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Statistics / Probability and Statistics for Engineering and the Sciences 9 / Chapter 1 / Problem 42E

Probability and Statistics for Engineering and the Sciences | 9th Edition | ISBN: 9781305251809 | Authors: Jay L. Devore

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Answer: a. If a constant c is added to each xi in a

Chapter 1, Problem 42E

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QUESTION:

Problem 42E

a. If a constant c is added to each xi in a sample, yielding yi = xi + c, how do the sample mean and median of the yis relate to the mean and median of the xis? Verify your conjectures.

b. If each xi is multiplied by a constant c, yielding yi = cxi, answer the question of part (a). Again, verify your conjectures.

Questions & Answers

QUESTION:

Problem 42E

a. If a constant c is added to each xi in a sample, yielding yi = xi + c, how do the sample mean and median of the yis relate to the mean and median of the xis? Verify your conjectures.

b. If each xi is multiplied by a constant c, yielding yi = cxi, answer the question of part (a). Again, verify your conjectures.

ANSWER:

Answer :

Step 1 of 2:

If a constant c is added to each xi in a sample, yielding yi = xi + c

Then how do the sample mean and median of the yis relate to the mean and median of the xis.

Then,

Mean is

$\overline{y}$ = $\frac{\Sigma{}{y}_{i}}{n}$

= $\frac{\Sigma{}({x}_{i}+\ c)\ }{n}$

= $\frac{\Sigma{}{x}_{i}}{n}$ + $\frac{nc}{n}$

= $\overline{x}$ + c

$\$ the median of ( ${x}_{1}+\ c$ , ${x}_{2}+\ c$ + ……. + ${x}_{n}+\ c$ )

Median of ( ${x}_{1}$ + ${x}_{2}$ + ……..+ ${x}_{2}$ ) + c = $\overline{x}$ + c

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