The parks department of a certain city administered a survey consisting of 5 yes/no questions. Among the 6,655 completed surveys,...

OWNING THE DATASET

Let's start by understanding what we're working with. The table shows 5 different response patterns from a survey with \(\mathrm{6,655}\) total respondents:

Key insight: Rather than looking at each row separately, we should immediately notice which patterns contain the most respondents. Patterns 3 and 1 together account for \(\mathrm{5,517}\) respondents (over 80% of all responses). This observation will dramatically simplify our analysis.

Note: For questions about majority, we need to determine if more than half of all respondents answered "yes" to each question. With \(\mathrm{6,655}\) total respondents, the majority threshold is \(\mathrm{3,328}\) (half of \(\mathrm{6,655}\) is \(\mathrm{3,327.5}\), so we need at least \(\mathrm{3,328}\) for a majority).

ANALYZING STATEMENT C (Starting with the clearest case)

Statement C Translation:
Original: "The majority of respondents answered 'yes' to Question C."
What we're looking for:

• Do more than \(\mathrm{3,328}\) respondents (majority threshold) answer "yes" to Question C?

In other words: Is the total count of "yes" responses to Question C greater than half of all respondents?

Let's sort the data by Question C responses to group all "yes" patterns together:

Now we can immediately see that Pattern 3 alone has \(\mathrm{3,512}\) respondents who answered "yes" to Question C. This already exceeds our majority threshold of \(\mathrm{3,328}\)!

We can stop here and conclude: Statement C is MAJORITY YES. The majority of respondents answered "yes" to Question C.

Teaching callout: Notice how we started with Question C instead of Question A because the visual evidence was strongest. When analyzing tables, always look for the clearest case first to build momentum and potentially save time.

ANALYZING STATEMENT A

Statement A Translation:
Original: "The majority of respondents answered 'yes' to Question A."
What we're looking for:

• Do more than \(\mathrm{3,328}\) respondents (majority threshold) answer "yes" to Question A?

In other words: Is the total count of "yes" responses to Question A greater than half of all respondents?

Let's sort the data by Question A responses:

Looking at the sorted table, we can see:

• Only Patterns 1 and 2 show "yes" for Question A
• The total "yes" responses = \(\mathrm{2,005 + 120 = 2,125}\)
• This is significantly less than our majority threshold of \(\mathrm{3,328}\)

Therefore: Statement A is MAJORITY NO. The majority of respondents did not answer "yes" to Question A.

Teaching callout: We didn't need to calculate exact percentages. Simply comparing our count (\(\mathrm{2,125}\)) to the majority threshold (\(\mathrm{3,328}\)) is sufficient. This threshold approach saves considerable time compared to calculating and comparing precise percentages.

ANALYZING STATEMENT E

Statement E Translation:
Original: "The majority of respondents answered 'yes' to Question E."
What we're looking for:

• Do more than \(\mathrm{3,328}\) respondents (majority threshold) answer "yes" to Question E?

In other words: Is the total count of "yes" responses to Question E greater than half of all respondents?

Let's sort by Question E responses:

From the sorted table, we can immediately see:

• Only Patterns 4 and 5 show "yes" for Question E
• Total "yes" responses = \(\mathrm{1,006 + 12 = 1,018}\)
• This is far below our majority threshold of \(\mathrm{3,328}\)

Therefore: Statement E is MAJORITY NO. The majority of respondents did not answer "yes" to Question E.

Teaching callout: Notice how the two largest patterns (1 and 3) both showed "no" for Question E. This visual cue already suggested the answer before we did any calculations. Looking for these dominant patterns can often give you a quick answer.

FINAL ANSWER COMPILATION

Reviewing our findings for each statement:

• Statement A: MAJORITY NO (\(\mathrm{2,125}\) "yes" responses < \(\mathrm{3,328}\) threshold)
• Statement C: MAJORITY YES (\(\mathrm{3,512+}\) "yes" responses > \(\mathrm{3,328}\) threshold)
• Statement E: MAJORITY NO (\(\mathrm{1,018}\) "yes" responses < \(\mathrm{3,328}\) threshold)

Our answer is: Only Statement C is MAJORITY YES.

LEARNING SUMMARY

Skills We Used

• Threshold thinking: Instead of calculating exact percentages, we simply checked if counts exceeded the halfway point (\(\mathrm{3,328}\))
• Strategic prioritization: We started with the clearest case (Question C) where visual evidence was strongest
• Pattern recognition: We identified the largest respondent groups and used them to drive our analysis
• Sorting for clarity: We sorted the table for each question to quickly see patterns

Strategic Insights

• The "Dominant Patterns" Principle: Always identify the largest data groups first. If they align on an answer, you often don't need detailed calculations.
• Sorting reveals patterns: For each question, sorting reorganized the data to make the answer visually apparent.
• Approximate vs. exact: For Questions A and E, rough estimates were sufficient - we didn't need to calculate exact percentages.

Common Mistakes We Avoided

• Calculating precise percentages (like 31.93%, 84.88%) when we only needed to know if a majority existed
• Analyzing questions in sequential order (A, C, E) rather than prioritizing the most obvious case first
• Adding all numbers exactly when rough estimates were sufficient

Remember: In table analysis questions, the fastest approach is often to sort, identify dominant patterns, and compare to thresholds rather than calculating exact values when not required.