Question

1. quadrat sampling: you are conducting a population study in a meadow to estimate the number of grasshoppers. you use three quadrats, each measuring 2m x 2m, and record the total number of grasshoppers for all 3 quadrats after 3 trials: trial number of grasshoppers 1 8 2 5 3 10 a. calculate the total area sampled (all three quadrats). show your work. b. if you use only the number of grasshoppers found in trial 3, estimate the grasshopper population for a meadow that covers 200m². show your work.

Explanation:

Step1: Calculate area of one quadrat

The area of a single quadrat with length $l = 2m$ and width $w=2m$ is calculated using the formula for the area of a rectangle $A_{1}=l\times w$. So, $A_{1}=2\times2 = 4m^{2}$.

Step2: Calculate total area of three quadrats

Since we have 3 quadrats, and the area of one quadrat is $A_{1} = 4m^{2}$, the total area sampled $A_{total}=3\times A_{1}=3\times4 = 12m^{2}$.

Step3: For part B, find density in trial 3

In trial 3, the number of grass - hoppers is $n = 10$ in an area of $A_{1}=4m^{2}$. The density $d$ (number of grass - hoppers per square meter) is $d=\frac{n}{A_{1}}=\frac{10}{4}=2.5$ grass - hoppers per $m^{2}$.

Step4: Estimate population for 200 $m^{2}$ meadow

If the density is $d = 2.5$ grass - hoppers per $m^{2}$ and the area of the meadow is $A = 200m^{2}$, then the estimated population $N=d\times A=2.5\times200 = 500$.

Answer:

A. The total area sampled is $12m^{2}$.
B. The estimated grass - hopper population for a $200m^{2}$ meadow is 500.