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In a certain set of numbers, 12.5 is 1.5 units of standard d
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23 Nov 2018, 05:56
23 Nov 2018, 05:56
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In a certain set of numbers, 12.5 is 1.5 units of standard deviation above the mean, and 8.9 is 0.5 units of standard deviation below the mean. What is the mean of the set?
Give your answer to the nearest 0.1.
Give your answer to the nearest 0.1.
Show: :: OA
9.8
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Re: In a certain set of numbers, 12.5 is 1.5 units of standard d
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26 Nov 2018, 07:43
26 Nov 2018, 07:43
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Carcass wrote:
In a certain set of numbers, 12.5 is 1.5 units of standard deviation above the mean, and 8.9 is 0.5 units of standard deviation below the mean. What is the mean of the set?
Give your answer to the nearest 0.1.
Give your answer to the nearest 0.1.
Show: :: OA
9.8
-----------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 unit of standard deviation = 4
2 units of standard deviations = 8
3 units of standard deviations = 12
1.5 units of standard deviations = 6
0.25 units of standard deviations = 1
etc
So, if the mean of a set is 9, and the standard deviation is 4, then:
2 units of standard deviations ABOVE the mean = 17 [since 9 + 2(4) = 17]
1.5 units of standard deviations BELOW the mean = 3 [since 9 - 1.5(4) = 3]
3 units of standard deviations ABOVE the mean = 21 [since 9 + 3(4) = 21]
etc.
-----------ONTO THE QUESTION!---------------------
12.5 is 1.5 units of standard deviation ABOVE the mean
Let M = the mean
Let D = 1 unit of standard deviation
So, we can write: M + 1.5D = 12.5
8.9 is 0.5 units of standard deviation BELOW the mean
We can write: M - 0.5D = 8.9
What is the mean of the set?
So far, we have:
M - 0.5D = 8.9
M + 1.5D = 12.5
We need to solve this system for M
Take top equation and multiply both sides by 3 to get:
3M - 1.5D = 26.7
M + 1.5D = 12.5
Now ADD the two equations to get: 4M = 39.2
Solve, to get: M = 39.2/4 = 9.8
Answer: 9.8
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Re: In a certain set of numbers, 12.5 is 1.5 units of standard d
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08 Nov 2024, 17:59
08 Nov 2024, 17:59
General formulae is (Mean-X)/SD = A unit SD(be y). We get two equation the first of which is 12.5=1.5y+Mean the second of which is 8.9=Mean-0.5y. After solving the equations will find 9.8 for Mean.
