 The equation for the Simpsons index is this. D equals 1 minus the sum of lowercase n multiplied by n minus 1, divided by capital N times n minus 1. The variables in this equation are D, which is the diversity index, lowercase n, which represents the number of individuals in a single species, and capital N, which represents the number of individuals in the entire population. Our sample problem is going to contain five species. If you want to find the Simpsons index for this population, the first step is going to be finding the value of the numerator. The easiest way to break this down is imagining that the numerator, n times n minus 1, is its own equation. You need to input the population values for each species, and then find the sum of each of these values. In our example, the numerator would look something like this. 13 times 13 minus 1 plus 42 times 42 minus 1, etc. After you input all of the values, your equation should look something like this. Next, you need to find the value of the denominator. To do this, you need to take the total population number and input it into capital N. A quick side note, I have taken the population values that we calculated in the previous step and added them together to find a total of 2,612. Now, our denominator using the capital N of our sample population, which is 100, should equal to 100 times 100 minus 1 or 9,900. Now, all that's left is to solve for the index value. After completing your calculation, you should get 0.74. Remember that the closer to 1 your index value is, the more diverse the population is. This means that our sample population is pretty diverse.