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

These questions are excellent to build up on the fundamentals.

The wording should be carefully broken down to arrive at the correct answer.

Given mean= 20.0

Given standard deviation= 3.0

2.5 standard deviations = 2.5 * 3 = 7.5

Distance b/w value and mean must be greater than 7.5

This can be on either side of the graph.

So Mean - SD and Mean +SD is the range or 20-7.5 and 20+7.5

or 12.5 and 27.5

So the value must be either less than 12.5 or more than 27.5

Only a fits the requirement

(option a)


D.S
GMAT SME

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.)

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

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)

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

can someone draw the solution visually ?

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

Hey dave13 ,

Here is the visual representation:



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

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?

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

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

Is this a formula or something? Please help me out with the concept here.

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)

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.

-------ASIDE----------
A little extra background on standard deviations above and below the mean

If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc


So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean = 17 [since 9 + 2(4) = 17]
1.5 standard deviations BELOW the mean = 3 [since 9 - 1.5(4) = 3]
3 standard deviations ABOVE the mean = 21 [since 9 + 3(4) = 21]
etc.
-----------------------------
So, 2.5 standard deviations = (2.5)(3) = 7.5

20 - 7.5 = 12.5
So, 12.5 is 2.5 standard deviations BELOW the mean

20 + 7.5 = 27.5
So, 27.5 is 2.5 standard deviations ABOVE the mean

Answer choice A (12) is more than 2.5 standard deviations from the mean

Answer: A

I didn't understand as to how are we saying - "the value must be less than 12.5 or greater than 27.5"? Need some explanation please:)