Question

g Each year the density of 7 species of Odonata (dragonflies and damselflies) is monitored in a wetland preserve. If the density of each species is to be compared with the density of every other species, how many comparisons must be made

Answer 1

Answer:

There are 21 comparisons to be made.

Step-by-step explanation:

The number of species of Odonata monitored every year is, n = 7.

It is provided that the density of each species is compared with each other.

The number of ways to compare the species (N) without repetition is:

$N=\frac{n(n-1)}{2}\\=\frac{7(7-1)}{2}\\=\frac{7\times6}{2}\\=21$

Thus, there are 21 comparisons.

The 21 comparisons are as follows:

Specie 1 is compared with the remaining 6.

Specie 2 has already with he 1st so it is compared with the remaining 5.

Specie 3 has already with he 1st and 2nd so it is compared with the remaining 4.

Specie 4 has already with he 1st, 2nd and 3rd so it is compared with the remaining 3.

Specie 5 has already with he 1st, 2nd, 3rd and 4th so it is compared with the remaining 2.

Specie 6 has already with he 1st, 2nd, 3rd, 4th and 5th so it is compared with the remaining 1.

And the specie 7 has already been compared with the others.

Total number of comparisons = 6 + 5 + 4 + 3 + 2 + 1 = 21.