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Intern  Joined: 27 Dec 2011
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If a certain sample of data has a mean of 20.0 and a standard deviatio  [#permalink]

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27 00:00

Difficulty:   15% (low)

Question Stats: 74% (01:00) correct 26% (01:20) wrong based on 584 sessions

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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 08 Oct 2019, 04:47, edited 2 times in total.
Edited the question
Math Expert V
Joined: 02 Sep 2009
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Re: If a certain sample of data has a mean of 20.0 and a standard deviatio  [#permalink]

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14
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

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.

PLEASE DO NOT REWORD OR SHORTEN THE QUESTIONS YOU POST!
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Posts: 682
Re: If a certain sample of data has a mean of 20.0 and a standard deviatio  [#permalink]

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2
So from the mean means below the mean?
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Posts: 10008
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Re: If a certain sample of data has a mean of 20.0 and a standard deviatio  [#permalink]

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

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1
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
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Re: If a certain sample of data has a mean of 20.0 and a standard deviatio  [#permalink]

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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 standard deviatio  [#permalink]

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1
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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Joined: 04 Jun 2016
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Re: If a certain sample of data has a mean of 20.0 and a standard deviatio  [#permalink]

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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

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

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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 ? Board of Directors V
Status: Stepping into my 10 years long dream
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Re: If a certain sample of data has a mean of 20.0 and a standard deviatio  [#permalink]

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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 [ 13.53 KiB | Viewed 12155 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 standard deviatio  [#permalink]

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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 standard deviatio  [#permalink]

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

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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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Originally posted by AweG on 30 Mar 2018, 04:06.
Last edited by AweG on 05 Apr 2018, 04:08, edited 1 time in total.
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Re: If a certain sample of data has a mean of 20.0 and a standard deviatio  [#permalink]

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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.

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

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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

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.

PLEASE DO NOT REWORD OR SHORTEN THE QUESTIONS YOU POST!

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

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Isnt the language confusing? why is the word away missing.

which of the numbers is 2.5SD from the mean? (12 is close to 12.5 & 26.5 is close to 27.5)
or
which of the numbers is 2.5SD away from the mean? (in this case only 12)
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Re: If a certain sample of data has a mean of 20.0 and a standard deviatio  [#permalink]

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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

Any value which is less than 12.5 or more than 27.5 is 2.5 standard deviations from the mean.

Only option A fits the bill in this question and hence the right answer.
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Re: If a certain sample of data has a mean of 20.0 and a standard deviatio  [#permalink]

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