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If a certain sample of data has a mean of 20.0 and a

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If a certain sample of data has a mean of 20.0 and a  [#permalink]

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New post Updated on: 11 Apr 2012, 01:56
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If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5

Originally posted by sapna44 on 11 Apr 2012, 01:46.
Last edited by Bunuel on 11 Apr 2012, 01:56, edited 1 time in total.
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Re: In a certain sample of data has mean = 20 and standard de  [#permalink]

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New post 11 Apr 2012, 01:55
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sapna44 wrote:
In a certain sample of data has mean = 20 and standard deviation = 3 , which of the following values is more than 2.5 standard deviation from mean ?

A. 12
B. 13.5
C. 17
D. 23.5
E. 26.5


Question should read:
If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5

Value is more than 2.5SD from the mean means that the distance between the mean and the value must be more than 2.5*SD=7.5. So the value must be either less than 20-7.5=12.5 or more than 20+7.5=27.5.

Answer: A.

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Re: If a certain sample of data has a mean of 20.0 and a  [#permalink]

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New post 25 Feb 2013, 20:51
So from the mean means below the mean?
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Re: If a certain sample of data has a mean of 20.0 and a  [#permalink]

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New post 25 Feb 2013, 20:57
1
fozzzy wrote:
So from the mean means below the mean?


No. 'Away from the mean' means either 'below the mean' or 'above the mean'.
(Bunuel has mentioned that the answer will be a value either less than 12.5 or greater than 27.5, in the post above.)
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Re: If a certain sample of data has a mean of 20.0 and a  [#permalink]

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New post 25 Feb 2013, 21:22
Hi,

I thought that a SD of 2.5 from a MEAN of 20 would be a value dispersed 2.5 units away from 20, So I subtracted 2.5 from 20 and got the answer wrong.

Can you please explain why did we multiply SD with 2.5?

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Re: If a certain sample of data has a mean of 20.0 and a  [#permalink]

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New post 25 Feb 2013, 21:40
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sanman wrote:
Hi,

I thought that a SD of 2.5 from a MEAN of 20 would be a value dispersed 2.5 units away from 20, So I subtracted 2.5 from 20 and got the answer wrong.

Can you please explain why did we multiply SD with 2.5?

Cheers


There are two different things here:

SD is 3.
We need to find values which are 2.5 SD away from the mean.

When we say that a value is at mean, it is 20.
When we say that a value is 1 SD away from mean, it means the value is 3 away from mean (because 1 SD is 3). So it can be either 17 or 23.
When we say that a value is 2 SD away from mean, it means that the value is 2*3 away from mean (because 2 SD is 6). So it can be either 14 or 26.
When we say that a value is 2.5 SD away from mean, it means that the value is 2.5*3 away from mean. So it can be either 12.5 or 27.5.

Since we want a value which is more than 2.5 SD away, the value must be less than 12.5 or greater than 27.5.
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Re: If a certain sample of data has a mean of 20.0 and a  [#permalink]

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New post 19 Nov 2013, 15:51
2.5 * 3 = 7.5

20 - 7.5 = 12.5
20 + 7.5 = 27.5

Limits: 12.5 and 27.5

Ans A (12 is out of the limits)
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Re: If a certain sample of data has a mean of 20.0 and a  [#permalink]

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New post 23 Jul 2016, 07:17
1
sapna44 wrote:
If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5


Answer is A

Range of SD will be = mean -2.4 SD + mean + 2.5 SD
Range = 12.5 to 27.5
The only value that falls outside the range is 12 which is lower than 12.5

A
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If a certain sample of data has a mean of 20.0 and a  [#permalink]

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New post 17 Mar 2018, 05:24
sapna44 wrote:
If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5



can someone draw the solution visually ? :-)

is the standandrd deviation the same as distance from the mean ? :?
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If a certain sample of data has a mean of 20.0 and a  [#permalink]

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New post 17 Mar 2018, 09:46
1
dave13 wrote:
can someone draw the solution visually ? :-)

is the standandrd deviation the same as distance from the mean ? :?


Hey dave13 ,

Here is the visual representation:

Attachment:
Untitled.jpg
Untitled.jpg [ 13.53 KiB | Viewed 2938 times ]


Also, standard deviation means distance from the mean only.

Remember, when I say 1 S.D. , it means 3 points below mean and 3 points above mean.

When I say 2 S.D,, it means 6 points below mean and 6 points above mean.

