JEE Mains · Maths · STD 11 - 13. statistics
The mean and standard deviation of \(40\) observations are \(30\) and \(5\) respectively. It was noticed that two of these observations \(12\) and \(10\) were wrongly recorded. If \(\sigma\) is the standard deviation of the data after omitting the two wrong observations from the data, then \(38 \sigma^{2}\) is equal to\(.........\)
- A \(238\)
- B \(239\)
- C \(240\)
- D \(241\)
Answer & Solution
Correct Answer
(A) \(238\)
Step-by-step Solution
Detailed explanation
Wrong mean \(=\mu_{1}=30\) Wrong \(S.D\) \(=\sigma_{1}=5\) \(\frac{\sum x _{ i }}{40}=30\) \(\sum x _{ i }=1200\) \(\sigma_{1}^{2}=25\) \(\frac{\sum x _{ i }^{2}}{40}-30^{2}=25\) \(\sum x _{ i }^{2}=925 \times 40=37000\) New sum \(=\sum x _{ i }^{\prime}=1200-10-12=1178\) New…
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