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Solved: a. If a constant c is added to each xi in a
Chapter 1, Problem 42E(choose chapter or problem)
a. If a constant c is added to each \(x_{i}\) in a sample, yielding \(y_{i}=x_{i}+c\), how do the sample mean and median of the \(y_{i} \mathrm{s}\) relate to the mean and median of the \(x_{i} \mathrm{s}\)? Verify your conjectures.
b. If each \(x_{i}\) is multiplied by a constant c, yielding \(y_{i}=c x_{i}\), answer the question of part (a). Again, verify your conjectures.
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QUESTION:
a. If a constant c is added to each \(x_{i}\) in a sample, yielding \(y_{i}=x_{i}+c\), how do the sample mean and median of the \(y_{i} \mathrm{s}\) relate to the mean and median of the \(x_{i} \mathrm{s}\)? Verify your conjectures.
b. If each \(x_{i}\) is multiplied by a constant c, yielding \(y_{i}=c x_{i}\), answer the question of part (a). Again, verify your conjectures.
ANSWER:Step 1 of 3
We are asked to verify the conjectures.
If the n observations in a sample are denoted by \(x_{1}\), \(x_{2}\), \(x_{n}\), the sample mean is,
\(\bar{x}=\frac{x_{1}+x_{2}+\ldots \ldots+x_{n}}{n}=\frac{\sum_{i=1}^{n} x_{i}}{n}\) ……..(1)
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Review this written solution for 59901) viewed: 2212 isbn: 9780538733526 | Probability And Statistics For Engineering And The Sciences - 8 Edition - Chapter 1 - Problem 42e
Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.
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