Does that make sense?
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Re: If a certain sample of data has a mean of 20.0 and a  [#permalink]

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New post 17 Mar 2018, 13:11
abhimahna wrote:
dave13 wrote:
can someone draw the solution visually ? :-)

is the standandrd deviation the same as distance from the mean ? :?


Hey dave13 ,

Here is the visual representation:

Attachment:
Untitled.jpg


Also, standard deviation means distance from the mean only.

Remember, when I say 1 S.D. , it means 3 points below mean and 3 points above mean.

When I say 2 S.D,, it means 6 points below mean and 6 points above mean.

Does that make sense?



Hello abhimahna, many thanks for taking time to explain, i have just a couple of questions :)

If you say “ id standard deviation is then it is 6 points from the mean. And if mean is 20, then you from 23 you jump to 27, shouldn’t it be 26, than 29 (i mean your drawing)

Another question regarding the question itself :)
If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

"more than 2.5 standard deviation from the mean" :? i f i mupltiply 2.5 by 3 i get 7.5. So are we looking for number that is more than 7.5 ? :? What does waord "value" itself mean ?

20 -7.5 = 12.5 and 20+7.5 = 27.5 so what ? what is the logic behind choosing A ? :? i know you are bored with my questions:) hope you can still reply :)

A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5
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Re: If a certain sample of data has a mean of 20.0 and a  [#permalink]

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New post 17 Mar 2018, 22:37
1
dave13 wrote:
Hello abhimahna, many thanks for taking time to explain, i have just a couple of questions :)

If you say “ id standard deviation is then it is 6 points from the mean. And if mean is 20, then you from 23 you jump to 27, shouldn’t it be 26, than 29 (i mean your drawing)

Another question regarding the question itself :)
If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

"more than 2.5 standard deviation from the mean" :? i f i mupltiply 2.5 by 3 i get 7.5. So are we looking for number that is more than 7.5 ? :? What does waord "value" itself mean ?

20 -7.5 = 12.5 and 20+7.5 = 27.5 so what ? what is the logic behind choosing A ? :? i know you are bored with my questions:) hope you can still reply :)

A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5


Hey dave13 .

Where do you see 27? :P :lol: (P.S.: That was a typo and I have corrected the same)

Your statement "So are we looking for number that is more than 7.5 ?" is incorrect.

What the question means is you have to find out the numbers that are beyond 2.5 Standard deviations.

So, as you mentioned, we already know that the range we are getting for 2.5 standard deviations is 12.5 - 27.5

So, anything outside this range is the correct answer. Hence, option A is correct.

Remember more than 2.5 S.D means beyond 2.5 S.D.

Does that make sense?
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If a certain sample of data has a mean of 20.0 and a  [#permalink]

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New post Updated on: 05 Apr 2018, 04:08
1
sapna44 wrote:
If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5


SD is a measure of how far away the values are form the average so you have to find the value that is NOT inside [mean-2.5*SD , mean+2.5*SD] <=> [20-2.5*3 , 20+2.5*3] <=> [12.5 , 27.5] only good answer is A
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Re: If a certain sample of data has a mean of 20.0 and a  [#permalink]

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New post 04 Apr 2018, 17:26
1
sapna44 wrote:
If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5


2.5 standard deviations above the mean is 2.5 x 3 + 20 = 7.5 + 20 = 27.5.

2.5 standard deviations below the mean is 20 - 2.5 x 3 = 20 - 7.5 = 12.5.

Thus, a value more than 2.5 standard deviations from the mean would be one that is either greater than 27.5 or less than 12.5. So the correct answer is 12.

Answer: A
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Re: If a certain sample of data has a mean of 20.0 and a  [#permalink]

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New post 04 Aug 2018, 04:56
Bunuel wrote:
sapna44 wrote:
In a certain sample of data has mean = 20 and standard deviation = 3 , which of the following values is more than 2.5 standard deviation from mean ?

A. 12
B. 13.5
C. 17
D. 23.5
E. 26.5


Question should read:
If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5

Value is more than 2.5SD from the mean means that the distance between the mean and the value must be more than 2.5*SD=7.5. So the value must be either less than 20-7.5=12.5 or more than 20+7.5=27.5.

Answer: A.

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Is this a formula or something? Please help me out with the concept here.
Re: If a certain sample of data has a mean of 20.0 and a &nbs [#permalink] 04 Aug 2018, 04:56
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