Certainly! We will follow a step-by-step approach to create a scatter plot to visualize the relationship between study time and test scores.
### Step-by-Step Solution:
1. Understand the Data:
- We have study times (in minutes) and corresponding test scores.
- Study Times (min): 14, 21, 27, 34, 41, 46, 52, 58
- Test Scores: 63, 68, 66, 71, 77, 75, 78, 86
2. Prepare the Scatter Plot:
- We will plot study time on the x-axis and test scores on the y-axis.
- Each pair of (study time, test score) will be a point on the plot.
3. Plot the Data:
- Label the x-axis as "Study Time (min)" and the y-axis as "Test Score".
- Title the graph as "Study Time vs Test Score".
Here is the step-by-step process without using any specific programming language:
### Drawing the Scatter Plot:
1. Set Up Your Axes:
- Draw two perpendicular lines to represent the x-axis (horizontal) and y-axis (vertical).
- Label the x-axis from 10 minutes to 60 minutes in increments (e.g., 10, 20, 30, 40, 50, 60).
- Label the y-axis from 60 to 90 in increments (e.g., 60, 70, 80, 90).
2. Title and Label:
- Write "Study Time (min)" below the x-axis.
- Write "Test Score" beside the y-axis.
- Title the graph "Study Time vs Test Score" at the top center of the plot area.
3. Plot Each Point:
- For each pair (x,y), where x is the study time and y is the test score, plot the point:
- (14, 63)
- (21, 68)
- (27, 66)
- (34, 71)
- (41, 77)
- (46, 75)
- (52, 78)
- (58, 86)
### Example:
Let's sketch a few points to illustrate:
- For the point (14, 63):
- Move horizontally to x = 14 on the x-axis.
- Move vertically up to y = 63 on the y-axis.
- Mark the point where they intersect.
- For the point (21, 68):
- Move horizontally to x = 21 on the x-axis.
- Move vertically up to y = 68 on the y-axis.
- Mark the point where they intersect.
4. Repeat for All Points:
- Continue plotting the remaining points using the same method.
5. Grid:
- Optional: Adding a grid can help in precisely locating points, making the plot easier to read.
6. Inspect the Scatter Plot:
- Once all points are plotted, you can observe any trends, patterns, or correlations between study time and test scores.
### Conclusion:
By plotting each point, we can visually analyze whether there is any correlation between study time and test scores. For example, we might observe that as study time increases, test scores generally tend to increase, indicating a positive correlation.
This process helps in understanding the dataset and revealing potential relationships between the variables.
