Some values of a function and its 3-unit moving average are given. Supply the missing information: $$\begin{array} { | l | l | l | l | l | l | l | l | }
\hline \boldsymbol { x } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline \boldsymbol { r } ( \boldsymbol { x } ) & 2 & 3 & & 14 & & 4 & 20 \
\hline \text { average } & \text { undefined } & \text { undefined } & 5 & & 11 & & \
\hline
\end{array}$$

A)$\begin{array} { | l | l | l | l | l | l | l | l | }
\hline \boldsymbol { x } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline r ( x ) & 2 & 3 & 10 & 14 & 9 & 4 & 20 \
\hline \text { average } & \text { undefined } & \text { undefined } & 5 & 9 & 11 & 9 & 11 \
\hline
\end{array}$
B)$\begin{array} { | l | l | l | l | l | l | l | l | }
\hline \boldsymbol { x } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline \boldsymbol { r } ( \boldsymbol { x } ) & 2 & 3 & 10 & 14 & 9 & 4 & 20 \
\hline \text { average } & \text { undefined } & \text { undefined } & 5 & 9 & 11 & 9 & 11 \
\hline
\end{array}$
C)$\begin{array} { | l | l | l | l | l | l | l | l | }
\hline \boldsymbol { x } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline \boldsymbol { r } ( \boldsymbol { x } ) & 2 & 3 & 10 & 14 & 9 & 4 & 20 \
\hline \text { average } & \text { undefined } & \text { undefined } & 5 & 9 & 11 & 12 & 14 \
\hline
\end{array}$

Question

Some values of a function and its 3-unit moving average are given. Supply the missing information: $$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline \boldsymbol { x } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline \boldsymbol { r } ( \boldsymbol { x } ) & 2 & 3 &   & 14 &   & 4 & 20 \
\hline \text { average } & \text { undefined } & \text { undefined } & 5 &   & 11 &   &   \
\hline
\end{array}$$

A)$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline \boldsymbol { x } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline r ( x ) & 2 & 3 & 10 & 14 & 9 & 4 & 20 \
\hline \text { average } & \text { undefined } & \text { undefined } & 5 & 9 & 11 & 9 & 11 \
\hline
\end{array}$ 
B)$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline \boldsymbol { x } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline \boldsymbol { r } ( \boldsymbol { x } ) & 2 & 3 & 10 & 14 & 9 & 4 & 20 \
\hline \text { average } & \text { undefined } & \text { undefined } & 5 & 9 & 11 & 9 & 11 \
\hline
\end{array}$ 
C)$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline \boldsymbol { x } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline \boldsymbol { r } ( \boldsymbol { x } ) & 2 & 3 & 10 & 14 & 9 & 4 & 20 \
\hline \text { average } & \text { undefined } & \text { undefined } & 5 & 9 & 11 & 12 & 14 \
\hline
\end{array}$

Quizplus · Accepted Answer

The 3-unit moving average is calculated by summing three consecutive values of $r(x)$ and dividing by 3. For $x=3$, the average is given as 5, which means the sum of $r(1)$, $r(2)$, and $r(3)$ must be 15. Given $r(1) = 2$ and $r(2) = 3$, $r(3)$ must be $15 - (2 + 3) = 10$. For $x=4$, the average involves $r(2)$, $r(3)$, and $r(4)$, which sums to $3 + 10 + 14 = 27$, and $27/3 = 9$. Continuing this process for each $x$ allows us to fill in the missing values correctly as shown in option B.

Some Values of a Function and Its 3-Unit Moving Average