For each of the 22 faculty members in a university's statistics department, the graph shows the faculty member's monthly salary,...
GMAT Graphics Interpretation : (GI) Questions
For each of the 22 faculty members in a university's statistics department, the graph shows the faculty member's monthly salary, in euros (€), and time since doctorate- the number of years since that faculty member earned his or her doctorate in statistics. The graph also shows a trend line for the data.
From each drop-down menu, select the option that creates the most accurate statement based on the information provided.
Owning the Dataset
Table 1: Text Analysis
| Text Component | Literal Content | Simple Interpretation |
|---|---|---|
| Subject Matter | 22 faculty members in a university's statistics department | Examines salary and experience of all 22 department faculty members |
| Y-axis Variable | monthly salary, in euros (\(€\)) | How much each faculty member earns monthly in euros |
| X-axis Variable | time since doctorate - number of years since earning their doctorate in statistics | Counts years since each professor received their PhD in statistics |
| Additional Feature | the graph also shows a trend line for the data | Trend line illustrates average relationship between salary and experience |
Table 2: Chart Analysis
| Chart Component | What's Shown | Interpretation |
|---|---|---|
| Chart Type | Scatter plot with trend (regression) line | Each dot = one faculty member; line shows average trend |
| X-axis Range | 0 to 30 years since doctorate | Experience levels from new to 30 years post-doctorate |
| Y-axis Range | \(€0\) to \(€8,000\) monthly salary | Faculty salaries cover wide range; most between \(€3,000\) and \(€7,000\) |
| Data Points | 22 black dots | Data represents all faculty members in department |
| Trend Line Slope | Positive, about \(€80\) per year | Average salary increases \(€80\)/month for each additional year |
| Data Spread | Points scattered above and below trend line | Substantial variation in salaries not explained by experience alone |
Key Insights
- On average, each additional year since earning a doctorate is associated with about \(€80\) higher monthly salary, according to the trend line.
- The highest paid faculty member earns about \(€7,000\) per month with roughly 18 years of post-doctorate experience, but salary does not steadily increase for all.
- Significant variation exists around the trend line, indicating that factors other than years since doctorate (such as field, rank, performance, or negotiation) strongly affect salary.
Step-by-Step Solution
Question 1: Interpreting the Trend Line: Salary Increase per Year
Complete Statement:
The trend line suggests that, for a faculty member whose time since doctorate is at least 2 years, each 1-year increase in time since doctorate corresponds to an increase, to the nearest \(€10\), [BLANK 1] of monthly salary.
Breaking Down the Statement
- Statement Breakdown 1:
- Key Phrase: trend line suggests
- Meaning: The answer should be based on the trend line (not individual points).
- Relation to Chart: The blue line summarizing overall salary experience.
- Important Implications: We're finding the general average increase, not any specific person's salary increase.
- Key Phrase: trend line suggests
- Statement Breakdown 2:
- Key Phrase: each 1-year increase in time since doctorate
- Meaning: We're examining how salary changes as years since doctorate increases by 1.
- Relation to Chart: This is the slope of the trend line ('rise over run', salary per year).
- Important Implications: We should find the amount the line rises for each year to get the answer.
- Key Phrase: each 1-year increase in time since doctorate
What is needed: The average increase in salary (euros) that occurs for every one year increase in time since doctorate as shown by the trend line.
Solution:
- Condensed Solution Implementation:
Use two points far apart on the trend line to estimate the slope (change in salary divided by change in years). - Necessary Data points:
Trend line at 5 years: \(€4,400\). Trend line at 25 years: \(€6,000\).- Calculations Estimations:
Difference in salary: \(€6,000 - €4,400 = €1,600\). Difference in years: \(25 - 5 = 20\). Slope = \(€1,600 ÷ 20 = €80\) per year. - Comparison to Answer Choices:
Answer choices are 40, 70, and 80. Our calculation gives \(€80\), which matches the third choice.
- Calculations Estimations:
FINAL ANSWER Blank 1: 80
Question 2: Identifying the Most Experienced Highest-Paid Faculty Member
Complete Statement:
For the faculty member whose monthly salary is greatest, the time since doctorate is [BLANK 2] years.
Breaking Down the Statement
- Statement Breakdown 1:
- Key Phrase: faculty member whose monthly salary is greatest
- Meaning: Find the faculty member with the highest salary (highest vertical point on the chart).
- Relation to Chart: Locate the single black dot farthest up the y-axis (salary axis).
- Key Phrase: faculty member whose monthly salary is greatest
- Statement Breakdown 2:
- Key Phrase: time since doctorate
- Meaning: For this specific person, find their years since doctorate (the x-value of that dot).
- Relation to Chart: Check the horizontal (x) position of the highest dot.
- Key Phrase: time since doctorate
What is needed: The number of years since doctorate for the individual with the highest salary.
Solution:
- Condensed Solution Implementation:
Find the highest dot (salary) on the chart, then track down to the x-axis to read the corresponding years since doctorate. - Necessary Data points:
The highest salary is shown as about \(€7,000\) per month.- Calculations Estimations:
From the highest point, track straight down to the x-axis. It lines up very closely with 18 years. - Comparison to Answer Choices:
Choices are 18, 20, 22, or 25. 18 matches our estimate.
- Calculations Estimations:
FINAL ANSWER Blank 2: 18
Summary
To answer both questions, use the trend line for average increases (question 1) and find the outlier/highest point for the largest salary (question 2). This approach highlights the difference between analyzing overall trends and identifying specific data points.
Question Independence Analysis
The two questions are independent: the first requires interpreting the trend line for a general relationship, while the second requires identifying an individual data point. Knowing the answer to one does not provide information for the other.