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The mean of a set of 30 observations is 75. If each other observation is multiplied by a non-zero number λ and then each of them is decreased by 25, their mean remains the same. Then λ is equal to
- 10/3
- 4/3
- 1/3
- 2/3
Correct answer: 4/3
Solution
The mean remains unchanged when each observation is scaled by a factor and then adjusted by a constant, provided the scaling factor and the adjustment are balanced. In this case, multiplying by λ and subtracting 25 must offset each other to maintain the original mean, leading to the conclusion that λ must be 4/3.
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