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List M(not shown) consists of 8 different integers, each of

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List M(not shown) consists of 8 different integers, each of

by eitijan » Thu Mar 03, 2016 6:09 am
4, 6, 8f 10,12, 14, 16,18, 20, 22

List M(not shown) consists of 8 different integers,each of which is in the list shown. What is the standard deviation of the numbers in list M?

(1) The average (arithmetic mean) of the numbers in list M is equal to the average of the numbers in the list shown.
(2) List Mdoes not contain 22.


For the list of 10 nos, mean = Mean of 8 terms (M) = 13
Statement 1:

Here,
S(n terms)= n/2{2a+(n-1)d}
where, n= no of terms in the list
a= first term of the list
d= constant difference of the term with the succeeding term
Mean= Sum/n
13= (8/2[2a + 7*2])/8
This gives value of a=6

Also, S(n terms) = n/2[a+l]
where, l = last term of the list

13= 8/2[6+l]/8
gives l =20

i.e. we know the list M
and so Statement 1 is sufficient.

Please correct me if I am wrong as OA is not A but C.
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by DavidG@VeritasPrep » Thu Mar 03, 2016 6:33 am
eitijan wrote:4, 6, 8, 10,12, 14, 16,18, 20, 22

List M(not shown) consists of 8 different integers,each of which is in the list shown. What is the standard deviation of the numbers in list M?

(1) The average (arithmetic mean) of the numbers in list M is equal to the average of the numbers in the list shown.
(2) List Mdoes not contain 22.


For the list of 10 nos, mean = Mean of 8 terms (M) = 13
Statement 1:

Here,
S(n terms)= n/2{2a+(n-1)d}
where, n= no of terms in the list
a= first term of the list
d= constant difference of the term with the succeeding term
Mean= Sum/n
13= (8/2[2a + 7*2])/8
This gives value of a=6

Also, S(n terms) = n/2[a+l]
where, l = last term of the list

13= 8/2[6+l]/8
gives l =20

i.e. we know the list M
and so Statement 1 is sufficient.

Please correct me if I am wrong as OA is not A but C.
The problem with this approach is that the formula is for evenly spaced sets, but we don't know if M is evenly spaced. All we know is that the mean is 13. So you could have the set: 6, 8, 10,12, 14, 16,18, 20. (If it's evenly spaced.) But you could also have: 4, 8, 10,12, 14, 16,18, 22. These sets will have different standard deviations. So the statement alone is not sufficient.
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by GMATGuruNY » Thu Mar 03, 2016 8:27 am
4, 6, 8, 10, 12, 14, 16, 18, 20, 22

List M(not shown) consists of 8 different integers, each of which is in the list shown(above). What is the standard deviation of the numbers in list M?

(1) The average (arithmetic mean) of the numbers in list M is equal to the average of the numbers in the list shown.
(2) List M does not contain 22.

Thanks
The list above contains 10 integers.
List M contains 8 of these integers.
To determine the standard deviation of list M, we need to know WHICH 2 INTEGERS from the list above are NOT included in list M.

For any set of evenly spaced numbers:
average = median = (biggest+smallest)/2.
sum = number*average.

Thus, for the list of 10 integers above:
Average = (4+22)/2 = 13.
Sum = 10*13 = 130.

Statement 1: The average (arithmetic mean) of the numbers in list M is equal to the average of the numbers in the list shown.
Thus, the average of the 8 integers in list M = 13.
Sum = 8*13 = 104.
Since the sum of the 8 integers in list M (104) is 26 less than the sum of the 10 integers in the list above (130), the 2 integers NOT included in list M must have a sum of 26.
Thus, any of the following could be the pair NOT included in list M:
4+22, 6+20, 8+18, 10+16, 12+14.
INSUFFICIENT.

Statement 2: List M does not contain 22.
No way to determine the OTHER integer not included in list M.
INSUFFICIENT.

Statements 1 and 2 combined:
Since the 2 integers not included in list M must have a sum of 26, and 22 is one of these integers, the other integer not included in list M must be 4.
SUFFICIENT.

The correct answer is C.
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