If the mean of ^@ 6 ^@ observations ^@ x, x + 2, x + 4, x + 6, x + 8, x + 10^@ is ^@ 10 ^@, find the value of ^@ x. ^@


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Answer:

^@ 5 ^@

Step by Step Explanation:
  1. We know, @^ \text { Mean } = \dfrac {\text{Sum of observations}} {\text{Number of observations}} @^
  2. Thus, mean of the given observations @^ = \dfrac { x + x + 2+ x + 4+ x + 6+ x + 8+ x + 10 } { 6 } = \dfrac { 6 x + 30 } { 6 } @^ But we are given that the mean is ^@ 10. ^@ @^ \begin{aligned} \therefore \space & \dfrac { 6 x + 30 } { 6 } = 10 \\ \implies & 6 x + 30 = 60 \\ \implies & 6 x = 30 \\ \implies & x = 5 \end{aligned} @^
  3. Hence, the value of ^@ x ^@ is ^@ 5 ^@.

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