Let's break this down comprehensively:
Question 1: What is the dependent variable?
- The dependent variable is the number of developing clams.
Question 2: What is the independent variable?
- The independent variable is the water temperature.
Question 3: What is the optimum temperature for clam development?
- The optimal temperature for clam development is 30 degrees Celsius. This is because the number of developing clams is highest at this temperature (140 clams).
Question 4: What is the mean number of clams per sample?
- To find the mean number of clams per sample, we sum up all the clam counts and divide by the number of samples.
Clam counts: 72, 92, 120, 140, 99, 72, 36, 0
Sum of clam counts = 72 + 92 + 120 + 140 + 99 + 72 + 36 + 0 = 631
Number of samples = 8
Therefore, the mean number of clams per sample = 631 / 8 = 78.875
So, the mean number of clams per sample is 78.875.
Question 5: Approximately how many clams would be developing in 10 degrees Celsius water?
- To find this, we need to perform an interpolation since 10 degrees Celsius is not included in the given temperatures.
For interpolation, we use the data points closest to 10 degrees Celsius, which are 15 degrees and 20 degrees with corresponding clam counts of 72 and 92.
The formula for linear interpolation is:
[tex]\( \text{predicted\_clams} = \text{count1} + (\text{desired\_temp} - \text{temp1}) \times \frac{(\text{count2} - \text{count1})}{(\text{temp2} - \text{temp1})} \)[/tex]
Plugging in the values:
[tex]\( \text{predicted\_clams} = 72 + (10 - 15) \times \frac{(92 - 72)}{(20 - 15)} \)[/tex]
[tex]\( \text{predicted\_clams} = 72 + (-5) \times \frac{20}{5} \)[/tex]
[tex]\( \text{predicted\_clams} = 72 - 20 = 52 \)[/tex]
Therefore, approximately 52 clams would be developing in 10 degrees Celsius water.
Question 6: What is it called when you make predictions about data not yet recorded, such as the prediction we made in question number 5?
- Making predictions about data not yet recorded is called extrapolation.
To summarize:
1. The dependent variable is the number of developing clams.
2. The independent variable is the water temperature.
3. The optimum temperature for clam development is 30 degrees Celsius.
4. The mean number of clams per sample is 78.875.
5. Approximately 52 clams would be developing in 10 degrees Celsius water.
6. Making predictions about data not yet recorded is called extrapolation.
