In a certain sample of data, mean is = 25 and standard deviation is

Question

In a certain sample of data, mean is = 25 and standard deviation is = 5 , then which of the following values is more than 3 standard deviation from mean ?

A. 8
B. 15
C. 21
D. 33
E. 4

globaldesi · Answer

the deviation difference is calculated as m+- td where m is mean , d is deviation and t is the term

so two values are m+4d and m-4d
25+20; 25-20
44 and 5
E satisfies as 4

nitishjain0109 · Answer

Wouldn't "which value is more than 3 eviations be" more than 5 that is 6? Which is not the part of answer?

AndrewN · Answer

There are two considerations here:

a  range  of values, not a particular value, will lie within any given standard deviation   a standard deviation is the same distance from the mean in either direction, so if    mean is = 25 and   standard deviation is = 5 , then  about the mean , each deviation would be + or - 5 from the mean:

Value : 5, 10, 15, 20,  25 , 30, 35, 40, 45
 S.D. : -4, -3, -2, -1,  mean , +1, +2, +3, +4
 Range : (0-5], (5-10], (10-15], (15-20], (20-30),  more than 3 standard deviations from the mean , then we need to look for a value that would lie at least 4 standard deviations from the mean, or, in other words, either greater than or equal to 45 or  less than  or equal to 5. Since there are no values in the answer choices beyond 33, we have to look at the opposite end of the spectrum, and there, only 4 satisfies the question. Thus,   the answer must be (E)  .

I hope this helps. Good luck with your studies.

- Andrew

anirchat · Answer

I think the asnwer should be 8. 4 would be ans answer if teh question was to find a value at least 4 SD from the mean.

RJJ · Answer

wouldn't A and E be the answer?

Bunuel · Answer

The wording isn’t perfect, but the question is essentially asking which value lies more than 3 standard deviations away from the mean — that is, either less than 25 - 3 * 5 = 10 or greater than 25 + 3 * 5 = 40. The only value that satisfies this is 4. Here are some similar questions with better wording: https://gmatclub.com/forum/for-a-certai ... 28661.html https://gmatclub.com/forum/a-vending-ma ... 93351.html Hope it helps.

RJJ · Answer

isn't 8 also less than 10 ?? or is option a supposed to be 18 ?

Bunuel · Answer

Ah, yes, I initially thought it was 18 too — definitely not a well-worded question.

Archiving the question.

In a certain sample of data, mean is = 25 and standard deviation is

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