Mean - deviation

[Guest]

Hi, one more question I cannot understand how to solve:

If 58 is 2 standart deviation below the mean and 98 - 3 standart deviation above the mean, what is mean?

[divya8486]

Hi,
we can first write the problem as equations. If 58 is 2 S.D below the mean then it can be written as,
(let us consider m as mean and s as S.D.)
58=m-2s
next if 98 is 3 S.D above the mean,this can be re-written as:
98=m+3s.
Now since we have two equations,solving them we can find out the value of mean and the S.D. The answer that i got is mean is 74 and S.D is 8.

Please correct me if I am wrong.

[RonPurewal]

Hi,
we can first write the problem as equations. If 58 is 2 S.D below the mean then it can be written as,
(let us consider m as mean and s as S.D.)
58=m-2s
next if 98 is 3 S.D above the mean,this can be re-written as:
98=m+3s.
Now since we have two equations,solving them we can find out the value of mean and the S.D. The answer that i got is mean is 74 and S.D is 8.

Please correct me if I am wrong.

absolutely correct.

notice one important theme at work here:
in problems in which you're given a numerical value of the standard deviation, it's actually completely unimportant that it's called "the standard deviation".

let me illustrate.
in this problem, let's remove all references to the standard deviation, and instead refer to it as the "pink flamingo".
then we have:
98 is 3 pink flamingoes above the mean --> 98 = mean + 3(PF)
58 is 2 pink flamingoes below the mean --> 58 = mean - 2(PF)

subtract these two equations:
98 - 58 = 5(PF)
40 = 5(PF)
8 = pink flamingo

the rest follows.

this is an interesting twist on the standard deviation: there are LOTS of gmatprep problems on which the value of the standard deviation is specified, and, uncannily enough, NONE of those problems require an actual understanding of what "standard deviation" means. instead, on ALL of them, all you have to do is treat the SD as though it were some other random quantity (like "pink flamingo").

by contrast, on problems featuring a standard deviation that's NOT given a numerical value - such as problems on which you have to figure out whether the addition of certain numbers to a set will increase or decrease the standard deviation, without actually knowing the value of the standard deviation itself - you actually do need to understand the conceptual significance of the standard deviation itself.

[lockhart.lady]

Hi,
we can first write the problem as equations. If 58 is 2 S.D below the mean then it can be written as,
(let us consider m as mean and s as S.D.)
58=m-2s
next if 98 is 3 S.D above the mean,this can be re-written as:
98=m+3s.
Now since we have two equations,solving them we can find out the value of mean and the S.D. The answer that i got is mean is 74 and S.D is 8.

Please correct me if I am wrong.

Can someone please explain how to use the two equations to solve for both m and s? I thought I could do it by substitution, but I'm hitting a wall and did not get m = 74 and s = 8 when I tried to solve.

Thanks!

[RonPurewal]

if you subtract one equation from the other one (or, equivalently, multiply one of them by -1 on both sides and then add them), then the m's will cancel and you'll be left with one variable.