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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 combined mean of all 250 items?

Options

  1. A43
  2. B44
  3. C45
  4. D46

Correct answer

B. 44

Step-by-step solution

Here, n1=100,xˉ1=50,σ1=5n2=150,xˉ2=40,σ2=6xˉ12=100×50+150×40100+150=5000+6000250=11000250=44\begin{aligned} & n_1=100, \quad \bar{x}_1=50, \quad \sigma_1=5 \\ & n_2=150, \bar{x}_2=40, \sigma_2=6 \\ & \bar{x}_{12}=\frac{100 \times 50+150 \times 40}{100+150} \\ & =\frac{5000+6000}{250}=\frac{11000}{250}=44 \end{aligned} Hence, combined mean of all 250 items =44=44.
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