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In a certain set of numbers, 12.5 is 1.5 units of standard deviation

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Bunuel
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In a certain set of numbers, 12.5 is 1.5 units of standard deviation [#permalink] New post   28 Jan 2019, 02:28
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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?

A. 8.9
B. 9.1
C. 9.5
D. 9.8
E. 12.5
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Archit3110
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Re: In a certain set of numbers, 12.5 is 1.5 units of standard deviation [#permalink] New post   28 Jan 2019, 04:02
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Bunuel 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?

A. 8.9
B. 9.1
C. 9.5
D. 9.8
E. 12.5



given
12.5= M+1.5SD
8.9=M-0.5SD
solve for M
we get
M= 9.8
IMO D
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Re: In a certain set of numbers, 12.5 is 1.5 units of standard deviation [#permalink] New post   22 Feb 2020, 19:29
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From the prompt we can infer that the mean is thrice as close to 8.9 as it is to 12.5. That’s a ratio of 3:1 for a total of 4 ratio units. Take the total distance there (12.5 - 8.9) 3.6, split it four ways and there’s your answer: one ratio unit (0.9) to the right of 8.9.

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Re: In a certain set of numbers, 12.5 is 1.5 units of standard deviation [#permalink] New post   22 Feb 2020, 18:57
Archit3110 wrote:
Bunuel 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?

A. 8.9
B. 9.1
C. 9.5
D. 9.8
E. 12.5



given
12.5= M+1.5SD
8.9=M-0.5SD
solve for M
we get
M= 9.8
IMO D


Can you please explain the operation?

12.5= M+1.5SD —> M = 11
8.9=M-0.5SD —> M = 9.4

We have 2 values for M and none is 9.8

If mix both ecuations:
12.5 + 8.9 = 2M + 1SD —> M = (21.4 - 1SD) / 2. If SD = 1 then M = 10.2

The answer still far from 9.8

Can you please kindly explain me what is wrong in my reasoning?

I solve it in a more subjective way. The mean has to be between 9.4 and 11 because 12.5 - 1.5 = 11 and 8.9 + 0.5 = 9.4. With that in mind only C and D can be the answer, C is to close to the minimum value of the range, so it has to be D.

Is this intuition is right?

But I still do not know how to find the answer with a straightforward math.

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Re: In a certain set of numbers, 12.5 is 1.5 units of standard deviation [#permalink] New post   28 Mar 2020, 03:21
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Andresmadeddie

12.5= M+1.5SD —> M = 11
8.9=M-0.5SD —> M = 9.4

You have considered SD value to be 1 which is not correct. 1.5SD is actually (1.5 x Standard deviation value), where Standard deviation value is unknown.

Hence, there are two variables (M & SD) and two equations. We can solve them to find M, like below:

M +(1.5 x SD) = 12.5
M - (0.5 x SD) = 8.9
--------------------------
This will give you M = 9.8 or SD = 1.8. Hence answer is Mean = 9.8, option D.

I hope this helps :)
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Re: In a certain set of numbers, 12.5 is 1.5 units of standard deviation [#permalink] New post   28 Mar 2020, 09:37
Thank you! I got a “yeyo time” now seems so obvious that I feel ashamed .
It helps. Thank you!

“Yeyo time” = the brain is So burned that obvious things do not looks obvious at all.

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Re: In a certain set of numbers, 12.5 is 1.5 units of standard deviation [#permalink] New post   29 Mar 2020, 00:26
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My solution:

8.9.........0,5........mean..........1,5.........12.5

Ratio is 1:3 (0,5:1,5)
Total distance = 12.5 - 8.9 = 3.6
3.6 / 4 = 0.9
It means that 0.5 distance = 0.9

Mean = 8.9 + 0.9 = 9.8 | 12.5 - (0,9*3)= 12.5 - 2.7 = 9.8

9.8 is the answer

Bunuel
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In a certain set of numbers, 12.5 is 1.5 units of standard deviation [#permalink] New post   29 Mar 2020, 04:00
Hi Bunuel

Can we write 1.5SD as 1SD + 0.5SD ?

If yes, then by this approach we are getting wrong answer.

Please help.
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Re: In a certain set of numbers, 12.5 is 1.5 units of standard deviation [#permalink] New post   29 Mar 2020, 04:04
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a12bansal wrote:
Hi Bunuel

Can we write 1.5SD as 1SD + 0.5SD ?

If yes, then by this approach we are getting wrong answer.

Please help.


The standard deviation is some number, so naturally, 1.5 SD = 1 SD + 0.5 SD but how are you getting different answer from this?
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Re: In a certain set of numbers, 12.5 is 1.5 units of standard deviation [#permalink] New post   29 Mar 2020, 04:15
Bunuel wrote:
a12bansal wrote:
Hi Bunuel

Can we write 1.5SD as 1SD + 0.5SD ?

If yes, then by this approach we are getting wrong answer.

Please help.


The standard deviation is some number, so naturally, 1.5 SD = 1 SD + 0.5 SD but how are you getting different answer from this?



Sorry Bunuel,

I did some wrong calculation.

Thanks a lot for your prompt reply.
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Re: In a certain set of numbers, 12.5 is 1.5 units of standard deviation [#permalink] New post   06 Jan 2022, 23:05
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Bunuel 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?

A. 8.9
B. 9.1
C. 9.5
D. 9.8
E. 12.5


12.5 is 1.5 SD above mean and 8.9 is 0.5 SD below mean. This means that 12.5 - 8.9 = 3.6 accounts for total 2 SD.
Hence 1 SD = 1.8 and 0.5 SD = 0.9.

8.9 is 0.5 SD below the mean so mean = 8.9 + 0.9 = 9.8

Answer (D)
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Re: In a certain set of numbers, 12.5 is 1.5 units of standard deviation [#permalink] New post   19 Jul 2023, 13:02
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M +(1.5 x SD) = 12.5 ------(1)
M - (0.5 x SD) = 8.9 ------(2)
If we multiply eqn(2) with 3, then
M +(1.5 x SD) = 12.5
3M - (1.5 x SD) = 26.7
--------------------------
4M = 39.2
M = 39.2/4 = 9.8
Hope this will help you to understand.
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Re: In a certain set of numbers, 12.5 is 1.5 units of standard deviation [#permalink] New post   19 Jul 2023, 22:28
Based on the given data, consider mean =m and standard deviation = d
therefore m+1.5s=12.5______(1)
m-0.5s=8.9______(2)
solving eq (1) and (2)
we get m=9.8
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Re: In a certain set of numbers, 12.5 is 1.5 units of standard deviation [#permalink]
19 Jul 2023, 22:28
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