Question

Calculate the missing values of A, B, C, D, E, and F.

Answer 1

`\begin{gathered} A)\text{ 302.0} \\ B)\text{ 386.0} \\ C)\text{ 351.0} \\ D)\text{ 404.0} \\ E)\text{ 348.2} \\ F)\text{ 387.8} \end{gathered}`

Step-by-step explanation:

Here, we want to calculate the moving averages

To calculate this, we sum up the sales value for a period (years) divided by the number of years

For example, to calculate the moving average for 3 years (2015-2017) , we sum up the sales value for these 3 years and divide by 3

We proceed as follows:

A) If we add the values for 2015-2017 , we get the moving average for 2016 which is the middle year.

`\begin{gathered} \frac{A\text{ +326 + 344 }}{3}\text{ = 324} \\ \\ A\text{+ 670 = 3\lparen324\rparen} \\ A\text{= 972-670} \\ A\text{ = 302.0} \end{gathered}`

B) To get B, we can use the 3-year moving average for 2017-2019

Mathematically, we have that as follows:

`\begin{gathered} \frac{344\text{ + 383 + B}}{3}\text{ = 371} \\ \\ B\text{ = 3\lparen371\rparen- 344-383 = 386.0} \end{gathered}`

C) C is the 3-year moving average for 2016-2018

Mathematically, we have that as:

`\begin{gathered} \frac{326\text{ + 344 + 383}}{3}\text{ = C} \\ C\text{ = 351.0} \end{gathered}`

D) D is the 3-year moving average for 2019-2021

We have that as:

`\begin{gathered} \frac{B+398\text{ + 428 }}{3}\text{ = D} \\ \\ \frac{386\text{ + 398 + 428}}{3}\text{ = 404.0} \end{gathered}`

E) E is the 5-year moving average of the years 2015-2019

Mathematically:

`\begin{gathered} \frac{A\text{ + 326 +344+383+ B}}{5}\text{ = E} \\ \\ \frac{302\text{ + 326 + 344 + 383 + 386}}{5}\text{ = 348.2} \end{gathered}`

F) F is the 5-year moving average of the years 2017-2021

Mathematically:

`\begin{gathered} \frac{344\text{ + 383 + B + 398 + 428}}{5} \\ \\ =\text{ }\frac{344\text{ + 383 + 386 + 398 + 428}}{5}\text{ = 387.8} \end{gathered}`