To determine the distribution pattern of the oyster larvae, we can analyze the data provided in the table. Here are the detailed steps we follow:
1. Organize the Data:
The data shows the density of oyster larvae at four different sites over three days:
- Day 1: Site W (40), Site X (22), Site Y (0), Site Z (7)
- Day 2: Site W (3), Site X (1), Site Y (14), Site Z (26)
- Day 3: Site W (2), Site X (6), Site Y (3), Site Z (1)
2. Flatten the Dataset:
Combine all the measurements into a single list:
[tex]\[
[40, 22, 0, 7, 3, 1, 14, 26, 2, 6, 3, 1]
\][/tex]
3. Calculate the Mean Density:
The mean density is obtained by summing all the values and then dividing by the number of values:
[tex]\[
\text{Mean Density} = \frac{40 + 22 + 0 + 7 + 3 + 1 + 14 + 26 + 2 + 6 + 3 + 1}{12} \approx 10.42
\][/tex]
4. Calculate the Variance:
Variance measures how much the densities deviate from the mean. It is calculated using the formula:
[tex]\[
\text{Variance} = \frac{\sum (x_i - \text{mean})^2}{N}
\][/tex]
Where [tex]\(N\)[/tex] is the number of values (12) and [tex]\(x_i\)[/tex] are the individual density values.
After calculations, the variance is approximately:
[tex]\[
146.91
\][/tex]
5. Determine the Distribution Pattern:
Based on the mean density and variance, we can infer the distribution pattern:
- Typically, a random distribution will have a variance close to the mean.
- A uniform distribution will have a smaller variance as all values are similar.
- A clumped distribution will have a higher variance due to many values being far from the mean.
Given:
- Mean density: approximately 10.42
- Variance: approximately 146.91
The high variance in this case indicates that the oyster larvae are not randomly nor uniformly distributed but are clumped in certain areas.
Thus, the distribution pattern of the oyster larvae is:
D. clumped
