The variance of 10 observations is 25. If 2 is multiplied to each of the observations and subsequently 7 is subtracted from each multiplied observation, then what is the new variance?
100
If each observation is transformed as \(Y=2X-7\), the variance scales by the square of the multiplying constant while the subtracted constant has no effect: \(\text{Var}(Y)=2^{2}\,\text{Var}(X)\). With \(\text{Var}(X)=25\), the new variance is \(4\times25=100\).
Similar Questions
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