Question

use the scatterplot to answer the following questions.

1. does this scatterplot represent univariate or bivariate data?
2. identify the independent variable.
3. complete the following:

as the number of bathroom passes increases,
the final exam grade
increases or decreases

1. describe the relationship between the two variables. make sure to use one of the following phrases as part of your description and explain why.

strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, no correlation.

1. approximate the final exam grade for a student with 10 bathroom passes.
2. how many bathroom passes is a student expected to have if the final exam grade is 80?
3. is the data point (12, 25) an example of interpolation or extrapolation? explain why.
4. add the point (2, 85) by plotting it on the scatterplot above.
5. describe what the point (5, 78) represents in the context of data.

Explanation:

Step1: Determine data - type

A scatter - plot with two variables (number of bathroom passes and final exam grade) represents bivariate data.

Step2: Identify independent variable

The independent variable is the one that is manipulated or changed. Here, the number of bathroom passes is the independent variable as it is not affected by the final exam grade.

Step3: Analyze trend

As we move from left to right (increase in number of bathroom passes) on the scatter - plot, the final exam grade decreases.

Step4: Determine correlation

The points on the scatter - plot show a general downward trend. But the points are not tightly clustered around a line. So, it is a weak negative correlation.

Step5: Estimate grade for 10 passes

Looking at the scatter - plot, when the number of bathroom passes ($x = 10$), the final exam grade is approximately 45.

Step6: Estimate passes for grade 80

Looking at the scatter - plot, when the final exam grade ($y = 80$), the number of bathroom passes is approximately 2.

Step7: Determine interpolation/extrapolation

The $x$ - values in the scatter - plot seem to be in the range of 0 - 10. For the point $(12,25)$, since $x = 12$ is outside the observed range of $x$ - values, it is an example of extrapolation.

Step8: Plot point

To plot the point $(2,85)$, find $x = 2$ on the x - axis and $y = 85$ on the y - axis and mark the point.

Step9: Interpret point

The point $(5,78)$ represents a student who has 5 bathroom passes and a final exam grade of 78.

Answer:

1. Bivariate data
2. Number of bathroom passes
3. Decreases
4. Weak negative correlation; because the points show a general downward trend but are not tightly clustered around a line.
5. 45
6. 2
7. Extrapolation; because the $x$ - value of 12 is outside the observed range of $x$ - values in the scatter - plot.
8. Plot the point where $x = 2$ and $y = 85$ on the scatter - plot.
9. A student with 5 bathroom passes and a final exam grade of 78.