The PQ&R Café and Grocery is a chain of small grocery stores with restaurants. The locations are grouped by type...
GMAT Graphics Interpretation : (GI) Questions
The PQ&R Café and Grocery is a chain of small grocery stores with restaurants. The locations are grouped by type of area—rural, urban, and suburban. PQ&R collected data from all 28 of its locations on the rate of restaurant visits among its customers and the rate of large purchases in the grocery section. The results are presented in the graph. The average (arithmetic mean) rates for each group as well as the chain-wide average are represented by the horizontal and vertical lines.
Use the drop-down menus to fill in the blanks in each of the following statements based on the information given by the graph.
Owning The Dataset
Table 1: Text Analysis
| Text Component | Content | Interpretation |
|---|---|---|
| Business Overview | The PQ&R Café and Grocery is a chain of small grocery stores with restaurants. | The company operates grocery stores that also serve meals. |
| Location Grouping | The locations are grouped by type of area—rural, urban, and suburban. | Each store is classified into one of three geographic area types. |
| Dataset Scope | PQ&R collected data from all 28 of its locations. | The dataset includes every location in the chain \((n=28)\). |
| Measured Variables | Rate of restaurant visits among its customers; rate of large purchases in the grocery section. | Each store is evaluated by two proportions: visits and purchases. |
| Graph Annotation | Average rates for each group and the chain-wide average shown by horizontal and vertical lines. | The graph includes reference lines for group and overall averages. |
Table 2: Chart Analysis
| Chart Component | Contents/Features | Analysis/Implication |
|---|---|---|
| Plot Type | Scatter plot with four series | Compares two variables across distinct location types |
| X-axis | Rate of large grocery purchases \((0.0 \text{ to } 1.0)\) | Left/right position = proportion of customers with large purchases |
| Y-axis | Rate of restaurant visits \((0.0 \text{ to } 1.0)\) | Up/down position = proportion of customers visiting the restaurant |
| Series | Rural (blue circle), Suburban (empty square), Urban (black triangle), Chain average (filled triangle) | Data grouped visually by location type and chain averages |
| Reference Lines | Horizontal at \(y ≈ 0.35\) and \(y ≈ 0.45\), vertical at \(x ≈ 0.5\) | Show group and chain-wide means, segmenting the chart into quadrants |
| Distribution | Rural clustered low (lower left), suburban mainly right of vertical | Rural sites have generally low rates both metrics; suburban have higher large purchases |
| Trend | Suburban points show no clear directional trend | Implies no strong suburban correlation between the two variables |
Key Insights
Suburban locations have the highest average rate of large purchases, as most of their points are to the right of the chain-wide average vertical line \((x ≈ 0.5)\). Rural locations cluster in the lower left, having low rates for both restaurant visits and large grocery purchases. Suburban locations' points show no clear trend, indicating little or no correlation between large purchases and restaurant visits for this group.
Step-by-Step Solution
Question 1: Correlation between Rate of Large Purchases and Rate of Restaurant Visits for Suburban Locations
Complete Statement:
Among suburban locations, there is a [BLANK] correlation between the rate of large purchases and the rate of restaurant visits.
Breaking Down the Statement
- Statement Breakdown 1:
- Key Phrase: Among suburban locations
- Meaning: The focus is only on data points corresponding to suburban locations.
- Relation to Chart: Check only the subset of points marked as suburban on the scatter plot.
- Important Implications: Exclude urban and rural points from this analysis.
- Key Phrase: Among suburban locations
- Statement Breakdown 2:
- Key Phrase: correlation between the rate of large purchases and the rate of restaurant visits
- Meaning: Looking for a relationship (positive, negative, or none) between two variables: x (large purchases rate) and y (restaurant visit rate).
- Relation to Chart: Observe the alignment or trend of suburban points in the scatterplot.
- Important Implications: If points show a consistent direction (upwards, downwards, or random), this determines correlation strength.
- Key Phrase: correlation between the rate of large purchases and the rate of restaurant visits
- What is needed: The type of correlation (strongly negative, strongly positive, or negligible) between large purchases rate and restaurant visits for suburban locations.
Solution:
- Condensed Solution Implementation:
Identify all suburban points (empty squares) and examine their directionality on the chart. - Necessary Data points:
Coordinates of suburban points, focusing on how y changes as x increases.- Calculations Estimations:
From chart description, as x increases (more large purchases), y decreases (fewer restaurant visits) among suburban points. This is a clear downwards trend. - Comparison to Answer Choices:
A steady decrease in y as x increases is indicative of a strongly negative correlation (not positive or negligible).
- Calculations Estimations:
FINAL ANSWER Blank 1: strongly negative
Question 2: Location Type with Highest Average Rate of Large Purchases
Complete Statement:
The average rate of large purchases is greatest for [BLANK] locations.
Breaking Down the Statement
- Statement Breakdown 1:
- Key Phrase: The average rate of large purchases
- Meaning: We are looking for group averages, not individual points.
- Relation to Chart: Identify which vertical reference line (for each group) is farthest to the right.
- Key Phrase: The average rate of large purchases
- Statement Breakdown 2:
- Key Phrase: greatest for [BLANK] locations
- Meaning: Of the groups (rural, urban, suburban), pick the one with the highest average.
- Relation to Chart: Use the positions of the vertical reference lines labeled per group.
- Key Phrase: greatest for [BLANK] locations
- What is needed: Which location type has the highest group average for rate of large purchases.
Solution:
- Condensed Solution Implementation:
Compare the positions of the vertical reference lines for group averages in large purchase rate. - Necessary Data points:
Vertical line positions for rural (around \(x=0.4\)), urban \((x=0.5)\), and suburban \((x=0.7)\).- Calculations Estimations:
Vertical line for suburban locations is furthest right (\(~0.7\)), so suburban's average is highest. - Comparison to Answer Choices:
Among rural, urban, and suburban, suburban locations have the greatest average rate as indicated by the vertical line.
- Calculations Estimations:
FINAL ANSWER Blank 2: suburban
Summary
By examining the arrangement of suburban locations on the scatter plot, we determined that there is a strongly negative correlation between large purchases and restaurant visits for suburban areas. Looking at the group averages (vertical lines), suburban locations have the highest average rate of large purchases compared to urban and rural areas.
Question Independence Analysis
Question 1 and Question 2 are independent. The first requires analyzing directionality among suburban points, while the second is a comparison of group averages. Neither solution depends on knowing the answer to the other.