Standard Deviation Problems 2

[freezer]

• For a certain exam a score of 58 is 2 standard deviations below the mean and a score of 98 is 3 standard deviations above mean. What was the mean score of the exam?

a) 16
b) 40
c) 72
d) 74
82

Could anyone give me step by step solution?

Thanks

[krishna_k1]

Answer is d.

74 - 58 = 16. so the sd is 8. 8 *3 + 74 = 98.

[aru4912]

M=> mean, S.D=> Standard Deviation

M-58 = 2 * S.D
M+3 * SD =98

Rearranging ..,
M-58=2SD
M-98 = -3SD

=> 5 SD = 40 => SD = 5

Subst. SD in anyone of the above eqn. will give you the mean.It is 74

[bhavinparekh]

D.

The way I figured it out was to take the difference between 58 & 98
98 - 58 = 40. This corresponds to 5 standard deviations for the question.

Hence, 40/5 = 8 is one standard deviation....

So Mean = 58 + 2*8 = 74; 98 - 3*8 = 74.

Hence D.

[CrackXam]

Can someone plz list the formulae for standard deviation!

Thanks

[Prawler]

[Sum (Variable - Mean ) ] / n

n= number of variables.

[krusta80]

[Sum (Variable - Mean ) ] / n

n= number of variables.

Not correct.

std dev = sqrt(Sum([Variable-Mean]^2)/n)

[Giscard]

You don't need to know std dev to solve this problem. 58 is 2*stuff down, 98 is 3*stuff up. Whatever this "stuff" might be, the answer is 74.

[bads123]

avg = 58 + 2d
avg = 98 - 3d
d = 8
avg = 74

[umgrad76]

I agree 98-85 = 40 ---> 40/5=8 ----> 58+2*8=74