the mean of 6 observation is 15. four of the observation are 10,18,23 and 9. of the remaining two observation one is four times the other. find them
Answers
Answer:
Given :
The mean of 6 observation is 15. four of the observation are 10,18,23 and 9. of the remaining two observation one is four times the other.
To find :
Remaining two observations
Solution :
★ Mean of 6 observation = 15
★ 4 observations = 10, 18, 23 & 9
★ Remaining two observations = One is four times the other.
\begin{gathered}\\\end{gathered}
Consider the first observation be x & the second observation be 4x
\begin{gathered}\\\end{gathered}
As we know that
\begin{gathered}\\\end{gathered}
{\bold \dag}\:{\boxed{\pmb{\tt{\red{Mean=\dfrac{Sum \: of \: the \: total \: observations}{Number\: of\: the \: observations}}}}}}†Mean=NumberoftheobservationsSumofthetotalobservationsMean=NumberoftheobservationsSumofthetotalobservations
\begin{gathered}\\\end{gathered}
\begin{gathered} \\ \implies \sf 15 = \dfrac{10 + 18 + 23 + 9 + x + 4x}{6} \\ \\ \implies \sf 15 = \dfrac{ 60 + 5x}{6} \\ \\ \implies \sf 90 = 60 + x \\ \\ \implies \sf 90 - 60 = x \\ \\ \implies \sf x = 30 \end{gathered}⟹15=610+18+23+9+x+4x⟹15=660+5x⟹90=60+x⟹90−60=x⟹x=30
Other two observations
x = 30
4x = 4 × 30 = 120
Therefore, other two observations are 30 & 120