Question

c. create a graph of the data that makes the increase in grades as study time increases appear even greater than it really is. explain how you chose the scale for your graph.

Explanation:

Step 1: Determine the Goal

We need to create a graph where the increase in grades with respect to study time appears more significant. This involves manipulating the scale of the axes.

Step 2: Choose the Axes Scales

• X - axis (Study Time): Use a smaller scale (e.g., each grid square represents 1 unit of time). This makes the time axis shorter relative to the grade axis.
• Y - axis (Grades): Use a larger scale (e.g., each grid square represents a larger unit of grade, like 5 or 10 points). This stretches the grade axis, making the increase in grades look steeper.

Step 3: Plot the Data

Assume some sample data: Let's say at time \( t = 1 \), grade \( g = 60 \); \( t = 2 \), \( g = 65 \); \( t = 3 \), \( g = 70 \); \( t = 4 \), \( g = 75 \).

• On the X - axis (time), mark 1, 2, 3, 4 with a small scale (e.g., each unit is 1 grid square).
• On the Y - axis (grades), mark 60, 65, 70, 75 with a large scale (e.g., each 5 - point increase is 1 grid square). Plot the points \((1,60)\), \((2,65)\), \((3,70)\), \((4,75)\) and draw a line through them.

Step 4: Explain the Scale Choice

By using a smaller scale on the X - axis (time) and a larger scale on the Y - axis (grades), the slope of the line (which represents the rate of increase of grades with time) appears steeper. This is because the change in \( y \) (grades) per unit change in \( x \) (time) is visually exaggerated. For example, if the X - axis has a scale of 1 unit per grid square and the Y - axis has a scale of 5 units per grid square, a change of 1 in \( x \) (1 unit of time) and 5 in \( y \) (5 units of grade) will look like a steeper line compared to if both axes had the same scale.

Answer:

To make the increase in grades with study time appear more significant:

1. X - axis (Study Time): Use a small scale (e.g., 1 unit of time per grid square).
2. Y - axis (Grades): Use a large scale (e.g., 5 - 10 units of grade per grid square).
3. Plot data points (e.g., \((1,60)\), \((2,65)\), \((3,70)\), \((4,75)\)) and draw a line. The steeper slope (due to axis scales) makes the increase look greater.