JEE Mains · Maths · STD 11 - 13. statistics
The mean of a set of \(30\) observations is \(75\). If each other observation is multiplied by a nonzero number \(\lambda \) and then each of them is decreased by \(25\), their mean remains the same. The \(\lambda \) is equal to
- A \(\frac{{10}}{3}\)
- B \(\frac{{4}}{3}\)
- C \(\frac{{1}}{3}\)
- D \(\frac{{2}}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{{4}}{3}\)
Step-by-step Solution
Detailed explanation
As mean is a linear operation, so if each observation is multipied by \(\lambda \) and decreased by \(25\) then the mean becomes \(75\) \(\lambda - 25\). According to the question, \(75\lambda - 25 = 75 \Rightarrow \lambda = \frac{4}{3}\).
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