Question

in exercises 7 and 8, make a scatter plot of the data. then describe the relationship between the data. 7. x: 3.1, 2.2, 2.5, 3.7, 3.9, 1.5, 2.7, 2.0; y: 1, 0, 1, 2, 0, 2, 3, 2. 8. x: 3, 4, 5, 6, 7, 8, 9, 10; y: 67, 67, 50, 33, 25, 21, 19, 4.

Explanation:

Step1: Analyze Problem 7

Step1.1: Identify Data Points

For problem 7, the data points are \((3.1, 1)\), \((2.2, 0)\), \((2.5, 1)\), \((3.7, 2)\), \((3.9, 0)\), \((1.5, 2)\), \((2.7, 3)\), \((2.0, 2)\).

Step1.2: Plot Scatter Plot

• Draw a coordinate system with \(x\)-axis and \(y\)-axis.
• Mark each data point on the coordinate plane.

Step1.3: Describe Relationship

Looking at the plotted points, there is no strong linear trend. The points seem to be somewhat scattered, but there might be a slight upward trend as \(x\) increases, but it's not very clear - cut.

Step2: Analyze Problem 8

Step2.1: Identify Data Points

For problem 8, the data points are \((3, 67)\), \((4, 67)\), \((5, 50)\), \((6, 33)\), \((7, 25)\), \((8, 21)\), \((9, 19)\), \((10, 4)\).

Step2.2: Plot Scatter Plot

• Draw a coordinate system with \(x\)-axis (ranging from 3 to 10) and \(y\)-axis (ranging from 4 to 67).
• Mark each data point \((x,y)\) on the plane.

Step2.3: Describe Relationship

When we plot these points, as \(x\) increases from 3 to 10, the \(y\)-values generally decrease. So there is a negative relationship between \(x\) and \(y\) (as \(x\) increases, \(y\) tends to decrease), and it looks like a somewhat strong negative trend, maybe even a non - linear (possibly exponential or quadratic - like) decrease as \(x\) gets larger (the decrease is more rapid as \(x\) increases from 8 to 10).

(Note: Since the problem asks to make scatter plots and describe relationships, the above steps outline how to approach each problem. If we were to actually draw the scatter plots, we would use graph paper or a graphing tool to mark the points. The description of the relationship is based on the general trend of the points.)

Answer:

For Problem 7:

• Scatter Plot: Plot the points \((3.1, 1)\), \((2.2, 0)\), \((2.5, 1)\), \((3.7, 2)\), \((3.9, 0)\), \((1.5, 2)\), \((2.7, 3)\), \((2.0, 2)\) on a coordinate plane.
• Relationship: The points are scattered with a slight possible upward trend, but no strong linear relationship.

For Problem 8:

• Scatter Plot: Plot the points \((3, 67)\), \((4, 67)\), \((5, 50)\), \((6, 33)\), \((7, 25)\), \((8, 21)\), \((9, 19)\), \((10, 4)\) on a coordinate plane.
• Relationship: As \(x\) increases, \(y\) generally decreases, showing a negative relationship (possibly a strong non - linear negative trend).