The table lists data on the 22 earthquakes of magnitude 7 or greater on the Richter Scale during a recent...

OWNING THE DATASET

Let's start by understanding this earthquake dataset with the intention of truly "owning" it before diving into the statements.

The dataset contains 22 earthquake records with information including:

• Depth (how deep the earthquake occurred)
• Latitude (positive for North hemisphere, negative for South)
• Time (when the earthquake occurred)

One quick observation that will be crucial: after sorting by depth, we notice an extremely skewed distribution with most earthquakes around 20-40km deep, but a few outliers at depths exceeding 500km. This pattern will be particularly helpful when comparing statistical measures.

Remember: In table analysis questions, sorting immediately reveals patterns that would take much longer to find manually!

ANALYZING STATEMENT 2: More than half of the earthquakes occurred north of the equator.

Statement 2 Translation:
Original: "More than half of the earthquakes occurred north of the equator."
What we're looking for:

• Earthquakes north of the equator have positive latitude values
• "More than half" means at least \(12\) out of the \(22\) earthquakes (since half would be \(11\))

In other words: Are there \(12\) or more earthquakes with positive latitude values?

Let's approach this efficiently by sorting the data by latitude (ascending order). This allows us to quickly see where the dividing line between negative and positive values occurs.

After sorting by latitude:

• If the 12th earthquake (counting from the lowest latitude) has a positive latitude, the statement is true
• If the 12th earthquake still has a negative latitude, the statement is false

Looking at our sorted data, we can see that the 12th value is still negative, which means we don't have more than half of the earthquakes in the northern hemisphere.

Statement 2 is No.

Teaching Note: Notice how sorting eliminated the need to count every single positive value. We only needed to check one position (the 12th record) to determine if more than half were positive. This position-based approach is much faster than counting all values.

ANALYZING STATEMENT 3: Exactly half of the earthquakes occurred between 10:00:00 and 20:00:00.

Statement 3 Translation:
Original: "Exactly half of the earthquakes occurred between 10:00:00 and 20:00:00."
What we're looking for:

• Earthquakes that occurred between 10:00:00 and 20:00:00 (inclusive)
• "Exactly half" means exactly \(11\) out of the \(22\) earthquakes

In other words: Are there exactly \(11\) earthquakes that occurred during this 10-hour window?

Let's sort the data by time (ascending). This makes it easy to identify where 10:00:00 and 20:00:00 fall in our list, creating a clear boundary for counting.

After sorting by time:

1. Find where 10:00:00 appears in the sorted list (or the first time greater than or equal to it)
2. Find where 20:00:00 appears (or the last time less than or equal to it)
3. Count the records between these boundaries (inclusive)

Looking at our sorted data, we can count the earthquakes that fall within this time range. We see that the number is not exactly \(11\).

Statement 3 is No.

Teaching Note: By sorting first, the time groupings became visually apparent, making counting much faster. Also, we could potentially terminate our count early - if we found \(12\) earthquakes in this time range, we'd immediately know the statement is false without counting further.

ANALYZING STATEMENT 1: The mean depth of the earthquakes was greater than the median depth.

Statement 1 Translation:
Original: "The mean depth of the earthquakes was greater than the median depth."
What we're looking for:

• The mean (average) of all earthquake depths
• The median (middle value) of all earthquake depths
• Whether the mean is larger than the median

In other words: Is the average depth pulled higher than the middle value?

Let's sort the data by depth (ascending) to easily find the median and evaluate the distribution pattern.

After sorting:

1. With \(22\) earthquakes, the median is the average of the 11th and 12th values \(= 25.5\mathrm{km}\)

Now, we need to determine if the mean is greater than \(25.5\mathrm{km}\). Here's where a key insight comes in:

• Looking at the sorted data, we notice a highly skewed distribution
• Most earthquakes are around 20-40km deep
• But there are extreme outliers with depths over 500km (specifically 607km, 586km, and 641km)

In a distribution with extreme high outliers (right-skewed), the mean is always pulled higher than the median. These few very deep earthquakes will dramatically increase the average while having no effect on the median.

To verify this mathematical property quickly: Just these three outliers sum to \(1,834\mathrm{km}\), which is much more than what would be needed to push the average above the median.

Statement 1 is Yes.

Teaching Note: This is a perfect example of how understanding data distributions saves calculation time. When you spot extreme outliers, you can often determine statistical relationships without calculating exact values. Right-skewed distributions always have \(\mathrm{mean} > \mathrm{median}\).

FINAL ANSWER COMPILATION

Statement 1: Yes (Mean depth > Median depth)
Statement 2: No (Not more than half of earthquakes occurred north of equator)
Statement 3: No (Not exactly half occurred between 10:00:00-20:00:00)

Therefore, the answer is: A (Yes No No)

LEARNING SUMMARY

Skills We Used

• Sorting as a First Step: Every analysis began with sorting, which revealed patterns instantly
• Position Recognition: For "more than half" questions, we only needed to check the position that marks the halfway point
• Distribution Recognition: We identified skewed data and applied statistical properties without calculation
• Boundary Recognition: For the time range, we quickly identified the starting and ending points after sorting

Strategic Insights

• Attack statements in order of simplicity: We tackled Statement 2 first because it required the least work
• Use distribution properties: The skewed depth distribution made Statement 1 solvable without calculation
• Focus on critical positions: For threshold questions (like "more than half"), focus only on the critical position

Efficiency Gains

• We avoided manually counting all positive latitude values
• We didn't need to calculate the exact mean of all 22 depth values
• We used sorting to create clear boundaries for the time range

Common Mistakes We Avoided

• Calculating the exact mean when only the relationship between mean and median mattered
• Counting every single value when checking only the critical position was sufficient
• Working through statements in the given order rather than the most efficient order

Remember: In table analysis questions, your first instinct should be to sort the data to reveal patterns. This simple step often transforms seemingly complex calculations into obvious visual insights!