Question

If the average of 6 observation is 42 and another 6 observation is 45 find the average of all 12 observation

Answer 1

$\mathbf{Average \: \: of \: \: all \: \: 12 \: \: observations = \frac{sum \: of \: 12 \: observations}{12} }$


Hence,

Average of 6 observations = ( sum of 6 observations ) / 6


=> 42 = ( sum of 6 observations ) / 6


$\mathbf{ => 252 = sum \: of \: 6 \: observations }\: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(i)$




Average of another 6 observations = ( sum if another 6 observations ) / 6


=> 45 = ( sum of another 6 observations ) / 6


$\mathbf{ => 270 = sum \: of \: another \: 6 \: observations} \: \: \: \: \: \: \: \: \: \: \: \: \: ...(ii)$




Hence,

Averages of all 12 observations = ( sum of 6 observations + sum of another 6 ) / 12



$=> Average \: \: of \: \: all \: \: 12 \: \: observations = \frac{256 + 270}{12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ( Putting \: \: values \: \: from \: \: ( i ) and ( ii ), )$




Average = ( 522 ) / 12


Average = 43.5




Hebce, Average of all 12 observations is 43.5

Answer 2

522/12= 43.5
Refer to the above attachment:)

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