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Standard Deviation.

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Standard Deviation.

by Ashetty » Fri Sep 23, 2011 6:52 am
9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5

The mean and standard deviation of the 8 number shown are 10.0 & 0.3 respectively. What percent of 8 numbers are with in 1 standard deviation of the mean?.

A.90%
B.85%
C.80%
D.75%
E.70%

Ans:[spoiler]D.75%[/spoiler]
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by gmatclubmember » Fri Sep 23, 2011 6:58 am
Ashetty wrote:9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5

The mean and standard deviation of the 8 number shown are 10.0 & 0.3 respectively. What percent of 8 numbers are with in 1 standard deviation of the mean?.

A.90%
B.85%
C.80%
D.75%
E.70%

Ans:[spoiler]D.75%[/spoiler]
One SD from mean means 9.7 (10-.3) to 10.3(10+.3)
6 nos. fall in this range out of total 8. So the chances are 75% (6/8).

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by Ashetty » Fri Sep 23, 2011 7:11 am
Still could,t understand..Can you please explain me in more detail??ThaNKS!!
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by knight247 » Fri Sep 23, 2011 7:29 am
9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5 are the set of numbers. The mean for this sample of numbers is 10

Lets draw a number line representing 10

|---------------10---------------|

Now, when the standard deviation of a set of numbers is a certain value eg.x, it means that all the elements of that set vary by x on either side of the mean i.e. they lie between 10-x and 10+x. Hope you are clear with that part.

Now, since we are told that SD is 0.3 and 1 standard deviation is still 0.3. It means that the elements all lie between 10-0.3 to 10+0.3 which is 9.7 to 10.3

|---------9.7-----10-----10.3--------|

How many elements in the set 9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5 lie in the range represented by the number line I've drawn above. Lets list them

9.9,9.9,9.9,10,10.2,10.2 i.e. 6 numbers out of the 8

(6/8)*100=75% Hence D


You may want to check this other problem to clarify ur doubts on SD
https://www.beatthegmat.com/standard-dev ... tml#409503
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by gmatclubmember » Fri Sep 23, 2011 7:30 am
gmatclubmember wrote:
Ashetty wrote:9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5

The mean and standard deviation of the 8 number shown are 10.0 & 0.3 respectively. What percent of 8 numbers are with in 1 standard deviation of the mean?.

A.90%
B.85%
C.80%
D.75%
E.70%

Ans:[spoiler]D.75%[/spoiler]
One SD from mean means 9.7 (10-.3) to 10.3(10+.3)
6 nos. fall in this range out of total 8. So the chances are 75% (6/8).

Cheers
Ami/-

One SD from mean means: mean+1*sd to mean-1*sd
2 SD from mean means : mean+2*sd to mean-2*sd.
this is how I got the range 9.7 to 10.3.
Hope this is clear now.
Plz ping again if not clear :)

Cheers
Ami/-
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by Brent@GMATPrepNow » Fri Sep 23, 2011 8:07 am
Ashetty wrote:#?, #?, #?, #?, #?, #?, #?, #?

The mean and standard deviation of the 8 number shown are something & something else respectively. What percent of 8 numbers are with in 1 standard deviation of the mean?.

A.90%
B.85%
C.80%
D.75%
E.70%

Ans:[spoiler]D.75%[/spoiler]
The distractors (incorrect answer choices) aren't very good here.
Notice that we can still answer the question, even if we don't know any of the values in the question.

The answer must be [spoiler]75%[/spoiler] since it is impossible for x/8 to equal any of the answer choices other than [spoiler]75%[/spoiler]

For example, there is no value of x such that x/8 = 90% (or 85%, or 80% etc)

I mention all of this to make the point that, even if we don't know the answer to a question, we can sometimes eliminate some answer choices.

Of course, here we could eliminate 4 answer choices without knowing what standard deviation means :-)

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by gmatclubmember » Fri Sep 23, 2011 8:25 am
Brent@GMATPrepNow wrote:
Ashetty wrote:#?, #?, #?, #?, #?, #?, #?, #?

The mean and standard deviation of the 8 number shown are something & something else respectively. What percent of 8 numbers are with in 1 standard deviation of the mean?.

A.90%
B.85%
C.80%
D.75%
E.70%

Ans:[spoiler]D.75%[/spoiler]
The distractors (incorrect answer choices) aren't very good here.
Notice that we can still answer the question, even if we don't know any of the values in the question.

The answer must be [spoiler]75%[/spoiler] since it is impossible for x/8 to equal any of the answer choices other than [spoiler]75%[/spoiler]

For example, there is no value of x such that x/8 = 90% (or 85%, or 80% etc)

I mention all of this to make the point that, even if we don't know the answer to a question, we can sometimes eliminate some answer choices.

Of course, here we could eliminate 4 answer choices without knowing what standard deviation means :-)

Cheers,
Brent

Brent,
Well that was a smart trick you pulled out :). Seems like your morning coffee is working :))


Cheers
Ami/-
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