Math Problem Statement
The scatterplot shows the median starting salaries and the median mid-career salaries for graduates at a selection of colleges. Complete parts (a) through (e) below. Mid-Careerequals=-6056+1.8811 Start Med 30 40 50 60 70 80 25 50 75 100 125 150 175 Start Median Salary (thousands of $) Mid-Career Salary (thousands of $)
A graph has a horizontal axis labeled "Start Median Salary (thousands of dollars)" from 30 to 80 in increments of 10 and a vertical axis labeled "Mid-Career Salary (thousands of dollars)" from 25 to 175 in increments of 25. A line ascends from left to right and forty points are scattered around the line as it ascends, with approximately half of the points above the line and half below the line. The line travels through the following points: (30, 50), (40, 69), (50, 88), (60, 107), (70, 126) and (80, 144). All points are approximate. Question content area bottom Part 1 a. As the data are graphed, which is the independent and which the dependent variable? The independent variable is median starting salary and the dependent variable is median mid-career salary. Part 2 b. Why do you suppose median salary at a school is used instead of the mean? A. Salary distributions are usually bell-shaped, making the median a more meaningful measure of center. B. Salary distributions are usually bimodal, making the median a more meaningful measure of center. C. Salary distributions are usually skewed, making the median a more meaningful measure of center. Your answer is correct.D. It is easier to calculate the median for a salary distribution instead of the mean. Part 3 c. Using the graph, estimate the median mid-career salary for a median starting salary of $ 50 comma 000$50,000. The median mid-career salary for a median starting salary of $ 50 comma 000$50,000 is about $88,00088,000. (Round to the nearest thousand as needed.) Part 4 d. Use the equation to predict the median mid-career salary for a median starting salary of $ 50 comma 000$50,000.
Solution
Part 4: Using the equation to predict the median mid-career salary for a median starting salary of $50,000.
We are given the equation:
Substitute the value of the median starting salary, , into the equation:
Now, calculate:
Thus, the predicted median mid-career salary for a median starting salary of $50,000 is $88,000.
Follow-up Questions:
- How would the prediction change if the starting salary was $60,000?
- Why is the slope of the equation important when interpreting the relationship between starting and mid-career salaries?
- How could outliers in the data affect the accuracy of this linear model?
- What assumptions are being made about the relationship between starting salary and mid-career salary in this model?
- How might this relationship differ for various types of college degrees (e.g., STEM vs. humanities)?
Tip:
Always check the correlation of the data points in the scatter plot with the regression line to ensure the linear model is a good fit.
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Scatterplot Analysis
Algebra
Formulas
Mid-Career Salary = -6056 + 1.8811 × Start Median Salary
Theorems
Linear Equation
Correlation
Suitable Grade Level
College Level
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