Chapter 8.1, Problem 37E

To determine

Tofind the overall inflation rate for the year.

Answer to Problem 37E

The overall inflation rate is $0.04875$ .

Explanation of Solution

Given information:

The following table records the annual inflation rate as measured each month for $13$ consecutive months.

  

Formula:

The area of an individual trapezoidal is $=\frac{1}{2}\left(b_1+b_2\right)\Delta x$

From given $n=12$ , $\Delta x=1$ ,

The area each and every month is calculated to be the summation of all the months,

  $\begin{array}{l}y=\frac{1}{2}\left(0.04+0.04\right)+\frac{1}{2}\left(0.04+0.05\right)+\frac{1}{2}\left(0.05+0.06\right)+\frac{1}{2}\left(0.06+0.05\right)+\\ \frac{1}{2}\left(0.05+0.04\right)+\frac{1}{2}\left(0.04+0.04\right)+\frac{1}{2}\left(0.04+0.05\right)+\frac{1}{2}\left(0.05+0.04\right)+\\ \frac{1}{2}\left(0.04+0.06\right)+\frac{1}{2}\left(0.06+0.06\right)+\frac{1}{2}\left(0.06+0.05\right)+\frac{1}{2}\left(0.05+0.05\right)\\ y=0.585\end{array}$

Taking average by diving the sum of the areas by the number of trapezoids,

  $\Rightarrow \frac{0.585}{12}=0.04875$

Therefore, the overall inflation rate is $0.04875$ .