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

Question

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

avigutman · Accepted Answer

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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Archit3110 · Answer

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

Andresmadeddie · Answer

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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Codebug4it · Answer

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

Andresmadeddie · Answer

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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Ravixxx · Answer

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

a12bansal · Answer

Hi  Bunuel

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

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

Please help.

Bunuel · Answer

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?

a12bansal · Answer

Sorry  Bunuel ,

I did some wrong calculation.

Thanks a lot for your prompt reply.

KarishmaB · Answer

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)

Shazzad777 · Answer

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.

Paras96 · Answer

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

bumpbot · Answer

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

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