The table summarizes the results of a recent study conducted by a market research firm. Each study participant viewed product...

OWNING THE DATASET

Let's start by understanding what we're looking at. This table shows comprehension percentages for six products (A-F) when presented in four different formats: paragraph, bar graph, scatterplot, and table.

Key insights from this dataset:

• Each row represents a product, and percentages tell us how well users comprehended the information
• Higher percentages indicate better comprehension
• The percentages range from as low as 4% to as high as 36%
• Some formats clearly work better than others for certain products

Notice how quickly scanning the table shows significant variation - this suggests that format effectiveness differs considerably by product. We'll use sorting strategically to make patterns instantly visible rather than calculating everything manually.

ANALYZING STATEMENT 2

Statement 2 Translation:

Original: "The format with the greatest range of comprehension percentages was the paragraph format."

What we're looking for:

• Calculate the range (maximum - minimum) for each format
• Determine if paragraph format has the largest range

In other words: Does paragraph format show the biggest difference between its highest and lowest percentages?

This statement deals with ranges, which become instantly visible after sorting. Let's tackle this first because sorting will make the ranges immediately apparent.

Let's sort each column to quickly find the minimum and maximum values:

Paragraph format (sorted): 8%, 9%, 12%, 13%, 35%, 36%

• \(\mathrm{Range} = 36\% - 8\% = 28\%\)

Bar graph (sorted): 8%, 10%, 21%, 27%, 34%, 34%

• \(\mathrm{Range} = 34\% - 8\% = 26\%\)

Scatterplot (sorted): 4%, 10%, 10%, 14%, 16%, 22%

• \(\mathrm{Range} = 22\% - 4\% = 18\%\)

Table (sorted): 10%, 14%, 16%, 16%, 18%, 25%

• \(\mathrm{Range} = 25\% - 10\% = 15\%\)

We can clearly see that the paragraph format has the greatest range at 28%. This statement DESCRIBES PARAGRAPH FORMAT.

Teaching Insight: Notice how sorting instantly revealed the minimum and maximum values without requiring us to scan the entire dataset multiple times. This approach works for any range question!

ANALYZING STATEMENT 3

Statement 3 Translation:

Original: "The format with the lowest median comprehension percentage was the scatterplot format."

What we're looking for:

• Calculate the median percentage for each format
• Determine if scatterplot has the lowest median

In other words: When we arrange all percentages for each format in order, is the middle value lowest for scatterplot?

We've already sorted our data for Statement 2, so finding medians is now extremely efficient. For 6 values, the median is the average of the 3rd and 4th values.

Paragraph format (already sorted): 8%, 9%, 12%, 13%, 35%, 36%

• \(\mathrm{Median} = \frac{12\% + 13\%}{2} = 12.5\%\)

Scatterplot (already sorted): 4%, 10%, 10%, 14%, 16%, 22%

• \(\mathrm{Median} = \frac{10\% + 14\%}{2} = 12\%\)

Just by looking at the sorted data, we can see the bar graph and table formats have higher medians. For example, the 3rd and 4th values for the table format are 16% and 16%, which is clearly higher than the scatterplot's median.

The scatterplot has a median of 12%, which is lower than the paragraph format's 12.5% and the other formats as well. This statement DOES NOT DESCRIBE PARAGRAPH FORMAT.

Teaching Insight: Building on our previous sorting pays off! We didn't need to re-sort or perform unnecessary calculations. Always look for ways to build on work you've already done.

ANALYZING STATEMENT 1

Statement 1 Translation:

Original: "The table format was the optimal format for the greatest number of products."

What we're looking for:

• Determine which format has the highest percentage for each product
• Count how many times each format is optimal
• Check if table format is optimal the most frequently

In other words: Is the table format the "winner" (highest comprehension) for more products than any other format?

Let's scan each product row to identify which format has the highest percentage:

Product A: Bar graph (27%) is highest
Product B: Paragraph (35%) is highest
Product C: Table (25%) is highest
Product D: Paragraph (36%) is highest
Product E: Bar graph (34%) is highest
Product F: Bar graph (34%) is highest

Now let's count how many times each format is optimal:

• Table: 1 product (C)
• Paragraph: 2 products (B, D)
• Bar graph: 3 products (A, E, F)
• Scatterplot: 0 products

The bar graph format is optimal for the greatest number of products (3), not the table format (which is only optimal for 1 product). This statement DOES NOT DESCRIBE PARAGRAPH FORMAT.

Teaching Insight: For this type of question, visual scanning with mental tracking is much faster than creating a new table. For datasets with few rows, scanning is nearly always more efficient than reconstructing data.

FINAL ANSWER COMPILATION

Let's compile our findings for each statement:

• Statement 1: DOES NOT DESCRIBE PARAGRAPH FORMAT (Table is not the optimal format for the most products)
• Statement 2: DESCRIBES PARAGRAPH FORMAT (Paragraph has the greatest range)
• Statement 3: DOES NOT DESCRIBE PARAGRAPH FORMAT (Scatterplot has the lowest median)

Therefore, our answer is: The statement(s) that correctly describe(s) the paragraph format is/are Statement 2 only.

LEARNING SUMMARY

Skills We Used

• Strategic Sorting: We sorted data once and built upon that for multiple statements
• Visual Pattern Recognition: We used sorting to make patterns visible rather than calculating everything
• Efficient Statement Sequencing: We tackled statements in order of analytical efficiency, not the given order

Strategic Insights

1. Sort First, Calculate Later: Sorting immediately revealed ranges and made median calculations simpler
2. Leverage Previous Work: We used our sorted data from Statement 2 to quickly solve Statement 3
3. Visual Scanning for Small Datasets: For just 6 products, scanning with mental tracking is faster than creating new tables

Common Mistakes We Avoided

• We didn't waste time creating a separate table for Statement 1
• We didn't recalculate medians by manually reordering data
• We didn't tackle statements in the given order, but in the order that maximized efficiency

This approach transforms what could be a time-consuming problem into one that can be solved with confidence. Remember that for any table analysis question, sorting is often your most powerful first step!