JEE Mains · Maths · STD 11 - 13. statistics
The mean and variance of \(10\) observations were calculated as \(15\) and \(15\) respectively by a student who took by mistake \(25\) instead of \(15\) for one observation. Then, the correct standard deviation is\(.....\)
- A \(4\)
- B \(6\)
- C \(2\)
- D \(8\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
\(n =10, \bar{x}=\frac{\sum x_{i}}{10}=15\) \(6^{2}=\frac{\sum x_{i}^{2}}{10}-(\bar{x})^{2}=15\) \(\sum_{i=1}^{10} x_{i}=150\) \(\sum_{i=1}^{9} x_{i}+25=150\) \(\sum_{i=1}^{9} x_{i}=125\) \(\sum_{i=1}^{9} x_{i}+15=140\) Actual mean \(=\frac{140}{10}=14=\bar{x}_{\text {nev }}\)…
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