To determine the most appropriate representation for displaying and describing what is happening to the amount of hot chocolate over time, we should first look at the data provided:
| Time (seconds) | 4 | 8 | 12 | 16 | 20 | 24 |
|------------------------|---|----|----|----|----|----|
| Hot Chocolate Amount (fluid ounces) | 3 | 5 | 65 | 8 | 11 | 14 |
When dealing with this type of data, we want to observe the relationship between the two variables: time and the amount of hot chocolate. The most appropriate representation in this case would be a scatter plot.
Steps to create a scatter plot:
1. Draw the Axes:
- The horizontal axis (x-axis) will represent time in seconds.
- The vertical axis (y-axis) will represent the amount of hot chocolate in fluid ounces.
2. Label the Axes:
- On the x-axis, label the points where 4, 8, 12, 16, 20, and 24 seconds are marked.
- On the y-axis, label the points where 3, 5, 65, 8, 11, and 14 fluid ounces are marked.
3. Plot the Points:
- Place a dot for each pair of data points (e.g., (4, 3), (8, 5), (12, 65), (16, 8), (20, 11), (24, 14)).
Here is a quick step-by-step visual guide to what your scatter plot should look like:
- The x-axis from 0 to 24 seconds, with tick marks at intervals (e.g., every 4 seconds).
- The y-axis from 0 to, let's say, 70 fluid ounces, with tick marks at suitable intervals (e.g., every 10 fluid ounces).
- For each time value on the x-axis, find the corresponding value on the y-axis and place a point at that coordinate.
This scatter plot will allow you to visually inspect the relationship between the time the machine was on and the amount of hot chocolate dispensed.
From the scatter plot, you will notice if there's an overall trend or any outliers in the data. In this specific example, you might observe that while most points suggest a gradual increase, there is an unusual jump at 12 seconds indicating a possible anomaly or error in measurement.
By using a scatter plot for this data, you are able to clearly visualize and analyze the relationship between the variables. This can help in identifying patterns or issues with the hot chocolate machine's performance over time.
