There are 6 observations in a set of data and their mean is 12. If each observation is multiplied by 2, find the new mean.

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Solution

$M e a n = \frac{S u m o f o b s e r v a t i o n s}{N u m b e r o f o b s e r v a t i o n s}$

Given, Mean = 12 and Number of observations = 6

$∴ 12 = \frac{S u m o f o b s e r v a t i o n s}{6}$

$\Rightarrow$ Sum of observations = 72

If each observation is multiplied by 2

New sum of observations is $= 72 \times 2 = 144$

$∴$ New Mean

$= \frac{144}{6} = 24$

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There are 6 observations in a set of data and their mean is 12. If each observation is multiplied by 2, find the new mean.

Mean=Sum of observationsNumber of observations Given, Mean = 12 and Number of observations = 6 ∴12=Sum of observations6 ⇒ Sum of observations = 72 If each observation is multiplied by 2 New sum of observations is =72×2=144 ∴ New Mean =1446=24