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
Answer
The remaining two observations are 6 and 24.
Step-by-step explanation:
Given that:
The mean of 6 observation is 15.
Four of the observation are 10, 18, 23 and 9.
The remaining two observation one is four times the other.
To Find:
What are the remaining two observations?
Let us assume:
Let the one observation be x.
Other observation = 4x
Formula used:
Mean = (Sum of observations)/(Number of observations)
Finding the remaining two observations:
According to the question.
⟶ 15 = (10 + 18 + 23 + 9 + x + 4x)/6
Cross multiplication.
⟶ 10 + 18 + 23 + 9 + x + 4x = 15 × 6
⟶ 60 + 5x = 90
⟶ 5x = 90 - 60
⟶ 5x = 30
⟶ x = 30/5
⟶ x = 6
Remaining observations are:
One observation = x = 6
Other observation = 4x = (4 × 6) = 24