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NDA 2014
Exam
NDA
Year
2014
Subject
Mathematics
Chapter
Statistics

NDA 2014 · Mathematics · Statistics

Paragraph : The mean and standard deviation of 100 items are 50, 5...

Paragraph : The mean and standard deviation of 100 items are 50, 5 and that of 150 items are 40, 6 respectively.
Question : What is the variance of all the 250 items?

Options

  1. A50.6
  2. B53.3
  3. C55.6
  4. D59.3

Correct answer

C. 55.6

Step-by-step solution

 Required variance =100[25+36]+150(36+16)250=6100+7800250=139025=55.6.\begin{aligned} & \text{ Required variance } \\ & =\frac{100[25+36]+150(36+16)}{250} \\ & =\frac{6100+7800}{250}=\frac{1390}{25}=55.6.\end{aligned}
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