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Which of the following contains the interval two standard deviations f
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02 Dec 2021, 10:04
02 Dec 2021, 10:04
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Which of the following contains the interval two standard deviations from the mean of a set of data with an arithmetic mean of 46 and a standard deviation of 4 ?
A. 38 to 46
B. 38 to 54
C. 42 to 50
D. 44 to 48
E. 46 to 50
A. 38 to 46
B. 38 to 54
C. 42 to 50
D. 44 to 48
E. 46 to 50
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Re: Which of the following contains the interval two standard deviations f
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02 Dec 2021, 10:25
02 Dec 2021, 10:25
Carcass wrote:
Which of the following contains the interval two standard deviations from the mean of a set of data with an arithmetic mean of 46 and a standard deviation of 4 ?
A. 38 to 46
B. 38 to 54
C. 42 to 50
D. 44 to 48
E. 46 to 50
A. 38 to 46
B. 38 to 54
C. 42 to 50
D. 44 to 48
E. 46 to 50
---------------ASIDE-----------------
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]
etc.
-------ONTO THE QUESTION!--------------------
We're looking for a number that is 2 standard deviations from the mean of a set of data with an arithmetic mean of 46 and a standard deviation of 4.
So, the number can be either 2 standard deviations ABOVE the mean or 2 standard deviations BELOW the mean. Let's calculate each value...
2 standard deviations BELOW the mean = 46 - 2(4) = 38
2 standard deviations ABOVE the mean = 46 + 2(4) = 54
So we're looking for an interval from 38 to 54
Answer: B
Re: Which of the following contains the interval two standard deviations f
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27 Dec 2021, 10:24
27 Dec 2021, 10:24
The calculation for this is pretty straightforward. You add and subtract from the mean a certain quantity that is obtained by multiplying the standard deviation of the data with another deviation that defines the distance of the data points from the mean on the normal distribution and this could be 1, 2 or 3.
So, we have
Mean ± (Data's Standard Deviation) * (1, 2 or 3)
46 ± (4*2)
= 46 ± 8 = 46 - 8 and 46 + 8
= 38 (the lower limit) and 54 (the upper limit).
Posted from my mobile device
So, we have
Mean ± (Data's Standard Deviation) * (1, 2 or 3)
46 ± (4*2)
= 46 ± 8 = 46 - 8 and 46 + 8
= 38 (the lower limit) and 54 (the upper limit).
Posted from my mobile device
