The table shows average annual percent changes in various categories related to productivity for industries in the Transportation and Warehousing...

Owning the Dataset

Let's begin by understanding what we're working with. This table shows percentage changes in various metrics across transportation (T) and warehousing (W) industries.

Key observations to help us solve efficiently:

• The table has 9 industries divided between transportation (T) and warehousing (W) sectors
• We're looking at 5 performance metrics for each industry (hourly output, total output, hours worked, unit labor cost, labor cost)
• Some values are negative (showing decreases) while others are positive (showing increases)
• The values are percentages, so we need to compare relative changes, not absolute numbers

Instead of trying to memorize all 45 data points (\(9 \times 5\) metrics), let's use strategic sorting to quickly find patterns and answers.

Analyzing Statement 2

Statement 2 Translation:

Original: "The industry with the highest percentage increase in hourly output was in the warehousing (W) sector."

What we're looking for:

• Find the top 3 industries by hourly output percentage
• Check if the #1 industry belongs to the warehousing (W) sector

In other words: Is the industry with the highest hourly output increase a warehousing company?

Let's tackle this statement first since it requires just a single sort operation.

Step 1: Sort the table by "Hourly output" column (in descending order)

After sorting, we can immediately see the top 3 performers:

• General warehousing (W): \(5.0\%\)
• Line-haul railroads (T): \(4.2\%\)
• Freight trucking, local (T): \(3.1\%\)

Result: The highest hourly output increase is indeed from a warehousing industry (General warehousing at \(5.0\%\)).

Statement 2 is YES.

Teaching Note: Notice how sorting instantly revealed our answer without requiring us to scan through all 9 industries. When faced with "highest" or "lowest" questions, sorting is almost always the fastest approach.

Analyzing Statement 3

Statement 3 Translation:

Original: "Every industry in the warehousing (W) sector had a higher percentage increase in labor cost than every industry in the transportation (T) sector."

What we're looking for:

• Compare labor cost increases between W and T sectors
• Check if ALL W industries have HIGHER labor cost increases than ALL T industries

In other words: Do all warehousing industries show bigger labor cost increases than any transportation industry?

Let's sort by the "Labor cost" column to quickly see the pattern.

Step 1: Sort the table by "Labor cost" column (in descending order)

After sorting, we can see the industries arranged from highest to lowest labor cost increase:

• General warehousing (W): \(6.7\%\)
• Refrigerated warehousing (W): \(4.8\%\)
• Couriers and messengers (W): \(4.5\%\)
• Freight trucking, local (T): \(4.3\%\)
• [Other transportation industries below]

Key Pattern: All the warehousing (W) industries are clustered at the top of the sorted list, above all transportation (T) industries.

Result: Every industry in the warehousing sector did indeed have a higher percentage increase in labor cost than every industry in the transportation sector.

Statement 3 is YES.

Teaching Note: This is where sorting truly transforms the problem. Instead of manually comparing each W industry against each T industry (which would require many comparisons), sorting created a visual pattern that answered our question instantly.

Analyzing Statement 1

Statement 1 Translation:

Original: "The freight trucking industries were the only industries that had positive percentage changes in all five metrics."

What we're looking for:

• Identify which industries had positive changes across all metrics
• Check if only freight trucking industries meet this criterion

In other words: Did only the freight trucking companies show increases in all categories?

Instead of checking every single value (which would be time-consuming), let's use an elimination strategy.

Step 1: Hunt for negatives by sorting each column one by one.

Let's sort each column and note which industries show negative values:

Hourly output (sorted):

• Negative values found for: Used household goods, Refrigerated warehousing, Couriers and messengers
• Eliminated 3 industries

Total output (sorted):

• Negative value found for: Used household goods
• This industry was already eliminated

Hours worked (sorted):

• Negative values found for: Line-haul railroads, Postal service
• Eliminated 2 more industries

Unit labor cost (sorted):

• Negative values found for: Air transportation, General warehousing, Line-haul railroads
• 1 new elimination (Air transportation), others already eliminated

Result of elimination: Only the local freight trucking and long-distance freight trucking industries never appear with negative values. These are the only two industries with positive percentage changes across all five metrics.

Statement 1 is YES.

Teaching Note: When looking for items that meet multiple criteria, elimination is often faster than verification. Each negative value we found immediately removed an industry from consideration, saving us from having to check all 45 data points.

Final Answer Compilation

Evaluating all three statements:

• Statement 1: YES (Only freight trucking industries had positive changes in all metrics)
• Statement 2: YES (The highest hourly output increase was in the warehousing sector)
• Statement 3: YES (All warehousing industries had higher labor cost increases than all transportation industries)

The correct answer is: All statements are yes.

Learning Summary

Skills We Used

• Strategic Sorting: We sorted columns to instantly reveal patterns, rankings, and outliers
• Elimination Strategy: For Statement 1, we hunted for negative values to quickly eliminate industries
• Visual Pattern Recognition: After sorting for Statement 3, we immediately saw all W industries clustered above T industries

Strategic Insights

• Tackle the easiest statement first: We started with Statement 2 because it required just one sort operation
• Hunt for disqualifying data: Instead of verifying all positives, we looked for any negatives to eliminate industries
• Let sorting reveal patterns: Sorting the labor cost column instantly showed the W vs. T pattern without calculations

Common Mistakes We Avoided

• We didn't waste time checking all 45 data points for Statement 1
• We didn't calculate exact differences when only the pattern mattered for Statement 3
• We didn't approach the statements in numerical order, but in order of solving efficiency

Next time you face a table analysis question, remember to sort first, eliminate where possible, and look for patterns that emerge after sorting. These techniques transform complex data verification tasks into quick visual assessments.