The list shown consists of the times, in seconds, that

[Guest]

70, 75, 80, 85, 90, 105, 105, 130,130,130

The list shown consists of the times, in seconds, that it took each of 10 students to run a distance of 400 meters. If the std. deviation of the 10 running times is 22.4 sec, rounded to nearest tenth of a second , how many of the 10 running times are more than 1 Std deviation below the mean of the 10 running times?

1) One
2) two
3)three
4) four
5)five

Answer is : 2

Source: Gmatprep 2

Can you please explain

[Guest]

I have an exam next week...So i will appreciate the explanation to above question from any smart fella here:)

[mbarshaik]

Calcluate the mean i,e 100

Now the question says values below one SD from teh mean. So find values below (100 - 22.4 = 77.6) there are only 2 values satisfying 70 and 75

Note if teh question says away from mean instead of below mean then we should also consider values > 100 + 22.4

Hope this helps.

[RonPurewal]

ah, yes, i can see why you might have some trouble deciphering this one.

in this problem, you have to memorize the english convention for interpreting this question.

the WRONG way to read this question is:
more than 1 standard deviation below the mean
this interpretation would compel you to find the number that's 1 standard deviation below the mean, and then look for values above that number. that is NOT what you're supposed to do.

the CORRECT way to read this question is:
more than 1 standard deviation below the mean
this interpretation compels you to find the number that's 1 standard deviation below the mean, and then look for values below that number. this is the correct interpretation.
in other words, it's the same as saying "less than the mean by a margin of more than 1 standard deviation".

YOU MUST KNOW THIS INTERPRETATION, as the language is, technically, ambiguous.
same goes for similar expressions, such as "more than 30 degrees below the boiling point". that expression would refer to temperatures below (boiling point - 30), for the same reasons.

--

note also that you don't need the concept of standard deviation at all to solve this problem. indeed, the problem is altogether unchanged if you replace "standard deviation" with "pink flamingo", as detailed here.

[guron]

mbarshaik,

The mean is (90+105)/2 = 97.5, not 100!
[editor: incorrect. that's the median, not the mean.]

And then 1 SDev below the mean is 97.5-22.4 = 75.1.

So, the answer 2 is still correct.

[komal.agrawal09]

I interpret it like: How many numbers are above 1 standard deviation Minus How many numbers are below mean of the numbers

In this case,the mean is 100
1 standard deviation=mean + sd=100+22.4=122.4

Numbers above 122.4=3
Numbers below mean=5
Difference is 2

Not very sure if this way is correct !

[RonPurewal]

I interpret it like: How many numbers are above 1 standard deviation Minus How many numbers are below mean of the numbers

In this case,the mean is 100
1 standard deviation=mean + sd=100+22.4=122.4

Numbers above 122.4=3
Numbers below mean=5
Difference is 2

Not very sure if this way is correct !

this is incorrect.

i posted a very exhaustive explanation of this question prompt just a couple of posts earlier:
post20154.html#p20154

[mariabfa]

is there a shorcut to find that the mean=100 without having to add all 10 different numbers and divide by 10? i know if the numbers were evenly spaced, we could just take the middle value but in this case the numbers are not evenly spaced...pls help! thank you

[shubham_sagijain]

Ron/Stacey ,

Please check whether my reasoning is correct here...

Mean = 100 and one Standard deviation = 100 - 22.4 = 77.6
So, we know now that 1 S.D = 77.6

Only 2 values will be less than 77.6 (i.e more than 1 S.D below the Mean)

If the statement would have said one standard deviation above the mean, then i would calculate 100 + 22.4 = 122.4...Right ?

And the answer would have been 3 (130, 130 ,130)...am i correct ?

Thanks,
Shubh

[jnelson0612]

Ron/Stacey ,

Please check whether my reasoning is correct here...

Mean = 100 and one Standard deviation = 100 - 22.4 = 77.6
So, we know now that 1 S.D = 77.6

Only 2 values will be less than 77.6 (i.e more than 1 S.D below the Mean)

If the statement would have said one standard deviation above the mean, then i would calculate 100 + 22.4 = 122.4...Right ?

And the answer would have been 3 (130, 130 ,130)...am i correct ?

Thanks,
Shubh

Exactly! Very good! :-)