According to the problem the biodiversity index is given by:
[tex]bi=\frac{\text{ total number of species }}{\text{ total number of individuals in the area}}[/tex]
In this problem we have 7 species. The find the total number of individuals in the area we just add the number of individuals in each specie, then we have:
[tex]15+2+10+1+16+4+5=53[/tex]
Plugging the values we found in the formula given we have:
[tex]bi=\frac{7}{53}[/tex]
Therefore, the biodiversity index is 7/53 (this is approximately 0.132 with three decimals)
