JEE Mains · Maths · STD 11 - 13. statistics
The first of the two samples in a group has \(100\) items with mean \(15\) and standard deviation \(3 .\) If the whole group has \(250\) items with mean \(15.6\) and standard deviation \(\sqrt{13.44}\), then the standard deviation of the second sample is:
- A \(5\)
- B \(8\)
- C \(4\)
- D \(6\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
\(n_{1}=100 \quad n=250\) \(\therefore n_{2}=250-100 \Rightarrow n_{2}=150\) \(\bar{x}=\frac{n_{1} \bar{x}_{1}+n_{2} \bar{x}_{2}}{n_{1}+n_{2}}\) \(15.6=\frac{100(15)+(150)\left(\bar{x}_{2}\right)}{250}\) \(\Rightarrow \overline{\mathrm{x}}_{2}=16\)…
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