Solution

Detailed explanation

\(\bar{x}_{combined} = \frac{n_1\bar{x}_1 + n_2\bar{x}_2}{n_1 + n_2} = \frac{(20)(25) + (30)(10)}{20 + 30} = \frac{500 + 300}{50} = \frac{800}{50} = 16\) \(d_1 = \bar{x}_1 - \bar{x}_{combined} = 25 - 16 = 9\) \(d_2 = \bar{x}_2 - \bar{x}_{combined} = 10 - 16 = -6\)…