For the set of numbers \(\{20,14,19,12,17,20,24\},\) let \(x\) equal the median, \(v\) equal the mean, \(w\) equal the

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For the set of numbers \(\{20,14,19,12,17,20,24\},\) let \(x\) equal the median, \(v\) equal the mean, \(w\) equal the mode, and \(y\) equal the range. Which of the following is true?

A. \(v<w<x<y\)

B. \(v<x<w<y\)

C. \(y<v<w<x\)

D. \(y<v<x<w\)

E. \(w<y<v<x\)

Answer: D

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VJesus12 wrote:
Fri Sep 04, 2020 6:02 am
For the set of numbers \(\{20,14,19,12,17,20,24\},\) let \(x\) equal the median, \(v\) equal the mean, \(w\) equal the mode, and \(y\) equal the range. Which of the following is true?

A. \(v<w<x<y\)

B. \(v<x<w<y\)

C. \(y<v<w<x\)

D. \(y<v<x<w\)

E. \(w<y<v<x\)

Answer: D

Solution:

In ascending order, the numbers are: 12, 14, 17, 19, 20, 20, 24.

Since x is the median, x = 19.

Since v is the mean, v = (12+14+17+19+20+20+24) / 7 = 18.

Since w is the mode, w = 20.

Since y is the range, y = 24 - 12 = 12.

We see that y < v < x < w.

Answer: D

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