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The n th term, where n > 1, in a series S of positive integers is

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The n th term, where n > 1, in a series S of positive integers is [#permalink]

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New post 05 Nov 2017, 22:15
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Question Stats:

42% (00:39) correct 58% (00:41) wrong based on 19 sessions

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The nth term, where n > 1, in a series S of positive integers is defined by \(t_n\) = \(t_{n-­1}+4\). What is the standard deviation of the
elements in S?

(1) The series contains 11 elements.
(2) The first element in the series is 7.
[Reveal] Spoiler: OA

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Re: The n th term, where n > 1, in a series S of positive integers is [#permalink]

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New post 05 Nov 2017, 23:08
Standard deviation is calculated by taking the differences of 'Arithmetic Mean' with each of the individual values, then squaring the differences, then taking average of these squares, and finally taking square root of the result so calculated. So if we can get all the differences (between Mean and individual values) we can calculate the standard deviation (whether we know individual values and/or mean or not).

Given is an AP series with a common difference of 4. Thus a, a+4, a+8, a+12,... and so on

(1) Series has 11 elements. So from a, a+4,... till a+40. So mean will be the middle value, 6th term, which is a+20. Now we can calculate all the differences between individual values and mean as: -20, -16, -12,... till 20. Standard deviation can be calculated. Sufficient.

(2) First element is 7. So this series is: 7, 11, 15, 19,.. and so on. But we dont know till where this series goes and thus we cannot calculate the mean of this series and we cannot have any idea about differences between individual values and mean. Standard deviation cannot be calculated. Insufficient.

Hence A answer

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Re: The n th term, where n > 1, in a series S of positive integers is [#permalink]

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New post 06 Nov 2017, 01:06
In simple terms, Standard Deviation is how far are values from the mean.
Series S is an Arthemetic Progression with difference 4.

1. We know there are 11 terms. No matter what are the terms, there relative distance from mean would remain same.
Sufficient.

2. We know the start of the series. SD would change based on no. of terms.
Insufficient.

A.
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Re: The n th term, where n > 1, in a series S of positive integers is   [#permalink] 06 Nov 2017, 01:06
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