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If the standard deviation of Set B is 12.5, then what is the standard
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26 Jun 2021, 02:39
26 Jun 2021, 02:39
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Set A: \(a, b, c, d, e\)
Set B: \(\frac{2}{3}a - 6, \frac{2}{3}b - 6, \frac{2}{3}c - 6, \frac{2}{3}d - 6, \frac{2}{3}e - 6\)
If the standard deviation of Set B is 12.5, then what is the standard deviation of Set A?
Set B: \(\frac{2}{3}a - 6, \frac{2}{3}b - 6, \frac{2}{3}c - 6, \frac{2}{3}d - 6, \frac{2}{3}e - 6\)
If the standard deviation of Set B is 12.5, then what is the standard deviation of Set A?
Show: ::
18.75
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If the standard deviation of Set B is 12.5, then what is the standard
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26 Jun 2021, 05:27
26 Jun 2021, 05:27
2
KarunMendiratta wrote:
Set A: \(a, b, c, d, e\)
Set B: \(\frac{2}{3}a - 6, \frac{2}{3}b - 6, \frac{2}{3}c - 6, \frac{2}{3}d - 6, \frac{2}{3}e - 6\)
If the standard deviation of Set B is 12.5, then what is the standard deviation of Set A?
Set B: \(\frac{2}{3}a - 6, \frac{2}{3}b - 6, \frac{2}{3}c - 6, \frac{2}{3}d - 6, \frac{2}{3}e - 6\)
If the standard deviation of Set B is 12.5, then what is the standard deviation of Set A?
Show: ::
18.75
Key concept #1: Adding or subtracting the same number from every number in a set does not change the standard deviation
Key concept #2: If every number in a set is multiplied by k, then the new standard deviation = (k)(old standard deviation)
Let S = the standard deviation of \({a, b, c, d, e}\)
By concept #2, the standard deviation of \({\frac{2}{3}a, \frac{2}{3}b, \frac{2}{3}c, \frac{2}{3}d, \frac{2}{3}e}\) \(= \frac{2}{3}S\)
By concept #1, the standard deviation of \({\frac{2}{3}a-6, \frac{2}{3}b-6, \frac{2}{3}c-6, \frac{2}{3}d-6, \frac{2}{3}e-6}\) \(= \frac{2}{3}S\)
If the standard deviation of Set B is 12.5, we can write: \(\frac{2}{3}S = 12.5\)
Multiply both sides of the equation by \(\frac{3}{2}\) to get: \(S = 18.75\)
Since S represents the standard deviation of Set A, the answer is \(18.75\)
General Discussion
Re: If the standard deviation of Set B is 12.5, then what is the standard
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27 Jun 2024, 08:32
27 Jun 2024, 08:32
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