pnf619 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 M does not contain 22.
Stuck on this question and taking a lot of time to solve it any good solutions for this question?
It's a good question and can be easily solved using your understanding of mean of AP.
The list shown has 10 equally spaced numbers. Their mean will be the average of middle two numbers i.e. average of 12 and 14 which is 13.
List M has 8 of these 10 numbers. We need the SD of 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.
The mean of list M is 13. But we don't know how the numbers of list M deviate from the mean. We can select 8 numbers in different ways to get mean of 13.
(2) List M does
not contain 22.
We are left with 9 numbers from which we select 8. The SD will be different depending on the numbers we select.
Using both, we have 9 numbers whose mean must be 13. One easy way we know in which we can select the numbers is drop 4 to get 8 equally spaced numbers whose mean will be 13.
List M - (6, 8, 10, 12, 14, 16, 18, 20)
Can you get the same mean by dropping some other number and keeping 4? Think about it - it is not possible. The number of numbers must stay 8. If you replace any other number by 4, the total sum will change which will change the mean. Hence, the only way to select list M is this one. We can easily find the SD here so both statements together are sufficient.
Answer (C)
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Karishma
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