Question

practice problem #2
background: clams were placed into various temperatures of water. use the information in the data table below in order to create a proper scientific graph and to answer the corresponding questions.

water temperature (°c)	number of developing clams
20	92
25	120
30	140
35	99
40	72
45	36
50	0

1. what is the dependent variable?
2. what is the independent variable?
3. what is the optimum temperature for clam development?
4. what is the mean number of clams per sample?
5. approximately how many clams would be developing in 10 degree celsius water?
6. what is it called when you make predictions about data not yet recorded, such as the prediction we made in question number 5?

Explanation:

Step1: Calculate the mean

Sum all the number of developing clams: $72 + 92+120 + 140+99+72+36+0=631$.
There are 8 data - points.
The mean formula is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 8$ and $\sum_{i=1}^{n}x_{i}=631$.
So, $\bar{x}=\frac{631}{8}=78.875\approx79$.

Step2: Analyze the optimum temperature

The optimum temperature is the one at which the number of developing clams is the highest. From the table, at $30^{\circ}C$, the number of developing clams is 140, which is the maximum value in the 'Number of Developing Clams' column.

Step3: Predict for 10 - degree Celsius water

Since the number of clams is decreasing as the temperature moves away from $30^{\circ}C$ in both directions and based on the trend in the data, we can make an estimate. As the temperature decreases from $15^{\circ}C$ (where there are 72 clams) to $10^{\circ}C$, we can assume a further decrease. A rough estimate could be 20 (this is an extrapolation based on the trend of the data).

Step4: Define the prediction term

Making predictions about data not yet recorded is called extrapolation.

Answer:

1. Number of developing clams
2. Water temperature
3. $30^{\circ}C$
4. 79
5. 20
6. Extrapolation