Chapter 1, Problem 56A

Solution

Interpretation: The average maximum area of the ozone hole between the years 2005-2009, 2000-2004, and 1995-1999 needs to be determined from the given data.

Concept Introduction: From a given data, the average value can be calculated by adding all the values between the range divided by the number of entries.

For example, the average of two values can be estimated as follows:

  $\text{Average}=\frac{\text{Sum of two values}}{2}$

According to the given plot, the area of the ozone hole between the years 2005 and 2009 is as follows:

Year	Ozone hole area
2005	24.7
2006	27.5
2007	24.3
2008	25.0
2009	23.7

The average value can be calculated as follows:

  $\begin{array}{c}\text{Average}=\frac{\text{Sum of all values}}{\text{Number of values}}\\ =\frac{24.7+27.5+24.3+25.0+23.7}{5}\\ =25.04\end{array}$

Thus, the average maximum area of an ozone hole between the years 2005 and 2009 is 25.04 ${\text{million km}}^2$ .

Similarly, the area of the ozone hole between the years 2000 and 2004 is as follows:

Year	Ozone hole area
2000	28.7
2001	24.8
2002	18.0
2003	27.6
2004	19.6

The average value can be calculated as follows:

  $\begin{array}{c}\text{Average}=\frac{\text{Sum of all values}}{\text{Number of values}}\\ =\frac{28.7+24.8+18.0+27.6+19.6}{5}\\ =23.74\end{array}$

Thus, the average maximum area of an ozone hole between the years 2000 and 2004 is 23.74 ${\text{million km}}^2$ .

Now, the area of the ozone hole between the years 1995 and 1999 is as follows:

Year	Ozone hole area
1995	22.1
1996	23.0
1997	22.1
1998	26.6
1999	23.1

The average value can be calculated as follows:

  $\begin{array}{c}\text{Average}=\frac{\text{Sum of all values}}{\text{Number of values}}\\ =\frac{22.1+23.0+22.1+26.6+23.1}{5}\\ =23.38\end{array}$

Thus, the average maximum area of an ozone hole between the years 1995 and 1999 is 23.38 ${\text{million km}}^2$ .