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With reference to this table, a statistician has proposed the following criteria for determining the "most geographically typical" of the listed Australian states/territories:
| State/territory | Land area (km^2) | Population (2006) | Population density (people/km^2) | % of population in capital |
|---|---|---|---|---|
| Australian Capital Territory | 2358 | 344200 | 137.53 | 99.6 |
| New South Wales | 800642 | 6967200 | 8.44 | 63 |
| Northern Territory | 1349129 | 219900 | 0.15 | 54 |
| Queensland | 1730648 | 4279400 | 2.26 | 46 |
| South Australia | 983482 | 1601800 | 1.56 | 73.5 |
| Tasmania | 68401 | 498200 | 7.08 | 41 |
| Victoria | 227416 | 5297600 | 22 | 71 |
| Western Australia | 2529875 | 2163200 | 0.79 | 73.4 |
For each of the four categories of statistics, a state/territory is typical if and only if it is neither among the 25% of listed states/territories with the least values for that category nor among the 25% of listed states/territories with the greatest values for that category.
For each of the following statements, select Yes if the statement is accurate based on the statistician's criteria; otherwise select No.
New South Wales is typical in more categories than any other listed state/territory.
No listed state/territory is more geographically typical than South Australia.
The Australian Capital Territory is not typical in any of the categories.
Let's start by understanding what we're working with in this table about Australian states:
The table shows 8 Australian states with 4 different measurements for each:
Key insight: The question defines "typical" as being in positions 3-6 when the states are sorted by any metric. This means the middle-ranked states are considered "typical," while the highest (positions 7-8) and lowest (positions 1-2) are not typical.
This understanding is crucial because we don't need to remember exact values - we just need to determine each state's position when sorted.
Original: "ACT is not typical in any category"
What we're looking for:
In other words: ACT is always among the extremes (very high or very low) in all categories.
Let's begin with Statement 3 because it focuses on just one state and has the simplest verification process. It's much easier to check one state across four categories than comparing multiple states.
Let's sort each category and check ACT's position:
Sorting by Land Area:
When we sort from smallest to largest, ACT is the smallest territory - position 1.
→ Not typical ✓
Sorting by Population:
When sorted from smallest to largest, ACT is the second smallest - position 2.
→ Not typical ✓
Sorting by Population Density:
When sorted from lowest to highest, ACT has the highest density - position 8.
→ Not typical ✓
Sorting by % in Capital City:
When sorted from lowest to highest, ACT has the highest percentage - position 8.
→ Not typical ✓
Conclusion: ACT is never in positions 3-6, so Statement 3 is Yes.
Teaching moment: Notice how sorting immediately reveals each state's position without requiring us to write down all the values or create a complex tracking table. This is much faster than calculating and comparing each value manually.
Original: "NSW is typical in more categories than any other state"
What we're looking for:
In other words: NSW must have the highest count of "typical" appearances.
Let's check NSW by sorting each category:
Sorting by Land Area:
NSW is in position 4 → Typical ✓
Sorting by Population:
NSW has the highest population (position 8) → Not typical ✗
Sorting by Population Density:
NSW is in position 6 → Typical ✓
Sorting by % in Capital City:
NSW is in position 4 → Typical ✓
NSW Summary: Typical in 3 categories (Land Area, Population Density, % in Capital)
Now, for Statement 1 to be true, no other state can be typical in 3 or more categories. Let's check SA, which is mentioned in Statement 2:
SA's typicality:
SA Summary: Typical in 3 categories (Land Area, Population, Population Density)
Since SA is also typical in 3 categories, NSW is not typical in more categories than any other state. Statement 1 is No.
Teaching moment: We strategically checked SA next since it's mentioned in Statement 2. This gives us information for both statements simultaneously, saving significant time.
Original: "No state is more typical than SA"
What we're looking for:
In other words: SA must be tied for the most "typical" appearances.
We've already established:
For Statement 2 to be false, we would need to find at least one state that is typical in all 4 categories. Let's scan our sorted lists to see if any state appears in positions 3-6 across all categories.
Checking for a state that appears in positions 3-6 in all categories:
Reviewing our sorted lists, we can see that no state appears in positions 3-6 for all four categories. Some states might be typical in 3 categories (like NSW and SA), but none are typical in all 4.
Conclusion: No state is more typical than SA, so Statement 2 is Yes.
Teaching moment: We didn't need to check every single state individually. Once we knew SA was typical in 3 categories, we just needed to determine if any state could be typical in all 4 categories. This targeted approach saved us from unnecessary work.
Let's compile our findings:
The answer is B (No/Yes/Yes).
Remember: Table analysis questions reward strategic thinking over comprehensive analysis. Focus on gathering just the information you need to answer each statement, and use sorting to quickly identify positions rather than calculating every value.
New South Wales is typical in more categories than any other listed state/territory.
No listed state/territory is more geographically typical than South Australia.
The Australian Capital Territory is not typical in any of the categories.