Question

If the mean of $5$ observations $x,x+2,x+4,x+6,x+8$ is $11$, then the mean of first three observations is $8$.

• A. True
• B. False

Answer 1

The correct option is B False

Step 1- Find the value of $x$.

Given observations: $x,x+2,x+4,x+6,x+8$

Here, the number of observations $=5$

The mean of given data is $11$

$$\begin{gathered} Mean=\frac{Sumofobservations}{Numberofobservation} \\ \therefore 11=\frac{x+(x+2)+(x+4)+(x+6)+(x+8)}{5} \\ \Rightarrow 5x+20=11\times 5 \\ \Rightarrow 5x+20=55 \\ \Rightarrow 5x=55-20 \\ \Rightarrow 5x=35 \\ \Rightarrow x=\frac{35}{5} \\ \Rightarrow x=7 \end{gathered}$$

Step 2- Find the value of the first three observations

$$\begin{gathered} x=7 \\ (x+2)=7+2=9 \\ (x+4)=7+4=11 \end{gathered}$$

Step 3- Find the mean of the first three observations.

$$\begin{gathered} Mean=\frac{Sumofobservation}{Numberofobservation} \\ =\frac{7+9+11}{3} \\ =\frac{27}{3} \\ =9 \end{gathered}$$

Hence, the mean of first three observations is not $8$.

Therefore, the given statement is fasle.