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16 May 2024, 00:58
Kudos
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Question Stats:
50% (01:17) correct
50% (00:06) wrong based on 2 sessions
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A list of numbers has a mean of 8 and a standard deviation of 2.5. If x is a number in the list that is 2 standard deviations above the mean, what is the value of x?
x=?
x=?
19 May 2024, 12:10
Kudos
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This is a question that requires knowledge of standard deviation. Given that mean of the list is 8 and standard deviation is 2.5.
Now if x was one standard deviation above mean that would mean that \(x = 8 +2.5 =10.5\).
However x is given to be two standard deviations above the mean so \(x = 8 +2.5 + 2.5 = 13\).
Hence the answer is \(13\).
Now if x was one standard deviation above mean that would mean that \(x = 8 +2.5 =10.5\).
However x is given to be two standard deviations above the mean so \(x = 8 +2.5 + 2.5 = 13\).
Hence the answer is \(13\).
19 May 2024, 12:11
Kudos
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A little extra background on standard deviations above and below the mean
If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc
So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean = 17 [since 9 + 2(4) = 17]
1.5 standard deviations BELOW the mean = 3 [since 9 - 1.5(4) = 3]
3 standard deviations ABOVE the mean = 21 [since 9 + 3(4) = 21]
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We're told that the mean is 8, and the standard deviation is 2.5
We're also told that x is 2 standard deviations ABOVE the mean
So, x = 8 + 2(2.5)
= 8 + 5
= 13
Answer: 13
If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc
So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean = 17 [since 9 + 2(4) = 17]
1.5 standard deviations BELOW the mean = 3 [since 9 - 1.5(4) = 3]
3 standard deviations ABOVE the mean = 21 [since 9 + 3(4) = 21]
----------------------------------------
We're told that the mean is 8, and the standard deviation is 2.5
We're also told that x is 2 standard deviations ABOVE the mean
So, x = 8 + 2(2.5)
= 8 + 5
= 13
Answer: 13
