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If the mean of a set of observations \mathrm{y_1, y_2, \ldots, y_n} is \mathrm{y}, then the mean of the observations \mathrm{y_{i-2 i}, where \: i=1,2, \ldots, n} is :

Option: 1

\mathrm{y-2}


Option: 2

\mathrm{y-2 n}


Option: 3

\mathrm{y=(n+1)}


Option: 4

None


Answers (1)

best_answer

To find the mean of the observations \mathrm{y_{(i-2 i)}}, where \mathrm{i=1,2, \ldots, n}, pattern of the new observations.
, we need to understand the pattern of the new observations.

Let's analyze the indices of the new observations:

When \mathrm{i=1}, the index of the new observation is \mathrm{y_{\left(1-2\times 1\right)}=y_{(-1)'}} which is not defined in this case.
When \mathrm{i= 2}, the index of the new observation is \mathrm{y_{\left(2-2\times 1\right)}=y_{(-2)}}' which is also not defined.

For \mathrm{i=3}, the index becomes \mathrm{y_{\left(3-2\times1\right)}=y_{(-3)'}}, which is not defined.

We can observe that for all \mathrm{i>2},the indices of the new observations are negative or beyond the given set of observations.
Since these observations are not defined, we cannot calculate their mean. 

Posted by

manish painkra

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