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

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

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

by Gmat_mission » Sun May 31, 2020 1:43 pm

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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 \(M\) does not contain 22.

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Source: Beat The GMAT — Data Sufficiency | Sun May 31, 2020 1:43 pm

JamesHammel: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Sun May 31, 2020 4:19 pm

Re: List \(M\) (not shown) consists of 8 different integers, each of which is in the list shown. What is the standard

by JamesHammel » Mon Jun 01, 2020 3:16 am

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To find the standard deviation we need: the mean, the set of numbers in the list.

1) The mean in the list = the mean of M. Since the list is equally spaced, we can calculate the mean by \(\frac{first\ number\ +\ last\ number}{2}\) = \(\frac{4+\ 22}{2}\) = 13

Since the given list has 10 elements, the sum will be 13 * 10 = 130
Since list M has 8 elements, the sum will be 13 * 8 = 104
The difference inbetween the lists is equal to the sum of the two missing numbers in list M. The difference is 26.
-> This is insufficient information as there are several ways of finding a difference of 26 (e.g 10+16 or 18+8)

2) We are told list M does not contain the number 22.
We do not know the mean of list M with this information, as we do not know what other number list M does not contain.
-> insufficient

C) With 1) and 2) combined we know that the second number not contained in the list will be 22 + x = 26. x = 4.

We know have all the information required to find the standard deviation
C) is the correct answer