The table gives information about teacher absenteeism in 21 school systems worldwide for 2012-2013. For each school system, the table...

OWNING THE DATASET

Let's start by understanding what we're working with in this teacher absence table. The table contains data about teacher absences across multiple education systems in different countries, including:

• System identification: System number and country
• Teacher quantity: Number of teachers in each system
• Absence metrics: Average days absent and percent chronically absent

Key insights for efficient solving:

• The data spans multiple countries (Countries C, D, F, G, and others)
• We have both raw numbers (teacher counts) and percentages (chronic absence rates)
• Some systems have dramatically higher chronic absence percentages than others
• The teacher counts vary significantly across systems (from small systems to large ones with tens of thousands)

Let's look at one example row to understand the relationships:

System	Country	Number of teachers	Average days absent	Percent chronically absent
8	D	6,642	11.7	27.12%

This system has a particularly high chronic absence rate - this kind of outlier will be valuable in our analysis!

ANALYZING STATEMENTS

Let's tackle these statements in the order that will be most efficient.

Analyzing Statement 2

Statement 2 Translation:
Original: "There is a positive correlation between the number of teachers in a system and the average number of days teachers are absent."
What we're looking for:

• Do systems with MORE teachers tend to have MORE average days absent?
• Or do systems with MORE teachers tend to have FEWER average days absent?

In other words: As teacher count increases, do absence days also increase?

To efficiently determine correlation, let's sort the data by "Number of teachers" in descending order.

Once sorted, we can visually scan the "Average days absent" column to see if there's a pattern:

Systems with larger teacher counts:

• Largest system (59,750 teachers): 8.8 days absent
• Other large systems: around 9-10 days absent

Systems with smaller teacher counts:

• Smaller systems: 13-15 days absent

The pattern is immediately clear - as teacher counts decrease ↓, absence days increase ↑. This shows a negative correlation, not a positive one.

We can confirm by checking the extremes: the largest system has one of the lowest absence rates, while the smallest systems have the highest absence rates.

Statement 2 is No. There is a negative correlation, not a positive one.

Teaching Tip: Notice how sorting made the pattern immediately visible - no complex calculations needed! When looking for correlations, sorting by one variable and scanning the other is much faster than calculating correlation coefficients.

Analyzing Statement 1

Statement 1 Translation:
Original: "The number of chronically absent teachers in Country D is greater than the number of chronically absent teachers in Country G."
What we're looking for:

• Calculate/compare the total number of chronically absent teachers in Country D
• Calculate/compare the total number of chronically absent teachers in Country G

In other words: Which country has more teachers who are chronically absent?

Let's sort by "Country" to group the systems by country. Now we can examine Countries D and G efficiently.

For Country D, we see:

• System 8: 6,642 teachers with 27.12% chronically absent
• System 21: 11,362 teachers with 6.07% chronically absent

For Country G:

• System 10: 9,114 teachers with 8.98% chronically absent
• System 20: 1,608 teachers with 17.29% chronically absent

Let's use the One-System Shortcut. For System 8 in Country D:

• 27.12% of 6,642 ≈ 27% of 6,600 ≈ 1,782 chronically absent teachers

For Country G, even if ALL teachers were absent at the highest rate:

• Maximum possible: 17.29% of (9,114 + 1,608) = 17.29% of 10,722 ≈ 17% of 10,700 ≈ 1,819

System 8 alone nearly matches the maximum possible for Country G. But when we add System 21 from Country D:

• 6.07% of 11,362 ≈ 6% of 11,400 ≈ 684 more chronically absent teachers

This puts Country D well above Country G. Statement 1 is Yes.

Teaching Tip: Notice how we spotted the outlier percentage (27.12%) and used it to our advantage. We didn't need exact calculations - just needed to determine which was larger. We also didn't waste time calculating the exact figures for Country G once we saw it couldn't exceed Country D.

Analyzing Statement 3

Statement 3 Translation:
Original: "The system with the median number of teachers is in the same country as the system with the median percent of chronically absent teachers."
What we're looking for:

• Identify the country of the system with the median number of teachers
• Identify the country of the system with the median percent chronically absent
• Check if these are the same country

In other words: Do the middle values for teacher count and chronic absence come from the same country?

With 21 systems in the table, the median will be the 11th value when sorted.

First, let's sort by "Number of teachers":

• Look at the 11th row from the top
• Note ONLY the country: Country F

Now, let's sort by "Percent chronically absent":

• Look at the 11th row from the top
• Note ONLY the country: Country C

Since \(\mathrm{Country\ F} \neq \mathrm{Country\ C}\), Statement 3 is No.

Teaching Tip: We didn't need to know the exact systems or values - just the countries. By focusing only on what matters (countries), we eliminated unnecessary processing. This country-only focus saved significant time.

FINAL ANSWER COMPILATION

Let's compile our findings:

• Statement 1: Yes (Country D has more chronically absent teachers than Country G)
• Statement 2: No (There is a negative correlation, not positive)
• Statement 3: No (The medians are in different countries)

Our answer is: Yes No No

LEARNING SUMMARY

Skills We Used

• Sorting as a primary strategy: We sorted the data in different ways to reveal patterns and simplify our work
• Strategic estimation: We used rough mental math for Statement 1 rather than precise calculations
• Focus on only what matters: For Statement 3, we only extracted the country names, ignoring everything else

Strategic Insights

• Outlier recognition: The high percentage (27.12%) in System 8 was the key to quickly solving Statement 1
• Pattern recognition after sorting: Sorting by teacher count made the negative correlation immediately visible
• Minimal information extraction: For finding medians, we only needed to identify countries, not calculate exact values

Common Mistakes We Avoided

• We didn't calculate exact numbers of chronically absent teachers for every system
• We didn't create a scatter plot or calculate correlation coefficients for Statement 2
• We didn't waste time identifying specific systems or values for the medians in Statement 3

Applying These Skills Elsewhere

When approaching any table analysis problem:

1. Sort first, calculate last
2. Look for outliers and extreme values that might make the answer obvious
3. Extract only the information needed for the specific question
4. Use estimation when exact calculations aren't necessary
5. Focus on patterns that emerge after sorting

These techniques will save you significant time while maintaining perfect accuracy on GMAT table analysis questions!