The table gives information about the annual car show that a certain antique car club held in an open field...

Owning the Dataset: Car Show Registration Data

Let's start by understanding this car show registration table. We have data spanning multiple years (2004-2010) with key metrics:

• Number of pre-registered cars
• Number of cars registered on-site
• Total revenue collected

A quick scan reveals some interesting patterns. Looking at one example row:

• 2005: 32 pre-registered cars, 60 on-site registrations, \(\$1,040\) total revenue

Key insight: We know from the introduction that there are different registration fees for pre-registered cars (\(\$10\)) versus on-site registrations (\(\$12\)). This fee structure information will be crucial for analyzing statement 2.

Let's approach each statement strategically to minimize unnecessary calculations.

Analyzing Statement 1: It rained in 2004.

Statement 1 Translation:
Original: "It rained in 2004."
What we're looking for:

• Evidence in the data that would indicate rain in 2004
• Patterns that would suggest weather impacted car show attendance

In other words: Can we find data anomalies in 2004 that would likely be explained by rain?

Let's sort the table by "Number of cars registered on-site" to quickly identify any outliers:

Sorting Approach: When we sort by on-site registrations (ascending), 2004 immediately stands out with only 8 on-site registrations - dramatically lower than any other year.

This is a classic pattern we look for in data analysis questions - extreme outliers often tell a story. The number of on-site registrations in 2004 is dramatically lower than any other year (other years have 50+ on-site registrations).

Why is this significant? Rain would naturally deter day-of attendees from bringing their cars to an outdoor show, while having minimal impact on pre-registered participants who committed in advance.

We don't need to perform any calculations here - the visual pattern after sorting makes the answer obvious. When we see an extreme outlier in on-site attendance with relatively normal pre-registration numbers, adverse weather (rain) is the most logical explanation.

Statement 1 is Yes.

Analyzing Statement 2: Registration fees increased from 2005 to 2006.

Statement 2 Translation:
Original: "Registration fees increased from 2005 to 2006."
What we're looking for:

• Evidence that the per-car registration fees were higher in 2006 than in 2005
• A way to determine if the same fee structure applies to both years

In other words: Did the car show charge more per car in 2006 than in 2005?

Let's focus our attention only on the relevant years - 2005 and 2006. We'll verify if the original fee structure (\(\$10\) pre-registered, \(\$12\) on-site) applies to 2005, then check if 2006 shows evidence of increased fees.

For 2005:

• Expected revenue with original fees: \((32 \text{ pre-registered} \times \$10) + (60 \text{ on-site} \times \$12)\)
• Expected revenue: \(\$320 + \$720 = \$1,040\)
• Actual revenue shown: \(\$1,040\)
• The numbers match exactly, confirming 2005 uses the original fee structure.

For 2006:

• Expected revenue with original fees: \((28 \text{ pre-registered} \times \$10) + (67 \text{ on-site} \times \$12)\)
• Expected revenue: \(\$280 + \$804 = \$1,084\)
• Actual revenue shown: \(\$1,341\)
• Difference: \(\$257\) higher than expected

This significant difference between expected and actual revenue for 2006 (while 2005 matched perfectly) clearly indicates that fees increased. We don't need to calculate the exact new fee structure - the evidence of an increase is sufficient to answer the question.

Statement 2 is Yes.

Analyzing Statement 3: The average revenue per car was higher in 2010 than in any other year.

Statement 3 Translation:
Original: "The average revenue per car was higher in 2010 than in any other year."
What we're looking for:

• The average revenue per car for 2010
• Comparison with other years to see if 2010's average is highest

In other words: Did 2010 generate more revenue per car than all other years in the table?

Strategic approach: Rather than calculating all years immediately, let's first find 2010's average, then strategically check only the most promising competitors.

For 2010:

• Total revenue: \(\$1,650\)
• Total cars: 115 (pre-registered + on-site)
• Average revenue per car: \(\$1,650 \div 115 = \$14.35\)

Now, instead of calculating every year, let's visually scan for potential competitors. Years with the highest potential to beat 2010 would have:

1. High revenue AND
2. Low car count (this combination maximizes the average)

Based on a quick scan, the most promising competitors are:

For 2007:

• Total revenue: \(\$1,794\)
• Total cars: 127
• Average revenue per car: \(\$1,794 \div 127 = \$14.13\)

For 2006:

• Total revenue: \(\$1,341\)
• Total cars: 95
• Average revenue per car: \(\$1,341 \div 95 = \$14.12\)

The other years have lower revenue or higher car counts, making them unlikely to exceed 2010's average. After checking the most promising competitors, we confirm that 2010's average of \(\$14.35\) is indeed the highest.

Statement 3 is Yes.

Final Answer: All three statements are Yes.

Learning Summary

Skills We Used

• Strategic Sorting: Sorting by on-site registrations immediately revealed the 2004 weather anomaly, eliminating the need for extensive comparisons.
• Targeted Calculations: For Statement 2, we only needed to check if 2006's actual revenue exceeded the expected amount based on original fees.
• Strategic Sampling: For Statement 3, we calculated 2010's average first, then only checked the most promising competitors rather than all years.

Strategic Insights

1. Sort before calculating: Sorting often reveals patterns instantly, saving significant time on calculations.
2. Focus on relevant years only: Many table analysis questions only require examining a subset of the data.
3. Calculate the target value first: In comparison questions, find the value you're testing first, then strategically check only viable competitors.
4. Look for outliers immediately: Extreme values often provide immediate answers for certain types of questions.

Common Mistakes We Avoided

1. Unnecessary calculations: We didn't need to analyze all metrics for Statement 1 - sorting revealed the answer immediately.
2. Over-calculation: For Statement 2, we didn't need to determine the exact new fee structure - just that fees increased.
3. Exhaustive checking: For Statement 3, we didn't calculate averages for all years - only for 2010 and the most promising competitors.

Remember: In table analysis questions, your goal is to extract insights efficiently, not to perform every possible calculation. Strategic sorting and focused analysis will save you valuable time on test day!