The table lists 13 varieties of edible oils by smoke point, recommended heat, typical package size, and typical price for...

OWNING THE DATASET

Let's start by understanding what we're working with. This table shows information about different cooking oils with several key characteristics:

Column	What it tells us
Oil type	The specific oil (e.g., Peanut, Olive, Flaxseed, etc.)
Refined?	Whether the oil has been refined (Yes/No)
Smoke point	Temperature (°C) at which the oil begins to smoke
Recommended heat level	Whether the oil is best for medium or high heat cooking
Price per package	Cost in dollars
Package size	Volume in milliliters (mL)

Key insight: This table is perfect for sorting to reveal patterns. Looking at one example row gives us a sense of the relationships:

Olive Oil: Unrefined, 190°C smoke point, Medium heat, $14, 500mL

Notice the dataset contains both refined and unrefined oils, different heat levels, and various prices and package sizes. These characteristics will be crucial for efficiently evaluating the statements.

ANALYZING STATEMENT 1

Statement 1 Translation:

Original: "The range of smoke points for refined oils is greater than the range of smoke points for unrefined oils."

What we're looking for:

• Range of smoke points for refined oils (highest - lowest temperature)
• Range of smoke points for unrefined oils (highest - lowest temperature)
• Whether refined range > unrefined range

In other words: Do refined oils have a wider spread of smoke points than unrefined oils?

Efficient Approach

The most efficient way to tackle this is to sort the table by the "Refined?" column and then by "Smoke point" within each group.

Let's sort by "Refined?" first, then by "Smoke point" (ascending):

For refined oils:

• Lowest smoke point: 210°C
• Highest smoke point: 232°C
• Range: \(232°\mathrm{C} - 210°\mathrm{C} = 22°\mathrm{C}\)

For unrefined oils:

• Lowest smoke point: 49°C (both Flaxseed and Walnut)
• Highest smoke point: 190°C (Olive)
• Range: \(190°\mathrm{C} - 49°\mathrm{C} = 141°\mathrm{C}\)

Teaching moment: Notice how sorting immediately reveals the extremes without having to scan every single entry! This visual pattern is clear: unrefined oils have a much wider spread of smoke points (from 49°C to 190°C) while refined oils cluster tightly between 210°C-232°C.

Statement 1 is No - The range for unrefined oils (141°C) is much larger than the range for refined oils (22°C).

ANALYZING STATEMENT 2

Statement 2 Translation:

Original: "The median price per package for medium-heat oils is higher than the median price per package for high-heat oils."

What we're looking for:

• Median price of all medium-heat oils
• Median price of all high-heat oils
• Whether medium-heat median > high-heat median

In other words: Are medium-heat oils typically more expensive than high-heat oils?

Efficient Approach

Let's sort by "Recommended heat level" first, then by "Price per package" within each group.

For medium-heat oils:

• We have only 2 oils: $13 and $14
• With only 2 values, the median is simply their average: $13.50

For high-heat oils:

• We have 6 oils, sorted by price: $6, $7, $8, $9, $13, $15
• With an even number of values (6), the median is the average of the middle two: \((\$8 + \$9)/2 = \$8.50\)

Teaching moment: When you have very few values in one group (like only 2 medium-heat oils), calculating the median becomes extremely simple! Also, notice we didn't need to write out every single oil by name - we just needed the price values to find the median.

Statement 2 is Yes - The median price for medium-heat oils ($13.50) is indeed higher than the median price for high-heat oils ($8.50).

ANALYZING STATEMENT 3

Statement 3 Translation:

Original: "The median package size for refined oils is greater than the median package size for unrefined oils."

What we're looking for:

• Median package size of all refined oils
• Median package size of all unrefined oils
• Whether refined median > unrefined median

In other words: Do refined oils typically come in larger containers than unrefined oils?

Efficient Approach

Let's sort by "Refined?" first, then by "Package size" within each group.

For refined oils:

• We have 5 oils with package sizes (sorted): 500mL, 500mL, 750mL, 946mL, 1000mL
• With 5 values, the median is the middle value (3rd): 750mL

For unrefined oils:

• We have 8 oils with package sizes (sorted): 250mL, 250mL, 250mL, 375mL, 375mL, 500mL, 500mL, 500mL
• With 8 values, the median is the average of the 4th and 5th values: \((375\mathrm{mL} + 375\mathrm{mL})/2 = 375\mathrm{mL}\)

Teaching moment: After sorting, you can immediately see a pattern: refined oils generally come in larger containers. This visual pattern gives us confidence in our answer even before calculating the exact medians.

Statement 3 is Yes - The median package size for refined oils (750mL) is greater than the median package size for unrefined oils (375mL).

FINAL ANSWER COMPILATION

Reviewing our analysis of each statement:

Statement	Conclusion	Reasoning
Statement 1	No	Unrefined oils have a larger range (141°C) than refined oils (22°C)
Statement 2	Yes	Medium-heat oils have a higher median price ($13.50) than high-heat oils ($8.50)
Statement 3	Yes	Refined oils have a larger median package size (750mL) than unrefined oils (375mL)

Answer pattern: No, Yes, Yes

LEARNING SUMMARY

Skills We Used

• Sorting as the primary technique: Every statement was tackled by sorting first, which revealed patterns immediately
• Visual pattern recognition: After sorting, the patterns became visually obvious, reducing calculation time
• Quick median calculations: For even-numbered datasets, we averaged the middle two values; for odd-numbered datasets, we took the middle value

Strategic Insights

1. Sort strategically: Start by sorting on the grouping variable (Refined?, Heat level), then on the comparison variable (Smoke point, Price, Package size)
2. Use dataset size to your advantage: When a group has very few items (like only 2 medium-heat oils), calculations become trivial
3. Look for visual patterns: The clustering of values (like refined oils having similar smoke points) can tell you the answer faster than calculations
4. Know when precision isn't necessary: For large differences (like 141°C vs 22°C), even rough estimates would lead to the correct answer

Common Mistakes We Avoided

1. Manual grouping: Instead of manually listing every oil by category, we used sorting to instantly organize the data
2. Unnecessary calculations: We didn't calculate exact values when the visual pattern was clear enough
3. Equal effort for all statements: We recognized that some statements (like #1) had more obvious answers after sorting
4. Getting lost in details: We focused only on the specific data needed for each statement

Remember: Table Analysis questions reward those who can quickly organize data to reveal patterns. Sorting is almost always your best first step, as it transforms complex data into visually scannable patterns that often make the answer obvious without extensive calculations.