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: Identify dependent variable

The number of developing clams depends on water - temperature. So, the dependent variable is the number of developing clams.

Step2: Identify independent variable

The water - temperature is being manipulated, so it is the independent variable.

Step3: Find optimum temperature

The highest number of developing clams is 140 at 30°C, so the optimum temperature for clam development is 30°C.

Step4: Calculate mean number of clams

Sum of number of clams: \(72 + 92+120 + 140+99+72+36+0=531\). There are 8 samples. Mean \(\bar{x}=\frac{531}{8}=66.375\).

Step5: Predict number of clams at 10°C

Since the number of clams increases from 15°C to 30°C and then decreases, we might assume a linear - like trend before 15°C. But without more data, it's hard to be exact. If we assume a simple linear interpolation between 15°C (72 clams) and 20°C (92 clams), the rate of change is \(\frac{92 - 72}{20 - 15}=\frac{20}{5} = 4\) clams per degree. From 15°C to 10°C (a 5 - degree decrease), we might predict \(72-4\times5 = 52\) clams.

Step6: Define prediction term

Making predictions about data not yet recorded is called extrapolation.

Answer:

1. Number of developing clams
2. Water temperature
3. 30°C
4. 66.375
5. Approximately 52
6. Extrapolation