Question

problem a: using the following data, answer the questions below and then construct a line graph.
depth in meters number of bubbles / minute plant a number of bubbles / minute plant b
2 29 21
5 36 27
10 45 40
16 32 34
25 20 20
30 10 20

1. what is the dependent variable and why?
2. what is the independent variable and why?
3. what title would you give the graph?
4. what are the mean, median, and mode of all 3 columns of data?

a). depth : mean____ median__ mode____
b). bubble plant a.: mean ____ median__ mode____
c). bubbles plant b: mean ____ median__ mode____

Explanation:

Step1: Identify dependent variable

The number of bubbles per minute for each plant depends on the depth. So, the number of bubbles per minute for plant A and plant B are the dependent variables.

Step2: Identify independent variable

The depth is being manipulated or changed to observe its effect on the number of bubbles. So, depth is the independent variable.

Step3: Suggest graph title

A suitable title could be "Effect of Depth on Bubble - Production of Plant A and Plant B".

Step4: Calculate mean of depth

The data for depth is \(2,5,10,16,25,30\). Mean \(=\frac{2 + 5+10+16+25+30}{6}=\frac{88}{6}\approx14.67\)

Step5: Calculate median of depth

Arrange in ascending order: \(2,5,10,16,25,30\). Since \(n = 6\) (even), median\(=\frac{10 + 16}{2}=13\)

Step6: Calculate mode of depth

No value repeats, so mode is none.

Step7: Calculate mean of Plant A bubbles

The data for Plant A is \(29,36,45,32,20,10\). Mean\(=\frac{29+36+45+32+20+10}{6}=\frac{172}{6}\approx28.67\)

Step8: Calculate median of Plant A bubbles

Arrange in ascending order: \(10,20,29,32,36,45\). Median\(=\frac{29 + 32}{2}=30.5\)

Step9: Calculate mode of Plant A bubbles

No value repeats, so mode is none.

Step10: Calculate mean of Plant B bubbles

The data for Plant B is \(21,27,40,50,34,20\). Mean\(=\frac{21+27+40+50+34+20}{6}=\frac{192}{6} = 32\)

Step11: Calculate median of Plant B bubbles

Arrange in ascending order: \(20,21,27,34,40,50\). Median\(=\frac{27+34}{2}=30.5\)

Step12: Calculate mode of Plant B bubbles

No value repeats, so mode is none.

Answer:

1. The dependent variables are the number of bubbles per minute for plant A and plant B because they are the variables being measured and are affected by the depth.
2. The independent variable is depth because it is the variable that is being changed or controlled in the experiment.
3. "Effect of Depth on Bubble - Production of Plant A and Plant B"

4.
a) Depth: Mean: \(14.67\), Median: \(13\), Mode: None
b) Bubble Plant A: Mean: \(28.67\), Median: \(30.5\), Mode: None
c) Bubbles Plant B: Mean: \(32\), Median: \(30.5\), Mode: None