Question 2

We will estimate the total number of trees by sampling a small area.

Step 1 — Problem Understanding

Let's look at the picture. It shows many small dots. Each dot represents one tree. We need to find the total number of trees. Counting every single tree is very difficult. So, we will estimate the total number.

Step 2 — Model Formulation

We will divide the whole area into smaller parts. Let's divide the image into a grid. We will count trees in a few sample parts. Then we find the average number of trees per part. Finally, we multiply this average by the total parts.

Step 3 — Data Collection

Let's divide the image into 10 rows and 10 columns. This makes a total of 100 small squares. We will count trees in 5 randomly chosen squares. Suppose our counts are: 25, 30, 28, 27, 32 trees.

Step 4 — Model Calculation

First, we find the total trees in our sample squares.

$= 25 + 30 + 28 + 27 + 32$

$\boxed{142 \text{ trees}}$

Next, we find the average number of trees per square.

$= \frac{\text{Total trees in sample}}{\text{Number of sample squares}}$

$= \frac{142}{5}$

$\boxed{28.4 \text{ trees/square}}$

Now, we estimate the total number of trees in the forest.

$= \text{Average trees per square} \times \text{Total number of squares}$

$= 28.4 \times 100$

$\boxed{2840 \text{ trees}}$

Step 5 — Interpretation and Refinement

The calculated number is an estimate. It is not an exact count. To make the estimate better, we could count more sample squares. We could also use a larger sample area.

Answer

(i) The problem was solved using a sampling and averaging method. We divided the area into a grid, counted trees in sample squares, and then scaled up the average. (ii) The estimated number of trees in the forest is 2840. (iii) This number is an estimate, and its accuracy depends on the uniformity of tree distribution and the size and number of samples taken.