The table lists 21 options for one-way air travel from Milwaukee, Wisconsin, to Seattle, Washington, on March 20, 2011. Each...

Owning the Dataset

Let's start by understanding this flight options dataset with the intention of "owning the data" completely.

We have a table showing 21 different flight options between two cities, with information about airlines, flight times, and pricing. Each row represents a unique flight option, and we need to evaluate three statements about these options.

Key observations that will help us solve efficiently:

• The table includes both base prices and total prices (which include taxes and fees)
• There are multiple flights from the same airlines (especially Delta)
• Trip times vary significantly (we'll see exactly how much when we sort)
• Some base prices are identical across multiple flights

These observations suggest that sorting will be particularly powerful for our analysis. Rather than checking things manually, we'll use strategic sorting to reveal patterns instantly.

Analyzing Statement 2

Statement 2 Translation:
Original: "The median total trip time for the listed options is 7.28 hours."
What we're looking for:

• The middle value (11th) when all 21 trip times are arranged in order
• Whether this middle value equals exactly 7.28 hours

In other words: When we sort all flights by duration, is the middle flight exactly 7.28 hours long?

Let's approach this strategically. Since we need to find the median value, sorting is the perfect technique:

1. Let's sort the table by "Total trip time" from lowest to highest
2. Since we have 21 flights total, the median will be the 11th value in our sorted list
3. Looking at the 11th row after sorting, we can see the trip time is exactly 7.28 hours

This is much faster than trying to manually identify all trip times and finding the middle value. The sort function does all the work for us, and we simply need to locate the 11th position.

Statement 2 is YES.

Analyzing Statement 3

Statement 3 Translation:
Original: "Assuming mean speeds of the planes are roughly equal and only one of the airlines listed offers a nonstop flight, Air Tran is that flight's originating airline."
What we're looking for:

• Evidence that exactly one flight is significantly faster than all others
• Whether Air Tran is the airline operating this faster flight

In other words: Is Air Tran operating the one flight that's noticeably faster than all others (suggesting it's nonstop)?

The great news is that our table is already sorted by trip time from the previous statement! This is where strategic statement ordering pays off. With the data already sorted by trip time:

1. We can immediately see the shortest trip time is 4.23 hours (Air Tran)
2. The second shortest is 5.90 hours (Frontier)
3. That's a difference of 1.67 hours – a substantial gap!

This significant difference between the shortest and second-shortest flights strongly suggests the Air Tran flight is nonstop while all others have connections. No need to calculate percentages or exact differences – the gap is visually obvious in our sorted data.

Statement 3 is YES.

Analyzing Statement 1

Statement 1 Translation:
Original: "For all options having the same base price, the applicable taxes and fees are equal."
What we're looking for:

• Groups of flights with identical base prices
• Whether these flights also have identical taxes and fees
• Just ONE counterexample would make this statement false

In other words: Do flights with the same base price always have the same amount added for taxes and fees?

To check this efficiently:

1. Let's sort the table by "Base price" from lowest to highest
2. This grouping will immediately cluster together all flights with identical base prices
3. Looking at the first cluster, we see several Delta flights all with a base price of $162
4. Checking their total prices, we immediately notice differences: $177 vs $181

Since these flights have the same base price ($162) but different total prices ($177 vs $181), they must have different taxes and fees. We've found our counterexample!

Note how we stopped our analysis the moment we found a single contradiction. For "all" statements, finding just one counterexample is enough to disprove the entire statement.

Statement 1 is NO.

Final Answer Compilation

Reviewing our analysis:

• Statement 2: YES (The median trip time is indeed 7.28 hours)
• Statement 3: YES (Air Tran operates the single nonstop flight)
• Statement 1: NO (Flights with the same base price can have different taxes/fees)

Therefore, our answer is: YES, YES, NO

Learning Summary

Skills We Used

• Strategic Sorting: We sorted the data in ways that instantly revealed patterns
• Efficient Verification: For Statement 1, we stopped immediately after finding a counterexample
• Statement Reordering: We tackled the statements in the order 2-3-1 to minimize the number of sorts needed

Strategic Insights

1. Sort-First Approach: Always ask "Which column, if sorted, would make this statement easiest to verify?"
2. Sort Leverage: When possible, use the same sorted view to answer multiple statements
3. Minimal Checking: For "all" statements, finding just one counterexample is sufficient
4. Visual Pattern Recognition: Train your eye to spot significant differences without calculating exact values

Common Mistakes We Avoided

• We didn't waste time calculating taxes and fees for every flight
• We didn't manually find the median by listing all 21 trip times
• We didn't calculate the exact percentage difference between the shortest and second-shortest flights
• We didn't revert to checking every option when finding just one counterexample was sufficient

Remember, in Table Analysis questions, efficiency comes from leveraging the sorting function and knowing exactly what to look for after sorting. The approach we used here – sorting strategically and verifying only what's necessary – will help you solve even the most complex Table Analysis questions with confidence and speed!