Answer :
To determine the type of relationship between the hours after midnight and the temperature on that particular day in Kansas City, we first need to visualize the data using a scatter diagram.
Here's a step-by-step explanation:
1. Data Observation:
- The given data is a set of points where each point corresponds to the temperature recorded at specific times after midnight. The times are: 3, 6, 9, 12, 15, 18, 21, and 24 hours, with their respective temperatures.
2. Plot the Scatter Diagram:
- On a graph, plot the 'Hours after Midnight' on the x-axis and 'Temperature in Degrees Fahrenheit' on the y-axis. Mark each pair of values as a point on the chart.
3. Analyze the Scatter Plot:
- After plotting, observe the pattern formed by the points. The points may not form a perfect line or curve but look for the overall trend.
- In this dataset:
- The temperature starts relatively lower, increases to a peak, and then decreases again, suggesting a curved shape resembling a "U" or inverted "V".
4. Determine the Type of Relationship:
- Linear Function: Would result in a straight line; the data doesn't follow a straight line.
- Quadratic Function: Represents a parabolic trend which can open upward or downward. This generally fits when we see a rise to a peak and then a decrease.
- Cubic Function: Involves oscillations or multiple turns which don't match the plotted trend.
- No Relation: If points are scattered without any discernible pattern.
Given these observations, the points suggest a parabolic shape which indicates that a quadratic function is the most appropriate model of the relationship between the temperature and the hours after midnight. Thus, the type of relation that may exist between the two variables is a quadratic function.
Here's a step-by-step explanation:
1. Data Observation:
- The given data is a set of points where each point corresponds to the temperature recorded at specific times after midnight. The times are: 3, 6, 9, 12, 15, 18, 21, and 24 hours, with their respective temperatures.
2. Plot the Scatter Diagram:
- On a graph, plot the 'Hours after Midnight' on the x-axis and 'Temperature in Degrees Fahrenheit' on the y-axis. Mark each pair of values as a point on the chart.
3. Analyze the Scatter Plot:
- After plotting, observe the pattern formed by the points. The points may not form a perfect line or curve but look for the overall trend.
- In this dataset:
- The temperature starts relatively lower, increases to a peak, and then decreases again, suggesting a curved shape resembling a "U" or inverted "V".
4. Determine the Type of Relationship:
- Linear Function: Would result in a straight line; the data doesn't follow a straight line.
- Quadratic Function: Represents a parabolic trend which can open upward or downward. This generally fits when we see a rise to a peak and then a decrease.
- Cubic Function: Involves oscillations or multiple turns which don't match the plotted trend.
- No Relation: If points are scattered without any discernible pattern.
Given these observations, the points suggest a parabolic shape which indicates that a quadratic function is the most appropriate model of the relationship between the temperature and the hours after midnight. Thus, the type of relation that may exist between the two variables is a quadratic function.
