Real-Life Math
Your friend Sunita has a lovely herb garden in her backyard. Recently,
she had to take down a fence that blocked the yard from the lane. It'll cost
her a lot of money to put a new fence up, and personally, she likes being
able to see who's driving by so she can wave to her friends.
Sunita
doesn't like to spend too much time gardening. She just likes to leave the
garden alone and pick from it as the need arises (she makes an excellent ratatouille).
She's worried that the new exposure to the lane and all the traffic will change
her herb selection as the years pass.
This is where you come in. Sunita
knows you're an experienced ecologist. She hires you to determine the impact
of the exposure on her garden.
To do this, you must determine the community
similarity coefficient (CSC). This is a mathematical expression of the degree
of similarity between the garden before the fence went down and after it went
down.
First, you need to take an inventory of her garden on the day
she takes the fence down. Here's what it has:
Set A
- 30 basil
- 25 oregano
- 5 mint
- 14 sweet pea
- 3 parsley
Because you live in a temperate climate, the seasons have a minor
effect. You wait 3 months with the fence down and count the plants again.
You get:
Set B
- 25 basil
- 20 oregano
- 10 mint
- 5 sweet pea
- 6 parsley
- 5 dandelions
To calculate the CSC, you use this formula:
C = 2 x W / (A
+ B)
C is the coefficient.
W is the sum of the lower
values that are in both sets. For example, basil is present in both sets,
but 25 is the lower of the 2 values. Add up the lower value of all the plants
that are in both sets and that is W.
A is the sum total of all plants
in Set A.
B is the sum total of all plants in Set B.
C is the
amount of difference between the 2 inventories of Sunita's garden. You can
turn it into a percentage to say that her garden is only X percent
the same as it was 3 months ago.
Take bonus points if you can use your
results to guess how similar her garden will be 9 months from the day she
took the fence down.